Capital market finance: an introduction to primitive assets, derivatives, portfolio management and risk Volume 1
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Cham, Switzerland
Springer
[2022]
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| Series: | Springer texts in business and economics
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxxvii, 869 Seiten Diagramme |
| ISBN: | 9783030845988 |
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| 245 | 1 | 0 | |a Capital market finance |b an introduction to primitive assets, derivatives, portfolio management and risk |n Volume 1 |c Patrice Poncet, Roland Portait ; contributions by Igor Toder |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2022] | |
| 300 | |a xxxvii, 869 Seiten |b Diagramme | ||
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| 490 | 0 | |a Springer texts in business and economics | |
| 700 | 1 | |a Portait, Roland |e Verfasser |0 (DE-588)170766292 |4 aut | |
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| adam_text | Contents 1 Introduction: Economies and Organization of Financial Markets... 1.1 The Role of Financial Markets...................................................... 1.1.1 The Allocation of Cash Resources Over Time............... 1.1.2 Risk Allocation................................................................. 1.1.3 The Market as a Supplier of Information........................ 1.2 Securities as Sequences of Cash Flows........................................ 1.2.1 Definition of a Security (or Financial Asset).................. 1.2.2 Characterizing the Cash Flow Sequence......................... 1.3 Equilibrium, Absence of Arbitrage Opportunity, Market Efficiency and Liquidity................................................................. 1.3.1 Equilibrium and Price Setting......................................... 1.3.2 Absence of Arbitrage Opportunity (AAO) and the Notion of Redundant Assets........................................... 1.3.3 Efficiency........................................................................... 1.3.4 Liquidity............................................................................. 1.3.5 Perfect Markets................................................................. 1.4 Organization, a Typology of Markets, and Listing....................... 1.4.1 The Banking System and FinancialMarkets................... 1.4.2 A Simple Typology of Financial Markets....................... 1.4.3 Market Organization......................................................... 1.5
Summary ........................................................................................... Appendix: The World’s Principal Financial Markets.............................. Stock markets, market indexes andinterest rateinstruments ... Organized Derivative Markets (Futures and Options, Unless Otherwise Indicated).............................................................. 34 Suggestion for Further Reading........................................................ 35 Books....................................................................................... 35 Articles.................................................................................... 35 Part I 2 1 1 1 3 5 5 5 6 8 8 9 11 16 18 19 19 19 24 32 33 33 Basic Financial Instruments Basic Finance: Interest Rates, Discounting,Investments,Loans... 2.1 Cash Flow Sequences............................................................ 39 39 XV
Contents xvi Transactions Involving Two Cash Flos«, s 40 2.2.1 Transactions of Lending and Borrowing Going Risi lo Two Cash Flows os er One Period 41 2.2.2 Transactions svith Tsvo Cash Floss s oset Sesera! Periods................................................................. 42 2.2.3 Comparison of Simpleand Compound Interest 47 2.2.4 Two ”Complications ՜ in Practice 49 2.2.5 Continuous Rates................................................................ 53 2.2.6 General Equivalence Formulas lor Rates I hl lering in Convention and the Length ot the Reference Period 53 2.3 Transactions Involving an Arbitran Number of Cash Floss s Discounting and the Analysis of Investments 55 2.3.1 Discounting................................................................... 57 2.3.2 Yield to Maturity (YTMl, Discount Rate and Internal Rate of Return (IRR)................................... 63 2.3.3 Application to Investment Selection: Ilie Culena of the NPV and the IRR.................................... 2.3.4 Interaction Between Investing and Financing, and Financial Leverage...................................... b9 2.3.5 Some Guidelines for the Choice of an Appropriate Discount Rate.......................................... 72 2.3.6 Inflation. Real and Nominal Cash Floss s and Rates 74 2.4 Analysis of Long-Tenn Loans................................................. 7b 2.4.1 General Considerations and Definitions: YIM and Interest Rales........................................................................ 76 2.4.2 Amortization Schedule for a
Loan....................................... ՜9 2.5 Summary............................................................................................... 54 Appendix 1: Geometric Series and Discounting........................................... 55 Appendix 2: Using Financial Tables and Spreadsheets for Discount Computations................................................................................................... 57 1. Financial Tables........................................................................... 57 Suggested Reading.......................................................................................... 92 2.2 3 The Money Market and Its Interbank Segment.................................. 3.1 Interest Rate Practices and the Valuation of Securities................ 3.1.1 Interest Rate Practices on the Euro-Zone s Mones Market................................................................. 3.1.2 Alternative Practices and Conventions........................... 3.2 Money Market Instruments and Operations..................................... 3.2.1 The Short-Tenn Securities ofthe MonesMarkets. . 3.2.2 Repos. Carry Trades, andTemporaryTransfers of Claims................................................................................ 3.2.3 Other Trades....................................................................... 3.3 Participants and Orders of Magnitude of Trades.......................... 3.3.1 The Participants.................................................................. 93 94 95 99 KM) 1(M) 101 103 105 105
Contents 3.3.2 Orders of Magnitude.......................................................... Role of the Interbank Market and Central Bank Intervention. . . 3.4.1 Central Bank Money and the Interbank Market............. 3.4.2 Central Bank Interventions and Their Influence on Interest Rates...................................................... 110 3.5 The Main Monetary Indices.......................................................... 3.5.1 Indices Reflecting the Value of a Money-Market Rate on a Given Date................................................. 113 3.5.2 Indices Reflecting the Average Value of a Money-Market Rate During a Given Period. 115 3.6 Summary.......................................................................................... Suggestions for Further Reading............................................................... 106 107 107 The Bond Markets.................................................................................... 4.1 Fixed-Rate Bonds............................................................................ 4.1.1 Financial Characteristics and Yield to Maturity at the Date of Issue...................................................... 121 4.1.2 The Market Bond Value at an Arbitrary Date; the Influence of Market Rates and of the Issuer’s Rating. . . 4.1.3 The Quotation of Bonds.................................................. 4.1.4 Bond Yield References and Bond Indices..................... 4.2 Floating-Rate Bonds. Indexed Bonds, and Bonds with Cosenants............................................................................. 135
4.2.1 Floating-Rate Bonds and Notes........................................ 4.2.2 Indexed Bonds................................................................... 4.2.3 Bonds with Covenants (Optional Clauses)...................... 4.3 Issuing and Trading Bonds............................................................. 4.3.1 Primary and Secondary Markets...................................... 4.3.2 Treasury Bonds and Treasury Notes Issues: Reopening and STRIPS.................................... 139 4.4 International and Institutional Aspects; the Order of Magnitude of the Volume of Transactions........................................... 141 4.4.1 Brief Presentation of the International Bond Markets. . . 4.4.2 Tlie Main National Markets............................................ 4.5 Summary........................................................................................... Suggested Readings.................................................................................... 119 121 3.4 4 5 xvii Introduction to the Analysis of Interest Rate and Credit Risks. . . 5.1 Interest Rate Risk............................................................................. 5.1.1 Introductory Examples: The Influence of the Maturity of a Security on Its Sensitivity to Interest Rates............ 5.1.2 Variation. Sensitivi ty and Duration of a Fixed-Income Security.............................................................. 152 5.1.3 Alternative Expressions for the Variation, Sensitivity and Duration...................................................... 156 113 117 118 126 131 135
136 137 137 138 138 142 143 146 148 149 149 150
xviii Lumenis Some Properties of Sensitivity and Duration The Sensitivity Ot a Portfolio of Assets and I 1.11 ililics or of a Balance Sheet: Sensitiv itv and (laps 5.1.6 A More Accurate Estimate of İnletesi Rate Risk Convexity........................... 5.2 Introduction to Credit Risk............................... 5.2.1 Analysis of the Determinants of the Credit Spie.к! 5.2.2 Simplified Modeling of the Credit Spread, the ( іеЛп Triangle................................... 172 5.3 Summary ....................................................... Appendix 1............................................................... Default Probability. Recovery Rate and (redit Spread Suggested Reading................................................ 5.1.4 5.1.5 6 7 The Term Structure of Interest Rates 6.1 Spot Rales and Forward Rates...................... 6.1.1 The Yield Curve.......................... 6.1.2 Yields to Maturity and Zero Coupon Rates 6.1.3 Forward Interest Rates Implicit in the Spot Rate Curve................................. 1S4 6.2 Factors Determining the Shape of the Curve 6.2.1 The Curve Shape............... IS՜ 6.2.2 Expectations Hypothesis with IerniPremiums 6.2.3 Influence of the CreditSpread onYield Curves 6.3 Analy sis of Interest Rate Risk: Impact of Changes in the Slope and Shape of the Yield Curve................. 142 6.3.1 The Risk of a Change in the Slope ol the Yield Curve...................................................... 6.3.2 Multifactor Variation and Sensitivity and MihIcE of Yield Curves................. 6.4
Summary.......................................................................... Suggested Readings............................................................... Vanilla Floating Rate Instruments and Swaps 7.1 Floating Rate Instruments..................................................... 7.1.1 General Discussion and Notation......................... 7.1.2 “Replicable Assets: Valuation and Interest Rate and Spread Risks................................................ 212 7.2 Vanilla Swaps.......................................................................... 7.2.1 Definitions and Generalities About Swaps 7.2.2 Replication and Valuation of an Interest Rate Swap 7.2.3 Interest Rate. Counterparty and Credit Risks for an Interest Rate Swap............................................................ 7.2.4 Summary of the Various Types of Sw aps 7.3 Summary.......................................................................................... ĮSg k,| 167 170 170 174 Г5 175 176 Г7 1՝7 Г7 1’4 IS՝ 1SS 141 ll) 2 144 ՝ ?» Μ 2 5 2 6 2 6 22S 22S 232 241 24՜ 251
Contents Appendix..................................................................................................... Proof of lhe Equivalence Between Eq. (7.2’) and Proposition 1................................................................................... Suggested Reading..................................................................................... Books............................................................................................... Articles............................................................................................ 8 Stocks, Stock Markets, and Stock Indices........................................... 8.1 Stocks............................................................................................... 8.1.1 Basic Notions: Equity, Stock Market Capitalization, and Share Issuing.............................................. 256 8.1.2 Analysis of Stock Issues, Dilution, and Subscription Rights................................................................. 261 8.1.3 Market Performance of a Share and Adjusted Share Price................................................................... 8.1.4 Introduction to the Valuation of Firms and Shares; Interpretation and Use of the PER................... 266 8.2 Return Probability Distributions and the Evolution of Stock Market Prices...................................................................... 273 8.2.1 Stock Price on a Future Date, Stock Return, and Its Probability Distribution: Static Analysis......... 273 8.2.2 Modeling a Stock Price Evolution with a Stochastic Process:
Dynamic Analysis.............................. 276 8.3 Placing and Executing Orders and the Functioning of Stock Markets................................................................................ 284 8 3.1 Types of Orders................................................................. 8.3.2 The Clearing and Settlement System............................... 8.3.3 Investment Management................................................... 8.3.4 The Main Stock Markets.................................................. 8.4 Stock Market Indices...................................................................... 8.4.1 Composition and Calculation........................................... 8.4.2 The Main Indices.............................................................. 8.5 Summary......................................................................................... Appendix I................................................................................................. Skewness and Kurtosis of Log-Returns........................................ Appendix 2................................................................................................. Modeling Volatility with ARCH and GARCH............................ Suggestions for Further Reading.............................................................. Book Chapters................................................................................. Articles............................................................................................. For an Online Comparative Description of Investment Funds from
Different Countries................................................................ For an Online Description and Analysis of the Asset Management Industry..................................................................... xix 252 252 253 253 253 255 255 263 284 286 288 293 294 295 300 302 304 304 305 305 308 308 308 308 308
Contents XX Part II Futures and Options Futures and Forwards............................................................ 311 9.1 General Analysis of Forward and Futures Contracts Յւջ 9.1.1 Definition of a Forw ard Contract: Terminologe and Notation............................................... .42 9.1.2 Futures Contracts: Comparison ot Futures and l oiwaid Contracts................................................ 314 9.1.3 Unwinding aPosition Before Expiration 317 9.1.4 The Value of Forward andFutures Contracts 318 9.2 Cash-and-carry and the Relation Between Spot anil Forward Prices..................................................................... 319 9.2.1 Arbitrage, Cash-and-Carry. and Spot-Forward Pants 319 9.2.2 Forward Prices, Expected Spot Prices, and Risk Premiums............................................................. 324 9.3 Maximum and Optimal Hedging with Forward and Futures Contracts................................................................. 325 9.3.1 Perfect or Maximum Hedging............................ *26 9.3.2 Optimal Hedging and Speculation........................ 333 9.4 The Main Forward and Futures Contracts......................... 334 9.4.1 Contracts on Commodities........................................ 335 9.4.2 Contracts on Currencies (Foreign Exchanges» 338 9.4.3 Forward and Futures Contracts on Financial Securities (Stocks, Bonds. Negotiable Debt Securities i, FR A. and Contracts on Market Indices................................ 340 9.5 Summary................................................................................. *48
Appendix............................................................................................ *49 The Relationship Between Forward and Futures Prices *49 Suggestions for Further Reading.......................................................................*52 Books....................................................................................................... *52 Articles.....................................................................................................*52 9 10 Options (I): General Description. Parity Relations. Basic Concepts, and Valuation Using the Binomial Model *53 10.1 Basic Concepts, Call-Put Parity, and Other Restrictions (пип No Arbitrage................................................................................ *54 10.1.1 Definitions. Value at Maturity. Intrinsic Value. and Time Value................................................................. 354 10.1.2 The Standard Call-Put Parity.................................................. *58 10.1.3 Other Parity Relations..................................................... *61 10.1.4 Other Arbitrage Restrictions........................................... *M 10.2 A Pricing Model for One Period and Two States of the World.......................................................................... 367 10.2.1 Two Markets, Two States................................................ 368 10.2.2 Hedging Strategy and Option Value in the Absence of Arbitrage.............................................................. 369
Contents 10.2.3 The Risk-Neutral” Probability....................................... 10.2.4 The Risk Premium and the Market Price of Risk.......... 10.3 The Multi-period Binomial Model................................................ 10.3.1 The Model Framework and the Dynamics of the Underlying’s Price............................................. 377 10.3.2 Risk-Neutral Probability and Martingale Processes. . . 10.3.3 Valuation of an Option Using the Cox-Ross-Rubinstein Binomial Model................................................. 381 10.4 Calibration of (he Binomial Model and Convergence to the Black-Scholes Formula....................................................... 386 10.4.1 An Interpretation of Premiums in Terms of Probabilities of Exercise............................................. 10.4.2 Calibration and Convergence.......................................... 10.5 Summary.......................................................................................... Appendix 1.................................................................................................. Calibration of the Binomial Model................................................ * Appendix 2................................................................................................ Suggestions for Further Reading............................................................... Books............................................................................................... Articles............................................................................................. 11 Options (111:
Continuous-Time Models, Black-Scholes and Extensions.................................................................................................. 11.1 The Standard Black-Scholes Model.............................................. 11.1.1 The Analytical Framework and BS Model’s Assumptions....................................................... 400 11.1.2 Self-Financing Dynamic Strategies................................ 11.1.3 Pricing Using a Partial Differential Equation and the Black-Scholes Fonnula.................................... 402 1 1.1.4 Probabilistic Interpretation............................................... 11.2 Extensions of the Black-Scholes Formula................................... 11.2.1 Underlying Assets That Pay Out (Dividends, Coupons, etc.).................................................... 412 I 1.2.2 Options on Commodities................................................. 11.2.3 Options on Exchange Rates............................................ 11.2.4 Options on Futures and Forwards................................... 11.2.5 Variable But Deterministic Volatility............................. 11.2.6 Stochastic Interest Rates: The Black-Scholes-Merton (BSM) Model..................................................... 429 11.2.7 Exchange Options (Margrabe)........................................ 11.2.8 Stochastic Volatility (*)................................................... 11.3 Summary.......................................................................................... Appendix
I.................................................................................................. Historical and Risk-Neutral Probabilities and Changes in Probability........................................................................................ xxi 372 374 377 379 387 389 391 393 393 395 397 397 397 399 399 401 406 412 421 422 424 427 434 437 443 444 444
xxii 12 Contents Appendix 2................................................................ Changing the Probability Measure and the Numerane Appendix 3.................................................................. Alternative Interpretations of the Plack Scholes loimilla Suggested Reading................................................ Books................................................................ Articles............................................................. 446 446 449 449 451 451 451 Option Portfolio Strategies: Tools and Methods 12.1 Basic Static Strategies.................................... 12.1.1 The General P L Profile at Maliu its 12.1.2 The Main Static Strategics 12.1.3 Replication of an Arbitrais Pasoli bs a Sialic Option Portfoliot*)........................ 457 12.2 Historical and Implied Volatilities. Smile, Skew and leim Structure.................................................. 457 12.2.1 Historical Volatility..................... 12.2.2 The Implied Volatility..................... 12.2.3 Smile. Skew, Term Structure, and Volatility Suil.uc 12.3 Option Sensitivities (Greek Parameters) 12.3.1 The Della (б)............................................ 12.3.2 The Gamma (Г)....................................... 12.3.3 The Vega (о).............................................. 12.3.4 The Theta (0).............................................. 12.3.5 TheRho(p)............................................. 12.3.6 Sensitivity tothe Dividend Rate 12.3.7 Elasticity and Risk-ExpectedReturn Tradeoff 12.4 Dynamic Management of an Option Portfolio I sing (
heck Parameters............................................................ 4 5 12.4.1 Variation in the Value of a Position in the Short Tenn and GeneralConsiderations................................... 12.4.2 Delta-NeutralManagement.......................... 12.4.3 A Tool for Risk Management: The P l Matrix 12.5 Summary...................................................................................... Appendix 1.............................................................................................. Computing Partial Derivatives (Greeks)........................................ Appendix 2................................................................................................... Option Prices and the Underlying Price Probability Distribution....................................................................................... Appendix 3.................................................................................................. Replication of an Arbitrary Payoff with a Static Option Portfolio............................................................................................ Suggestions for Further Reading............................................................... Books................................................................................................ Articles.............................................................................................. 453 454 454 455 458 459 461 463 4M 467 468 4 0 471 472 473 4 5 4 6 485 4S6 4SS 488 403 403 496 496 498 498 498
Contents 13 14 xxiii American Options and Numerical Methods........................................ 13.1 Early Exercise and Call-Put Parity for American Options.......... 13.1.1 Early Exercise of American Options.............................. 13.1.2 Call-Put “Parity” for American Options......................... 13.2 Pricing American Options: Analytical Approaches..................... 13.2.1 Pricing an American Call on a Spot Asset Paying a Single Discrete Dividend or Coupon............ 517 13.2.2 Pricing an American Option (Call and Put) on a Spot Asset Paying a Continuous Dividend or Coupon.......... 13.2.3 Prices of American and European Options: Orders of Magnitude........................................................... 528 13.3 Pricing American Options with the Binomial Model.................. 13.3.1 Binomial Dynamics of Price S: The Case of a Discrete Dividend............................................................................ 13.3.2 Binomial Dynamics of Price S: The Continuous Dividend Case.................................................... 531 13.3.3 Pricing an American Option Using the Binomial Model.................................................................. 531 13.3.4 Improving the Procedure with a Control Variate........... 13.4 Numerical Methods: Finite Differences, Trinomial and ThreeDimensional Trees............................................................... 533 13.4.1 Finite Difference Methods (*).......................................... 13.4.2 Trinomial Trees................................................................. 13.4.3
Three-Dimensional Trees Representing Two Correlated Processes........................................................ 13.5 Summary.......................................................................................... Appendix 1.................................................................................................. Proof of the Smooth Pasting (Tangency) Condition (13.5b). . . Appendix 2.................................................................................................. Orthogonalization of the Processes In S։ and In Տշ and Construction of a Three-Dimensional Tree.................................. Suggestion for Further Reading................................................................ Books............................................................................................... Articles............................................................................................. 501 502 502 515 516 *Exotic Options......................................................................................... 14.1 Path-Independent Options.............................................................. 14.1.1 The Forward Start Option (with Deferred Start)............ 14.1.2 Digital and Double Digital Options................................ 14.1.3 Multi-underlying (Rainbow) Options (*)....................... 14.1.4 Options on Options or “Compounds”............................. 14.1.5 Quantos and Compos....................................................... 14.2 Path-Dependent Options................................................................
14.2.1 Barrier Options................................................................. 14.2.2 Digital Barriers................................................................. 549 550 550 551 555 559 560 567 567 573 520 529 529 533 534 539 541 543 545 545 546 546 547 547 548
Contents xxiv 14.2.3 Lookback Options i ’ i 575 14.2.4 Options on Ascrages( Asians 1 578 14.2.5 Chooser Options i * i 5K6 14.3 Summary............................ 587 Appendix 1................................... 589 ♦ ♦Value of a Colluso (. all 589 Appendix 2........................................ 591 ♦ ♦Lemmas ՕՈ Hitting Probabilities lol a Dulled Bi. anian Motion................................... 591 Appendix 3................................. 594 ♦ ♦Proof of the Ins erses” Relation loi Bârnei (ipini. 594 Appendix 4..................................... 595 ♦ ♦Valuing a Call l p and Out sudi 1 iB.nner । К Микс Appendix 5................................... 597 ♦ ♦ Valuing Rebates.............. 597 Appendix 6................................. 598 ♦ ♦Proof of the Pnce ol a Lookbas k ( all 98 Appendix 7........................................ 601 ♦ ♦Options on an Asetage Ptice N 1 Appendix 8.................................... (812 ♦♦Options ssith an Asetage Stuke (8)2 Suggestions for Further Reading MM Books................................... (8)4 Articles.......................................... MM 15 Futures Markets (2): Contracts on Interest Rates Notional Contracts....................... 15.1.1 Basket of Dehserable Secui itics i DS 1 and Notional Security.............. 15.1.2 The Euro-Bond Contract 15.1.3 Settlement and Conversion Factors 15.1.4 Cheapest to Delis er and Quoting Futures at Expiration.............. 613 15.1.5 Arbitrage and Cash-Futures Relationship 15.1.6 Interest Rate Sensitiv its ot Entures Pnces 15.1.7 Hedging Intriest Rate Risk Csmg Notional Bond
Contracts............................ 629 15.1.8 The Main Notional Contracts 15.2 Short-Tenn Interest Rate Contracts (STIR 11 -Month lotward Looking Rates and Backssard-Looking Overnight Avcragcsi 15.2.1 STIR З-Month Contracts (LIBOR Type. Fonvard Looking)........................................ 15.2.2 Futures Contracts on an Average Osemight Rate 15.2.3 Hedging Interest Rate Risk with STIR Contracts 15.3 Summary................................................................................. 15.1 N17 818 (8)8 881 611 618 б24 63՜ 641 Ml Μ՞ б5б 659
Contents Appendices................................................................................................. I Valuation of the Delivery Option.......................................................... 2 Relationship Between Forward and Futures Prices.............................. Suggestions for Further Reading.............................................................. Books............................................................................................... Articles............................................................................................ Internet Sites................................................................................... 16 Interest Rate Instruments: Valuation with the BSM Model, Hybrids, and Structured Products................................................ 667 16.1 Valuation of Interest Rate Instruments Using Standard Models. . . 16.1.1 Principles of Valuation and the Black-Scholes-Merton Model Generalized to Stochastic Interest Rates............ 16.1.2 Valuation of a Bond Option Using the BSM-Price Model................................................................. 671 16.1.3 Valuation of the Right to a Cash Flow Expressed as a Function of a Rate and the BSM-Rate Model............ 16.1.4 Convexity Adjustments for Non-vanilla Cash Flows (*)............................................................ 676 16.2 Nonstandard Swaps and Swaptions............................................... 16.2.1 Review of Swaps and Notation........................................ 16.2.2 Some Nonstandard
Swaps................................................ 16.2.3 Swap Options (or Swaptions).......................................... 16.3 Caps and Floors............................................................................... 16.3.1 Vanilla Caps...................................................................... 16.3.2 A Vanilla Floor................................................................. 16.4 Static Replicationsand Combinations; Structured Contracts. . . 16.4.1 Basic Instruments: Notation and General Remarks. . . 16.4.2 Replication of a Capped or Floored Floating-Rate Instrument Using a Standard Asset Associated with a Cap or a Floor................................................. 696 16.4.3 Collars............................................................................... 16.4.4 Non-standard Caps and Floors........................................ 16.4.5 Other Static Combinations; Structured Products; Contracts on Interest Rates with Profit-Sharing............ 16.5 Bonds with Optional Features and Hybrid Products..................... 16.5.1 Convertible Bonds........................................................... 16.5.2 Other Bonds with Optional Features.............................. 16.6 Summary.......................................................................................... Appendix..................................................................................................... The -Martingale Measure.......................................................... Suggestions for Further
Reading............................................................... Books............................................................................................... Articles............................................................................................. xxv 661 661 662 666 666 666 666 667 668 672 680 680 682 686 688 689 692 693 693 699 702 705 707 708 711 713 715 715 716 716 716
xxvi 17 18 Contents Modeling Interest Rates and Options on Intercast Rates 17.1 Models Based on the Dynamics ot Spot Rates 17.1.1 One-Factor Models t asuek, and(ox.Ingeisoll and Ross)..... 721 17.1.2 Fitting the Initial Yield C urse, the Hull and White Model. 17.1.3 Multifaclor Structures 17.2 Models Grounded on the Dynamics ol 1 orw.ud Rates 17.2.1 The Heath-Jam w Monon Minici t loo;, 17.2.2 The Libor (LMM) and Swap(SMM 1Maikét Models........................................... 17.3 Summary..................................................... Appendix 1................................................................ ♦The Vasicek Model............................... Appendix 2............................................................. ♦The LMM and SMM Models Suggestions for Further Reading..................... Books........................................................... Articles.................................................... Elements of Stochastic Calculus 18.1 Definitions. Notation, and General Considciations About Stochastic Processes................................. 766 18.1.1 Notation........................................... 18.1.2 Stochastic Processes: Délimitons. Notation, and General Framework.................. 66 18.2 Brownian Motion................................................. 18.2.1 The One-Dimensional Brow man Motion 18.2.2 Calculus Rules Relative to Brownian Motions 18.2.3 Multi-dimensional .Arithmetic BnmnunMotions 18.3 More General Processes Derived from the Brownian Motion. One-Dimensional Itõ and Diffusion Pnxcsses 18.3.1 One-Dimensional
Ito Processes....................... 18.3.2 One-Dimensional Diffusion Processes 18.3.3 Stochastic Integrals t* ).................................... 18.4 Differentiation of a Function of an Ito Pnxcss: Ito’sLemma 18.4.1 Itô’s Lemma.......................................................... 18.4.2 Examples of Application.......................................... 18.5 Multi-dimensional Itô and Diffusion Processes t * 1. 89 18.5.1 Multivariate Itô and Diffusion Processes 18.5.2 Ito’s Lemma (Differentiation of a Function of an n-Dimensional Itô Process)................................ 18.6 Jump Processes................................................................................. 18.6.1 Description of Jump Processes........................................ 18.6.2 Modeling Jump Processes................................................ 18.7 Summary........................................................................................... 7 J9 720 726 728 729 730 737 749 751 751 754 754 762 762 762 765 66 769 69 75 77 779 79 780 82 85 85 87 790 1H 793 793 793 794
Contents Suggestions for Further Reading............................................................... Books............................................................................................... 19 xxvii 796 796 *The Mathematical Framework of Financial Markets Theory.... 797 19.1 General Framework and Basic Concepts...................................... 798 19.1.1 The Probabilistic Framework........................................... 798 19.1.2 The Market, Securities, and Portfolio Strategies............ 799 19.1.3 Portfolio Strategies........................................................... 800 19.1.4 Contingent Claims, AAO, and CompleteMarkets... . 802 19.1.5 Price Systems.................................................................... 804 19.2 Price Dynamics as Ito Processes, Arbitrage Pricing Theory and the Markel Price of Risk..................................................... 805 19.2.1 Price Dynamics as Itô Processes..................................... 806 19.2.2 Arbitrage Pricing Theory in Continuous Time.............. 806 19.2.3 Redundant Securities and Characterizing the Base of Primitive Securities.......................................................... 808 19.3 The Risk-Neutral Universe and Transforming Prices into Martingales........................................................................... 809 19.3.1 Martingales, Driftless Processes, and Exponential Martingales....................................................................... 809 19.3.2 Price and Return Dynamics in the Risk-Neutral Universe. Transforming Prices into
martingales and Pricing Contingent Claims......................... 813 19.3.3 Characterizing a Complete market and Market Prices of Risk................................................................ 816 19.4 Change of Probability Measure, Radon-Nikodym derivative and Girsanov’s Theorem..................................................... 818 19.4.1 Changing Probabilities and the Radon-Nikodym Derivative................................................................... 818 19.4.2 Changing Probabilities and Brownian Motions: Girsanov’s Theorem.................................... 820 19.4.3 Formal Definition of RN Probabilities...................... 822 19.4.4 Relations between Viable Price Systems, RN Probabilities, and MPR.................................................... 823 19,5 Changing the Numeraire................................................................. 825 19.5.1 Numeraires........................................................................ 825 19.5.2 Numeraires and Probabilities that yield martingale Pnces................................................................................. 826 19.6 The P-Numeraire (OptimalGrowth or Logarithmic Portfolio). . . 832 19.6.1 Definition of lite Portfolio (h. H) as the P-Numeraire. . . 832 19.6.2 Characterization and Composition of the P-Numeraire Portfolio (h. Hi................................................................. 833 19.7 ** Incomplete Markets.................................................................... 836 19.7.1 MPR and the Kemel of the Diffusion Matrix ^(t).... 837 19.7.2
Deflators............................................................................ 840
xxviii C oritene 19.8 Summan............................. Appendix...................................... Construction of a One-to-one I oirespondeiK e ScOs Q and П................................ Suggestions l or further reading Books...................................... Articles.............................. 20 M2 844 844 M5 M5 846 The State Variables Model and the Valuation Partial DifTvrvntial Equation................................. M7 20.1 Analytical Framework and Notation M7 20.1.1 Dynamics of State Variables M7 20.1.2 The Asset Pricing Problem M8 20.2 Factor Decomposition of Returns M9 20.2.1 Expressing the Return JR as a Fuik lion ot ihe M9 20.2.2 Expressing the Return JR as а І unition ol the ..И , 850 20.3 Expected Asset Returns and Arbitrage Рік me Iheoix ՛ l’l ՛ in Continuous Time.. $50 20.3.1 First Formula lor Expected Retums 851 20.3.2 Continuous Time API in a State sanables Mode; 851 20.4 The General valuation PDF........... 853 20.4.1 Derivation of the General xalualion PDF 853 20.4.2 Market Prices of Risk and Risk Premia 854 20.4.3 The Relation between MPR and Excess Returns ՕՈ Primitive Securities and the Condition lot Maikét Completeness..................... 855 20.5 Applications to the Tenn Structure ofInterest Rates 857 20.5.1 Models with One State Variable 857 20.5.2 Multi-Factor models and xaluation ot Fixed buome Securities............................ 854 20.6 Pricing in the Risk-Neutral Unixcrsc 862 20.6.1 Dynamics of Retums, of Brownian Motions and of State Variables in the Risk-Neutral Inncrsc 862 20.6.2 The Valuation
PDF......................... 863 20.7 Discounting under Uncertainty and the Feynman Кас Theorem.................................................. 864 20.7.1 The Cauchy-Dirichlet PDF. and the Feynman К.к Theorem................................. 864 20.7.2 Financial Interpretation of the Fey nman Кас Theorem and Discounting under Uncertainty 865 20.8 Summary................................................................... 866 Appendix................................................................................... 86S Suggestions for Further Reading............................................ 864 Books.................................................................................. 864 Articles............................................................................. 860
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Contents 1 Introduction: Economies and Organization of Financial Markets. 1.1 The Role of Financial Markets. 1.1.1 The Allocation of Cash Resources Over Time. 1.1.2 Risk Allocation. 1.1.3 The Market as a Supplier of Information. 1.2 Securities as Sequences of Cash Flows. 1.2.1 Definition of a Security (or Financial Asset). 1.2.2 Characterizing the Cash Flow Sequence. 1.3 Equilibrium, Absence of Arbitrage Opportunity, Market Efficiency and Liquidity. 1.3.1 Equilibrium and Price Setting. 1.3.2 Absence of Arbitrage Opportunity (AAO) and the Notion of Redundant Assets. 1.3.3 Efficiency. 1.3.4 Liquidity. 1.3.5 Perfect Markets. 1.4 Organization, a Typology of Markets, and Listing. 1.4.1 The Banking System and FinancialMarkets. 1.4.2 A Simple Typology of Financial Markets. 1.4.3 Market Organization. 1.5
Summary'. Appendix: The World’s Principal Financial Markets. Stock markets, market indexes andinterest rateinstruments . Organized Derivative Markets (Futures and Options, Unless Otherwise Indicated). 34 Suggestion for Further Reading. 35 Books. 35 Articles. 35 Part I 2 1 1 1 3 5 5 5 6 8 8 9 11 16 18 19 19 19 24 32 33 33 Basic Financial Instruments Basic Finance: Interest Rates, Discounting,Investments,Loans. 2.1 Cash Flow Sequences. 39 39 XV
Contents xvi Transactions Involving Two Cash Flos«, s 40 2.2.1 Transactions of Lending and Borrowing Going Risi lo Two Cash Flows os er One Period 41 2.2.2 Transactions svith Tsvo Cash Floss s oset Sesera! Periods. 42 2.2.3 Comparison of Simpleand Compound Interest 47 2.2.4 Two ”Complications'՜ in Practice 49 2.2.5 Continuous Rates. 53 2.2.6 General Equivalence Formulas lor Rates I hl lering in Convention and the Length ot the Reference Period 53 2.3 Transactions Involving an Arbitran Number of Cash Floss s Discounting and the Analysis of Investments 55 2.3.1 Discounting. 57 2.3.2 Yield to Maturity (YTMl, Discount Rate and Internal Rate of Return (IRR). 63 2.3.3 Application to Investment Selection: Ilie Culena of the NPV and the IRR. 2.3.4 Interaction Between Investing and Financing, and Financial Leverage. b9 2.3.5 Some Guidelines for the Choice of an Appropriate Discount Rate. 72 2.3.6 Inflation. Real and Nominal Cash Floss s and Rates 74 2.4 Analysis of Long-Tenn Loans. 7b 2.4.1 General Considerations and Definitions: YIM and Interest Rales. 76 2.4.2 Amortization Schedule for a
Loan. ՜9 2.5 Summary. 54 Appendix 1: Geometric Series and Discounting. 55 Appendix 2: Using Financial Tables and Spreadsheets for Discount Computations. 57 1. Financial Tables. 57 Suggested Reading. 92 2.2 3 The Money Market and Its Interbank Segment. 3.1 Interest Rate Practices and the Valuation of Securities. 3.1.1 Interest Rate Practices on the Euro-Zone's Mones Market. 3.1.2 Alternative Practices and Conventions. 3.2 Money Market Instruments and Operations. 3.2.1 The Short-Tenn Securities ofthe MonesMarkets. . 3.2.2 Repos. Carry Trades, andTemporaryTransfers of Claims. 3.2.3 Other Trades. 3.3 Participants and Orders of Magnitude of Trades. 3.3.1 The Participants. 93 94 95 99 KM) 1(M) 101 103 105 105
Contents 3.3.2 Orders of Magnitude. Role of the Interbank Market and Central Bank Intervention. . . 3.4.1 Central Bank Money and the Interbank Market. 3.4.2 Central Bank Interventions and Their Influence on Interest Rates. 110 3.5 The Main Monetary Indices. 3.5.1 Indices Reflecting the Value of a Money-Market Rate on a Given Date. 113 3.5.2 Indices Reflecting the Average Value of a Money-Market Rate During a Given Period. 115 3.6 Summary. Suggestions for Further Reading. 106 107 107 The Bond Markets. 4.1 Fixed-Rate Bonds. 4.1.1 Financial Characteristics and Yield to Maturity at the Date of Issue. 121 4.1.2 The Market Bond Value at an Arbitrary Date; the Influence of Market Rates and of the Issuer’s Rating. . . 4.1.3 The Quotation of Bonds. 4.1.4 Bond Yield References and Bond Indices. 4.2 Floating-Rate Bonds. Indexed Bonds, and Bonds with Cosenants. 135
4.2.1 Floating-Rate Bonds and Notes. 4.2.2 Indexed Bonds. 4.2.3 Bonds with Covenants (Optional Clauses). 4.3 Issuing and Trading Bonds. 4.3.1 Primary'and Secondary Markets. 4.3.2 Treasury Bonds and Treasury Notes Issues: Reopening and STRIPS. 139 4.4 International and Institutional Aspects; the Order of Magnitude of the Volume of Transactions. 141 4.4.1 Brief Presentation of the International Bond Markets. . . 4.4.2 Tlie Main National Markets. 4.5 Summary. Suggested Readings. 119 121 3.4 4 5 xvii Introduction to the Analysis of Interest Rate and Credit Risks. . . 5.1 Interest Rate Risk. 5.1.1 Introductory Examples: The Influence of the Maturity of a Security on Its Sensitivity to Interest Rates. 5.1.2 Variation. Sensitivi ty and Duration of a Fixed-Income Security. 152 5.1.3 Alternative Expressions for the Variation, Sensitivity and Duration. 156 113 117 118 126 131 135
136 137 137 138 138 142 143 146 148 149 149 150
xviii Lumenis Some Properties of Sensitivity and Duration The Sensitivity Ot a Portfolio of Assets and I 1.11'ililics or of a Balance Sheet: Sensitiv itv and (laps 5.1.6 A More Accurate Estimate of İnletesi Rate Risk Convexity. 5.2 Introduction to Credit Risk. 5.2.1 Analysis of the Determinants of the Credit Spie.к! 5.2.2 Simplified Modeling of the Credit Spread, the ( іеЛп Triangle. 172 5.3 Summary'. Appendix 1. Default Probability. Recovery Rate and (redit Spread Suggested Reading. 5.1.4 5.1.5 6 7 The Term Structure of Interest Rates 6.1 Spot Rales and Forward Rates. 6.1.1 The Yield Curve. 6.1.2 Yields to Maturity and Zero Coupon Rates 6.1.3 Forward Interest Rates Implicit in the Spot Rate Curve. 1S4 6.2 Factors Determining the Shape of the Curve 6.2.1 The Curve Shape. IS՜ 6.2.2 Expectations Hypothesis with IerniPremiums 6.2.3 Influence of the CreditSpread onYield Curves 6.3 Analy sis of Interest Rate Risk: Impact of Changes in the Slope and Shape of the Yield Curve. 142 6.3.1 The Risk of a Change in the Slope ol the Yield Curve. 6.3.2 Multifactor Variation and Sensitivity and MihIcE of Yield Curves. 6.4
Summary. Suggested Readings. Vanilla Floating Rate Instruments and Swaps 7.1 Floating Rate Instruments. 7.1.1 General Discussion and Notation. 7.1.2 “Replicable" Assets: Valuation and Interest Rate and Spread Risks. 212 7.2 Vanilla Swaps. 7.2.1 Definitions and Generalities About Swaps 7.2.2 Replication and Valuation of an Interest Rate Swap 7.2.3 Interest Rate. Counterparty and Credit Risks for an Interest Rate Swap. 7.2.4 Summary of the Various Types of Sw aps 7.3 Summary. ĮSg k,| 167 170 170 174 Г5 175 176 Г7 1՝7 Г7 1’4 IS՝ 1SS 141 ll) 2 144 ՝ ?» Μ 2 5 2 6 2 6 22S 22S 232 241 24՜ 251
Contents Appendix. Proof of lhe Equivalence Between Eq. (7.2’) and Proposition 1. Suggested Reading. Books. Articles. 8 Stocks, Stock Markets, and Stock Indices. 8.1 Stocks. 8.1.1 Basic Notions: Equity, Stock Market Capitalization, and Share Issuing. 256 8.1.2 Analysis of Stock Issues, Dilution, and Subscription Rights. 261 8.1.3 Market Performance of a Share and Adjusted Share Price. 8.1.4 Introduction to the Valuation of Firms and Shares; Interpretation and Use of the PER. 266 8.2 Return Probability Distributions and the Evolution of Stock Market Prices. 273 8.2.1 Stock Price on a Future Date, Stock Return, and Its Probability Distribution: Static Analysis. 273 8.2.2 Modeling a Stock Price Evolution with a Stochastic Process:
Dynamic Analysis. 276 8.3 Placing and Executing Orders and the Functioning of Stock Markets. 284 8 3.1 Types of Orders. 8.3.2 The Clearing and Settlement System. 8.3.3 Investment Management. 8.3.4 The Main Stock Markets. 8.4 Stock Market Indices. 8.4.1 Composition and Calculation. 8.4.2 The Main Indices. 8.5 Summary. Appendix I. Skewness and Kurtosis of Log-Returns. Appendix 2. Modeling Volatility with ARCH and GARCH. Suggestions for Further Reading. Book Chapters. Articles. For an Online Comparative Description of Investment Funds from
Different Countries. For an Online Description and Analysis of the Asset Management Industry. xix 252 252 253 253 253 255 255 263 284 286 288 293 294 295 300 302 304 304 305 305 308 308 308 308 308
Contents XX Part II Futures and Options Futures and Forwards. 311 9.1 General Analysis of Forward and Futures Contracts Յւջ 9.1.1 Definition of a Forw ard Contract: Terminologe and Notation. .42 9.1.2 Futures Contracts: Comparison ot Futures and l oiwaid Contracts. 314 9.1.3 Unwinding aPosition Before Expiration 317 9.1.4 The Value of Forward andFutures Contracts 318 9.2 Cash-and-carry and the Relation Between Spot anil Forward Prices. 319 9.2.1 Arbitrage, Cash-and-Carry. and Spot-Forward Pants 319 9.2.2 Forward Prices, Expected Spot Prices, and Risk Premiums. 324 9.3 Maximum and Optimal Hedging with Forward and Futures Contracts. 325 9.3.1 Perfect or Maximum Hedging. *26 9.3.2 Optimal Hedging and Speculation. 333 9.4 The Main Forward and Futures Contracts. 334 9.4.1 Contracts on Commodities. 335 9.4.2 Contracts on Currencies (Foreign Exchanges» 338 9.4.3 Forward and Futures Contracts on Financial Securities (Stocks, Bonds. Negotiable Debt Securities i, FR A. and Contracts on Market Indices. 340 9.5 Summary. *48
Appendix. *49 The Relationship Between Forward and Futures Prices *49 Suggestions for Further Reading.*52 Books. *52 Articles.*52 9 10 Options (I): General Description. Parity Relations. Basic Concepts, and Valuation Using the Binomial Model *53 10.1 Basic Concepts, Call-Put Parity, and Other Restrictions (пип No Arbitrage. *54 10.1.1 Definitions. Value at Maturity. Intrinsic Value. and Time Value. 354 10.1.2 The Standard Call-Put Parity. *58 10.1.3 Other Parity Relations. *61 10.1.4 Other Arbitrage Restrictions. *M 10.2 A Pricing Model for One Period and Two States of the World. 367 10.2.1 Two Markets, Two States. 368 10.2.2 Hedging Strategy and Option Value in the Absence of Arbitrage. 369
Contents 10.2.3 The "Risk-Neutral” Probability. 10.2.4 The Risk Premium and the Market Price of Risk. 10.3 The Multi-period Binomial Model. 10.3.1 The Model Framework and the Dynamics of the Underlying’s Price. 377 10.3.2 Risk-Neutral Probability and Martingale Processes. . . 10.3.3 Valuation of an Option Using the Cox-Ross-Rubinstein Binomial Model. 381 10.4 Calibration of (he Binomial Model and Convergence to the Black-Scholes Formula. 386 10.4.1 An Interpretation of Premiums in Terms of Probabilities of Exercise. 10.4.2 Calibration and Convergence. 10.5 Summary. Appendix 1. Calibration of the Binomial Model. * Appendix 2. Suggestions for Further Reading. Books. Articles. 11 Options (111:
Continuous-Time Models, Black-Scholes and Extensions. 11.1 The Standard Black-Scholes Model. 11.1.1 The Analytical Framework and BS Model’s Assumptions. 400 11.1.2 Self-Financing Dynamic Strategies. 11.1.3 Pricing Using a Partial Differential Equation and the Black-Scholes Fonnula. 402 1 1.1.4 Probabilistic Interpretation. 11.2 Extensions of the Black-Scholes Formula. 11.2.1 Underlying Assets That Pay Out (Dividends, Coupons, etc.). 412 I 1.2.2 Options on Commodities. 11.2.3 Options on Exchange Rates. 11.2.4 Options on Futures and Forwards. 11.2.5 Variable But Deterministic Volatility. 11.2.6 Stochastic Interest Rates: The Black-Scholes-Merton (BSM) Model. 429 11.2.7 Exchange Options (Margrabe). 11.2.8 Stochastic Volatility (*). 11.3 Summary. Appendix
I. Historical and Risk-Neutral Probabilities and Changes in Probability. xxi 372 374 377 379 387 389 391 393 393 395 397 397 397 399 399 401 406 412 421 422 424 427 434 437 443 444 444
xxii 12 Contents Appendix 2. Changing the Probability Measure and the Numerane Appendix 3. Alternative Interpretations of the Plack Scholes loimilla Suggested Reading. Books. Articles. 446 446 449 449 451 451 451 Option Portfolio Strategies: Tools and Methods 12.1 Basic Static Strategies. 12.1.1 The General P L Profile at Maliu its 12.1.2 The Main Static Strategics 12.1.3 Replication of an Arbitrais Pasoli bs a Sialic Option Portfoliot*). 457 12.2 Historical and Implied Volatilities. Smile, Skew and leim Structure. 457 12.2.1 Historical Volatility. 12.2.2 The Implied Volatility. 12.2.3 Smile. Skew, Term Structure, and Volatility Suil.uc 12.3 Option Sensitivities (Greek Parameters) 12.3.1 The Della (б). 12.3.2 The Gamma (Г). 12.3.3 The Vega (о). 12.3.4 The Theta (0). 12.3.5 TheRho(p). 12.3.6 Sensitivity tothe Dividend Rate 12.3.7 Elasticity and Risk-ExpectedReturn Tradeoff 12.4 Dynamic Management of an Option Portfolio I sing (
heck Parameters. 4'5 12.4.1 Variation in the Value of a Position in the Short Tenn and GeneralConsiderations. 12.4.2 Delta-NeutralManagement. 12.4.3 A Tool for Risk Management: The P l Matrix 12.5 Summary. Appendix 1. Computing Partial Derivatives (Greeks). Appendix 2. Option Prices and the Underlying Price Probability Distribution. Appendix 3. Replication of an Arbitrary Payoff with a Static Option Portfolio. Suggestions for Further Reading. Books. Articles. 453 454 454 455 458 459 461 463 4M 467 468 4'0 471 472 473 4'5 4'6 485 4S6 4SS 488 403 403 496 496 498 498 498
Contents 13 14 xxiii American Options and Numerical Methods. 13.1 Early Exercise and Call-Put Parity for American Options. 13.1.1 Early Exercise of American Options. 13.1.2 Call-Put “Parity” for American Options. 13.2 Pricing American Options: Analytical Approaches. 13.2.1 Pricing an American Call on a Spot Asset Paying a Single Discrete Dividend or Coupon. 517 13.2.2 Pricing an American Option (Call and Put) on a Spot Asset Paying a Continuous Dividend or Coupon. 13.2.3 Prices of American and European Options: Orders of Magnitude. 528 13.3 Pricing American Options with the Binomial Model. 13.3.1 Binomial Dynamics of Price S: The Case of a Discrete Dividend. 13.3.2 Binomial Dynamics of Price S: The Continuous Dividend Case. 531 13.3.3 Pricing an American Option Using the Binomial Model. 531 13.3.4 Improving the Procedure with a Control Variate. 13.4 Numerical Methods: Finite Differences, Trinomial and ThreeDimensional Trees. 533 13.4.1 Finite Difference Methods (*). 13.4.2 Trinomial Trees. 13.4.3
Three-Dimensional Trees Representing Two Correlated Processes. 13.5 Summary. Appendix 1. Proof of the Smooth Pasting (Tangency) Condition (13.5b). . . Appendix 2. Orthogonalization of the Processes In S։ and In Տշ and Construction of a Three-Dimensional Tree. Suggestion for Further Reading. Books. Articles. 501 502 502 515 516 *Exotic Options. 14.1 Path-Independent Options. 14.1.1 The Forward Start Option (with Deferred Start). 14.1.2 Digital and Double Digital Options. 14.1.3 Multi-underlying (Rainbow) Options (*). 14.1.4 Options on Options or “Compounds”. 14.1.5 Quantos and Compos. 14.2 Path-Dependent Options.
14.2.1 Barrier Options. 14.2.2 Digital Barriers. 549 550 550 551 555 559 560 567 567 573 520 529 529 533 534 539 541 543 545 545 546 546 547 547 548
Contents xxiv 14.2.3 Lookback Options i ’ i 575 14.2.4 Options on Ascrages( Asians 1 578 14.2.5 Chooser Options i * i 5K6 14.3 Summary. 587 Appendix 1. 589 ♦ ♦Value of a Colluso (. all 589 Appendix 2. 591 ♦ ♦Lemmas ՕՈ Hitting Probabilities lol a Dulled Bi. anian Motion. 591 Appendix 3. 594 ♦ ♦Proof of the Ins erses” Relation loi Bârnei (ipini. 594 Appendix 4. 595 ♦ ♦Valuing a Call l p and Out sudi 1 iB.nner । К Микс Appendix 5. 597 ♦ ♦ Valuing Rebates. 597 Appendix 6. 598 ♦ ♦Proof of the Pnce ol a Lookbas k ( all '98 Appendix 7. 601 ♦ ♦Options on an Asetage Ptice N 1 Appendix 8. (812 ♦♦Options ssith an Asetage Stuke (8)2 Suggestions for Further Reading MM Books. (8)4 Articles. MM 15 Futures Markets (2): Contracts on Interest Rates Notional Contracts. 15.1.1 Basket of Dehserable Secui itics i DS 1 and Notional Security. 15.1.2 The Euro-Bond Contract 15.1.3 Settlement and Conversion Factors 15.1.4 Cheapest to Delis er and Quoting Futures at Expiration. 613 15.1.5 Arbitrage and Cash-Futures Relationship 15.1.6 Interest Rate Sensitiv its ot Entures Pnces 15.1.7 Hedging Intriest Rate Risk Csmg Notional Bond
Contracts. 629 15.1.8 The Main Notional Contracts 15.2 Short-Tenn Interest Rate Contracts (STIR 11 '-Month lotward Looking Rates and Backssard-Looking Overnight Avcragcsi 15.2.1 STIR З-Month Contracts (LIBOR Type. Fonvard Looking). 15.2.2 Futures Contracts on an Average Osemight Rate 15.2.3 Hedging Interest Rate Risk with STIR Contracts 15.3 Summary. 15.1 N17 818 (8)8 881 611 618 б24 63՜ 641 Ml Μ՞ б5б 659
Contents Appendices. I Valuation of the Delivery Option. 2 Relationship Between Forward and Futures Prices. Suggestions for Further Reading. Books. Articles. Internet Sites. 16 Interest Rate Instruments: Valuation with the BSM Model, Hybrids, and Structured Products. 667 16.1 Valuation of Interest Rate Instruments Using Standard Models. . . 16.1.1 Principles of Valuation and the Black-Scholes-Merton Model Generalized to Stochastic Interest Rates. 16.1.2 Valuation of a Bond Option Using the BSM-Price Model. 671 16.1.3 Valuation of the Right to a Cash Flow Expressed as a Function of a Rate and the BSM-Rate Model. 16.1.4 Convexity Adjustments for Non-vanilla Cash Flows (*). 676 16.2 Nonstandard Swaps and Swaptions. 16.2.1 Review of Swaps and Notation. 16.2.2 Some Nonstandard
Swaps. 16.2.3 Swap Options (or Swaptions). 16.3 Caps and Floors. 16.3.1 Vanilla Caps. 16.3.2 A Vanilla Floor. 16.4 Static Replicationsand Combinations; Structured Contracts. . . 16.4.1 Basic Instruments: Notation and General Remarks. . . 16.4.2 Replication of a Capped or Floored Floating-Rate Instrument Using a Standard Asset Associated with a Cap or a Floor. 696 16.4.3 Collars. 16.4.4 Non-standard Caps and Floors. 16.4.5 Other Static Combinations; Structured Products; Contracts on Interest Rates with Profit-Sharing. 16.5 Bonds with Optional Features and Hybrid Products. 16.5.1 Convertible Bonds. 16.5.2 Other Bonds with Optional Features. 16.6 Summary. Appendix. The -Martingale Measure. Suggestions for Further
Reading. Books. Articles. xxv 661 661 662 666 666 666 666 667 668 672 680 680 682 686 688 689 692 693 693 699 702 705 707 708 711 713 715 715 716 716 716
xxvi 17 18 Contents Modeling Interest Rates and Options on Intercast Rates 17.1 Models Based on the Dynamics ot Spot Rates 17.1.1 One-Factor Models t\ asuek, and(ox.Ingeisoll and Ross). 721 17.1.2 Fitting the Initial Yield C urse, the Hull and White Model. 17.1.3 Multifaclor Structures 17.2 Models Grounded on the Dynamics ol 1 orw.ud Rates 17.2.1 The Heath-Jam w Monon Minici t loo;, 17.2.2 The Libor (LMM) and Swap(SMM 1Maikét Models. 17.3 Summary. Appendix 1. ♦The Vasicek Model. Appendix 2. ♦The LMM and SMM Models Suggestions for Further Reading. Books. Articles. Elements of Stochastic Calculus 18.1 Definitions. Notation, and General Considciations About Stochastic Processes. 766 18.1.1 Notation. 18.1.2 Stochastic Processes: Délimitons. Notation, and General Framework. '66 18.2 Brownian Motion. 18.2.1 The One-Dimensional Brow man Motion 18.2.2 Calculus Rules Relative to Brownian Motions 18.2.3 Multi-dimensional .Arithmetic BnmnunMotions 18.3 More General Processes Derived from the Brownian Motion. One-Dimensional Itõ and Diffusion Pnxcsses 18.3.1 One-Dimensional
Ito Processes. 18.3.2 One-Dimensional Diffusion Processes 18.3.3 Stochastic Integrals t* ). 18.4 Differentiation of a Function of an Ito Pnxcss: Ito’sLemma 18.4.1 Itô’s Lemma. 18.4.2 Examples of Application. 18.5 Multi-dimensional Itô and Diffusion Processes t * 1. '89 18.5.1 Multivariate Itô and Diffusion Processes 18.5.2 Ito’s Lemma (Differentiation of a Function of an n-Dimensional Itô Process). 18.6 Jump Processes. 18.6.1 Description of Jump Processes. 18.6.2 Modeling Jump Processes. 18.7 Summary. 7 J9 720 726 728 729 730 737 749 751 751 754 754 762 762 762 765 '66 769 '69 '75 '77 779 '79 780 '82 '85 '85 '87 790 '1H 793 793 793 794
Contents Suggestions for Further Reading. Books. 19 xxvii 796 796 *The Mathematical Framework of Financial Markets Theory. 797 19.1 General Framework and Basic Concepts. 798 19.1.1 The Probabilistic Framework. 798 19.1.2 The Market, Securities, and Portfolio Strategies. 799 19.1.3 Portfolio Strategies. 800 19.1.4 Contingent Claims, AAO, and CompleteMarkets. . 802 19.1.5 Price Systems. 804 19.2 Price Dynamics as Ito Processes, Arbitrage Pricing Theory and the Markel Price of Risk. 805 19.2.1 Price Dynamics as Itô Processes. 806 19.2.2 Arbitrage Pricing Theory in Continuous Time. 806 19.2.3 Redundant Securities and Characterizing the Base of Primitive Securities. 808 19.3 The Risk-Neutral Universe and Transforming Prices into Martingales. 809 19.3.1 Martingales, Driftless Processes, and Exponential Martingales. 809 19.3.2 Price and Return Dynamics in the Risk-Neutral Universe. Transforming Prices into
martingales and Pricing Contingent Claims. 813 19.3.3 Characterizing a Complete market and Market Prices of Risk. 816 19.4 Change of Probability Measure, Radon-Nikodym derivative and Girsanov’s Theorem. 818 19.4.1 Changing Probabilities and the Radon-Nikodym Derivative. 818 19.4.2 Changing Probabilities and Brownian Motions: Girsanov’s Theorem. 820 19.4.3 Formal Definition of RN Probabilities. 822 19.4.4 Relations between Viable Price Systems, RN Probabilities, and MPR. 823 19,5 Changing the Numeraire. 825 19.5.1 Numeraires. 825 19.5.2 Numeraires and Probabilities that yield martingale Pnces. 826 19.6 The P-Numeraire (OptimalGrowth or Logarithmic Portfolio). . . 832 19.6.1 Definition of lite Portfolio (h. H) as the P-Numeraire. . . 832 19.6.2 Characterization and Composition of the P-Numeraire Portfolio (h. Hi. 833 19.7 ** Incomplete Markets. 836 19.7.1 MPR and the Kemel of the Diffusion Matrix ^(t). 837 19.7.2
Deflators. 840
xxviii C oritene 19.8 Summan. Appendix. Construction of a One-to-one I oirespondeiK e ScOs Q and П. Suggestions l'or further reading Books. Articles. 20 M2 844 844 M5 M5 846 The State Variables Model and the Valuation Partial DifTvrvntial Equation. M7 20.1 Analytical Framework and Notation M7 20.1.1 Dynamics of State Variables M7 20.1.2 The Asset Pricing Problem M8 20.2 Factor Decomposition of Returns M9 20.2.1 Expressing the Return JR as a Fuik lion ot ihe \ M9 20.2.2 Expressing the Return JR as а І unition ol the .И , 850 20.3 Expected Asset Returns and Arbitrage Рік me Iheoix ՛ \l’l ՛ in Continuous Time. $50 20.3.1 First Formula lor Expected Retums 851 20.3.2 Continuous Time API' in a State sanables Mode; 851 20.4 The General valuation PDF. 853 20.4.1 Derivation of the General xalualion PDF 853 20.4.2 Market Prices of Risk and Risk Premia 854 20.4.3 The Relation between MPR and Excess Returns ՕՈ Primitive Securities and the Condition lot Maikét Completeness. 855 20.5 Applications to the Tenn Structure ofInterest Rates 857 20.5.1 Models with One State Variable 857 20.5.2 Multi-Factor models and xaluation ot Fixed buome Securities. 854 20.6 Pricing in the Risk-Neutral Unixcrsc 862 20.6.1 Dynamics of Retums, of Brownian Motions and of State Variables in the Risk-Neutral Inncrsc 862 20.6.2 The Valuation
PDF. 863 20.7 Discounting under Uncertainty and the Feynman Кас Theorem. 864 20.7.1 The Cauchy-Dirichlet PDF. and the Feynman К.к Theorem. 864 20.7.2 Financial Interpretation of the Fey nman Кас Theorem and Discounting under Uncertainty 865 20.8 Summary. 866 Appendix. 86S Suggestions for Further Reading. 864 Books. 864 Articles. 860 |
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| id | DE-604.BV048585486 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:06:10Z |
| indexdate | 2024-07-10T09:42:13Z |
| institution | BVB |
| isbn | 9783030845988 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033961262 |
| oclc_num | 1352884630 |
| open_access_boolean | |
| owner | DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-355 DE-BY-UBR |
| physical | xxxvii, 869 Seiten Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in business and economics |
| spelling | Poncet, Patrice 1949- Verfasser (DE-588)170208885 aut Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk Volume 1 Patrice Poncet, Roland Portait ; contributions by Igor Toder Cham, Switzerland Springer [2022] xxxvii, 869 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer texts in business and economics Portait, Roland Verfasser (DE-588)170766292 aut Toder, Igor ctb (DE-604)BV048585467 1 Erscheint auch als Online-Ausgabe 978-3-030-84600-8 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033961262&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Poncet, Patrice 1949- Portait, Roland Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk |
| title | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk |
| title_auth | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk |
| title_exact_search | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk |
| title_exact_search_txtP | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk |
| title_full | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk Volume 1 Patrice Poncet, Roland Portait ; contributions by Igor Toder |
| title_fullStr | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk Volume 1 Patrice Poncet, Roland Portait ; contributions by Igor Toder |
| title_full_unstemmed | Capital market finance an introduction to primitive assets, derivatives, portfolio management and risk Volume 1 Patrice Poncet, Roland Portait ; contributions by Igor Toder |
| title_short | Capital market finance |
| title_sort | capital market finance an introduction to primitive assets derivatives portfolio management and risk |
| title_sub | an introduction to primitive assets, derivatives, portfolio management and risk |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033961262&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV048585467 |
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