Derivates, risk management & value:
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| 245 | 1 | 0 | |a Derivates, risk management & value |c Mondher Bellalah |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2010 | |
| 300 | |a XLV, 949 S. |b Ill., graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Angekündigt u.d.T.: Bellalah, Mondher: Options | ||
| 650 | 4 | |a Derivative securities | |
| 650 | 4 | |a Risk management | |
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| adam_text | CONTENTS
Dedication
v
Foreword by Edward
С.
PrescoU
vii
Foreword by Harry
M.
Markowitz ix
Foreword by James J.
Heekman
xi
Foreword by George M. Constantinides
xiii
About the Author
xv
PART I. FINANCIAL MARKETS AND
FINANCIAL INSTRUMENTS: BASIC
CONCEPTS AND STRATEGIES
1
CHAPTER
1.
FINANCIAL MARKETS, FINANCIAL
INSTRUMENTS, AND FINANCIAL CRISIS
3
Chapter Outline
............................ 3
Introduction
.............................. 4
1.1.
Trading Characteristics of Commodity Contracts:
The Case of Oil
......................... 7
1.1.1.
Fixed prices
...................... 7
1.1.2.
Floating prices
.................... 8
1.1.3.
Exchange of futures for Physical (EFP)
...... 8
1.2.
Description of Markets and Instruments: The Case of the
International Petroleum Exchange
.............. 8
1.3.
Characteristics of Crude Oils and Properties of Petroleum
Products
............................. 9
1.3.1.
Specific features of some oil contracts
....... 9
1.3.2.
Description of Markets and Trading Instruments:
The Brent Market
..................
ц
xviii Derivatives,
Risk Management and Value
1.4.
Description of Markets and Trading Instruments: The Case
of Cocoa
............................. 13
1.4.1.
How do the futures and physicals market work?
. . 14
1.4.2.
Arbitrage
....................... 14
1.4.3.
How is the ICCO price for cocoa beans calculated?
14
1.4.4.
Information on how prices are affected by changing
economic factors?
................... 15
1.4.5.
Cocoa varieties
.................... 15
1.4.6.
Commodities
—
Market participants: The case of
cocoa, coffee, and white sugar
............ 15
1.5.
Trading Characteristics of Options: The Case of Equity
Options
............................. 17
1.5.1.
Options on equity indices
.............. 17
1.5.2.
Options on index futures
.............. 17
1.5.3.
Index options markets around the world
...... 18
1.5.4.
Stock Index Markets and the underlying indices in
Europe
........................ 19
1.6.
Trading Characteristics of Options: The Case of Options on
Currency Forwards and Futures
................ 21
1.7.
Trading Characteristics of Options: The Case of Bonds and
Bond Options Markets
..................... 22
1.7.1.
The specific features of classic interest rate
instruments
...................... 22
1.7.2.
The specific features of mortgage-backed securities
25
1.7.3.
The specific features of interest rate futures, options,
bond options, and swaps
............... 26
1.8.
Simple and Complex Financial Instruments
......... 31
1.9.
The Reasons of Financial Innovations
............ 34
1.10.
Derivatives Markets in the World: Stock Options, Index
Options, Interest Rate and Commodity Options and Futures
Markets
............................. 36
1.10.1.
Global overview
................... 36
1.10.2.
The main indexes around the world: a historical
perspective
...................... 36
Summary
................................ 46
Questions
................................ 48
Exercises
............................ 48
Appendix
................................ 56
References
............................ 66
Contents xix
CHAPTER
2.
RISK MANAGEMENT, DERIVATIVES
MARKETS AND TRADING STRATEGIES
67
Chapter Outline
............................ 67
Introduction
.............................. 68
2.1.
Introduction to Commodity Markets: The Case of Oil
... 70
2.1.1.
Oil futures markets
.................. 70
2.1.2.
Oil futures exchanges
................ 70
2.1.3.
Delivery procedures
................. 70
2.1.4.
The long-term oil market
.............. 71
2.2.
Pricing Models
......................... 71
2.2.1.
The pricing of forward and futures oil contracts
. . 71
2.2.1.1.
Relationship to physical market
..... 71
2.2.1.2.
Term structure of prices
......... 72
2.2.2.
Pricing swaps
..................... 72
2.2.3.
The pricing of forward and futures commodity
contracts: General principles
............ 72
2.2.3.1.
Forward prices and futures prices: Some
definitions
................. 73
2.2.3.2.
Futures contracts on commodities
.... 74
2.2.3.3.
Futures contracts on a security with no
income
................... 74
2.2.3.4.
Futures contracts on a security with a
known income
............... 74
2.2.3.5.
Futures contracts on foreign currencies
. 75
2.2.3.6.
Futures contracts on a security with a
discrete income
.............. 75
2.2.3.7.
Valuation of interest rate futures
contracts
.................. 76
2.2.3.8.
The pricing of future bond contracts
. . 77
2.3.
Trading Motives: Hedging, Speculation, and Arbitrage
... 78
2.3.1.
Hedging using futures markets
........... 78
2.3.1.1.
Hedging: The case of cocoa
....... 79
2.3.1.2.
Hedging: The case of oil
......... 79
2.3.1.3.
Hedging: The case of petroleum products
futures contracts
............. 80
2.3.1.4.
The use of futures contracts by petroleum
products marketers, jobbers, consumers,
and refiners
................ 82
xx
Derivatives, Risk Management and Value
2.3.2.
Speculation using futures markets
......... 84
2.3.3.
Arbitrage and spreads in futures markets
..... 84
2.4.
The Main Bounds on Option Prices
.............. 85
2.4.1.
Boundary conditions for call options
........ 86
2.4.2.
Boundary conditions for put options
........ 86
2.4.3.
Some relationships between call options
...... 86
2.4.4.
Some relationships between put options
...... 88
2.4.5.
Other properties
................... 89
2.5.
Simple Trading Strategies for Options and their Underlying
Assets
.............................. 90
2.5.1.
Trading the underlying assets
............ 90
2.5.2.
Buying and selling calls
............... 91
2.5.3.
Buying and selling puts
............... 93
2.6.
Some Option Combinations
.................. 94
2.6.1.
The straddle
..................... 94
2.6.2.
The strangle
..................... 94
2.7.
Option Spreads
......................... 95
2.7.1.
Bull and bear spreads with call options
...... 95
2.7.2.
Bull and bear spreads with put options
...... 96
2.7.3.
Box spread
...................... 96
2.7.3.1.
Definitions and examples
......... 96
2.7.3.2.
Trading a box spread
........... 98
2.8.
Butterfly Strategies
....................... 99
2.8.1.
Butterfly spread with calls
.............. 99
2.8.2.
Butterfly spread with puts
.............. 100
2.9.
Condor Strategies
........................ 100
2.9.1.
Condor strategy with calls
.............. 100
2.9.2.
Condor strategy with puts
.............. 101
2.10.
Ratio Spreads
.......................... 102
2.11.
Some Combinations of Options with Bonds and Stocks
. . . 103
2.11.1.
Covered call: short a call and hold the underlying
asset
.......................... 103
2.11.2.
Portfolio insurance
.................. 103
2.11.3.
Mimicking portfolios and synthetic instruments
. . 104
2.11.3.1.
Mimicking the underlying asset
..... 104
2.11.3.2.
Synthetic underlying asset: Long call plus
a short put and bonds
.......... 104
2.11.3.3.
The synthetic put: put-call parity
relationship
................ 105
Contents xxi
2.12.
Conversions and Reversals
................... 106
2.13.
Case study: Selling Calls (Without Holding the Stocks/as an
Alternative to Short Selling Stocks/the Idea of Selling Calls
is Also an Alternative to Buying Puts)
............ 107
2.13.1.
Data and assumptions
................ 107
2.13.1.1.
Selling calls (without holding the stock)
107
2.13.1.2.
Comparing the strategy of selling calls
(with a short portfolio of stocks)
:
the
extreme case
................ 109
2.13.1.3.
Selling calls (holding the stock)
..... 110
2.13.2.
Leverage in selling call options (without holding the
stocks)
......................... 110
2.13.2.1.
Selling Call options (without holding the
stocks)
...................
Ill
2.13.2.2.
Leverage in selling Call options (without
holding the stocks): The extreme case
. 113
2.13.2.3.
Selling calls using leverage (and holding
the stock)
................. 113
2.13.3.
Short sale of the stocks without options
...... 113
2.14.
Buying Calls on
EMA
..................... 116
2.14.1.
Buying a call as an alternative to buying the stock:
(also as an alternative to short sell put options)
. . 116
2.14.1.1.
Data and assumptions
.......... 116
2.14.1.2.
Pattern of risk and return
........ 116
2.14.2.
Compare buying calls (as an alternative to portfolio
of stocks)
....................... 117
2.14.2.1.
Risk return in options
.......... 118
2.14.3.
Example by changing volatility to
20%....... 120
2.14.3.1.
Data and assumptions:
.......... 120
2.14.3.2.
Compare buying calls (as an alternative
to portfolio of stocks.)
.......... 121
2.14.3.3.
Leverage in buying call options (without
selling the underlying)
.......... 123
Summary
................................ 125
Questions
................................ 127
Case Study: Comparisons Between put and Call Options
...... 128
1.
Buying Puts and Selling Puts Naked
............. 128
1.1.
Buying puts
...................... 128
1.2.
Selling puts
...................... 129
xxii
Derivatives, Risk Management and Value
2.
Buying and Selling Calls
.................... 131
2.1.
Buying calls
...................... 131
2.2.
Selling a call
..................... 132
3.
Strategy of Buying a Put and Hedge and Selling a Put and
Hedge
.............................. 132
3.1.
Strategy of selling put and hedge: sell delta units of
the underlying
.................... 134
3.2.
Strategy of buy put and hedge: buy delta units of
the underlying
.................... 135
4.
Strategy of Buy Call, Sell Put, and Buy Call, Sell Put and
Hedge
.............................. 135
5.
Strategy of Buy Call, Sell Put: Equivalent to Holding the
Underlying
........................... 137
6.
Strategy of Buy Call, Sell Put and Hedge: Reduces Profits
and Reduces Losses
....................... 138
References
................................ 140
CHAPTER
3.
TRADING OPTIONS AND THEIR
UNDERLYING ASSET: RISK MANAGEMENT
IN DISCRETE TIME
141
Chapter Outline
............................ 141
Introduction
.............................. 141
3.1.
Basic Strategies and Synthetic Positions
........... 142
3.1.1.
Options and synthetic positions
........... 142
3.1.2.
Long or short the underlying asset
......... 144
3.1.3.
Long a call
...................... 144
3.1.4.
Short call
....................... 145
3.1.5.
Long a put
...................... 147
3.1.6.
Short a put
...................... 148
3.2.
Combined Strategies
...................... 150
3.2.1.
Long a straddle
.................... 150
3.2.2.
Short a straddle
................... 152
3.2.3.
Long a strangle
.................... 153
3.2.4.
Short a strangle
................... 156
3.2.5.
Long a tunnel
..................... 157
3.2.6.
Short a tunnel
.................... 158
3.2.7.
Long a call bull spread
................ 159
3.2.8.
Long a put bull spread
................ 159
Contents
xxiii
3.2.9.
Long a call bear spread
............... 161
3.2.10.
Selling a put bear spread
.............. 162
3.2.11.
Long a butterfly
................... 162
3.2.12.
Short a butterfly
................... 163
3.2.13.
Long a condor
.................... 163
3.2.14.
Short a condor
.................... 164
3.3.
How Traders Use Option Pricing Models: Parameter
Estimation
........................... 166
3.3.1.
Estimation of model parameters
.......... 167
3.3.1.1.
Historical volatility
............ 167
3.3.1.2.
Implied volatilities and option pricing
models
................... 170
3.3.2.
Trading and Greek letters
.............. 170
3.4.
Summary
............................ 174
Case Studies
.............................. 176
Exercises
................................ 208
Questions
................................ 175
References
................................ 217
PART II. PRICING DERIVATIVES AND THEIR
UNDERLYING ASSETS IN A DISCRETE-TIME
SETTING
219
CHAPTER
4.
OPTION PRICING: THE DISCRETE-
TIME APPROACH FOR STOCK OPTIONS
221
Chapter Outline
............................ 221
Introduction
.............................. 221
4.1.
The CRR Model for Equity Options
............. 222
4.1.1.
The mono-periodic model
.............. 222
4.1.2.
The multiperiodic model
............... 224
4.1.3.
Applications and examples
............. 226
4.1.3.1.
Applications of the CRR model within
two periods
................ 226
4.1.3.2.
Other applications of the binomial model
of CRR for two periods
.......... 228
4.1.3.3.
Applications of the binomial model of
CRR for three periods
.......... 231
4.1.3.4.
Examples with five periods
....... 234
xxiv
Derivatives, Risk Management and Value
4.2.
The Binomial Model and the Distributions to the Underlying
Assets
.............................. 237
4.2.1.
The Put-Call parity in the presence of several
cash-distributions
................... 237
4.2.2.
Early exercise of American stock options
...... 237
4.2.3.
The model
...................... 238
4.2.4.
Simulations for a small number of periods
..... 238
4.2.5.
Simulations in the presence of two dividend dates
. 246
4.2.6.
Simulations for different periods and several
dividends: The general case
............. 246
Summary
................................ 249
Questions
................................ 249
Appendix: The Lattice Approach
................... 249
References
................................ 258
CHAPTER
5.
CREDIT RISKS, PRICING BONDS,
INTEREST RATE INSTRUMENTS, AND THE TERM
STRUCTURE OF INTEREST RATES
259
Chapter Outline
............................ 259
Introduction
.............................. 259
5.1.
Time Value of Money and the Mathematics of Bonds
.... 260
5.1.1.
Single payment formulas
............... 261
5.1.2.
Uniform-series present worth factor (USPWF) and
the capital recovery factor (CRF)
.......... 262
5.1.3.
Uniform-series compound-amount factor (USCAF)
and the sinking fund factor (SFF
)......... 263
5.1.4.
Nominal interest rates and continuous compounding
265
5.2.
Pricing Bonds
.......................... 266
5.2.1.
A coupon-paying bond
................ 266
5.2.2.
Zero-coupon bonds
.................. 267
5.3.
Computation of the Yield or the Internal Rate of Return
. . 268
5.3.1.
How to measure the yield
.............. 268
5.3.2.
TheCY
........................ 269
5.3.3.
The YTM
....................... 269
5.3.4.
The YTC
. . ..................... 270
5.3.5.
The potential yield from holding bonds
...... 270
5.4.
Price Volatility Measures: Duration and Convexity
..... 271
5.4.1.
Duration
....................... 271
Contents xxv
5.4.2.
Duration of a bond portfolio
............ 273
5.4.3.
Modified duration
.................. 273
5.4.4.
Price volatility measures: Convexity
........ 274
5.5.
The Yield Curve and the Theories of Interest Rates
..... 275
5.5.1.
The shapes of the yield curve
............ 276
5.5.2.
Theories of the term structure of interest rates
. . 276
5.5.2.1.
The pure expectations theory
...... 276
5.6.
The YTM and the Theories of the Term Structure of Interest
Rates
.............................. 277
5.6.1.
Computing the YTM
................ 277
5.6.2.
Market segmentation theory of the term structure
278
5.7.
Spot Rates and Forward Interest Rates
............ 279
5.7.1.
The theoretical spot rate
.............. 279
5.7.2.
Forward rates
..................... 279
5.8.
Issuing and Redeeming Bonds
................. 281
5.9.
Mortgage-Backed Securities: The Monthly Mortgage
Payments for a Level-Payment Fixed-Rate Mortgage
.... 283
5.10.
Interest Rate Swaps
...................... 286
5.10.1.
The pricing of interest rate swaps
.......... 286
5.10.2.
The swap value as the difference between the prices
of two bonds
..................... 286
5.10.3.
The valuation of currency swaps
.......... 287
5.10.4.
Computing the swap
................. 289
Summary
................................ 289
Questions
................................ 290
References
................................ 291
CHAPTER
6.
EXTENSIONS OF SIMPLE BINOMIAL
OPTION PRICING MODELS TO INTEREST RATES AND
CREDIT RISK
293
Chapter Outline
............................ 293
Introduction
.............................. 293
6.1.
The Rendleman and Bartter Model (for details, refer to
Bellalah
et al.
1998)
for Interest-Rate Sensitive Instruments
294
6.1.1.
Using the model for coupon-paying bonds
..... 296
6.2.
Ho and Lee Model for Interest Rates and Bond Options
. . 297
6.2.1.
The binomial dynamics of the term structure
. . . 297
6.2.2.
The binomial dynamics of bond prices
....... 298
xxvi
Derivatives, Risk Management and Value
6.2.3.
Computation of bond prices in the Ho and Lee
model
......................... 298
6.2.4.
Option pricing in the Ho and Lee model
...... 299
6.2.5.
Deficiency in the Ho and Lee model
........ 302
6.3.
Binomial Interest-Rate Trees and the Log-Normal Random
Walk
............................... 303
6.4.
The Black-Derman-Toy Model (BDT)
............ 308
6.4.1.
Examples and applications
............. 309
6.5.
Trinomial Interest-Rate Trees and the Pricing of Bonds
. . 313
6.5.1.
The model
...................... 313
6.5.2.
Applications of the binomial and trinomial models
316
Summary
................................ 318
Questions
................................ 320
Appendix A: Ho and Lee model and binomial dynamics
of bond prices
.......................... 321
References
................................ 325
CHAPTER
7.
DERIVATIVES AND PATH-DEPENDENT
DERIVATIVES: EXTENSIONS AND GENERALIZATIONS
OF THE LATTICE APPROACH BY ACCOUNTING FOR
INFORMATION COSTS AND ILLIQUIDITY
327
Chapter Outline
............................ 327
Introduction
.............................. 327
7.1.
The Standard Lattice Approach for Equity Options: The
Standard Analysis
....................... 329
7.1.1.
The model for options on a spot asset with any pay
outs
.......................... 329
7.1.2.
The model for futures options
............ 330
7.1.3.
The model with dividends
.............. 330
7.1.3.1.
A known dividend yield
......... 331
7.1.3.2.
A known proportional dividend yield
. . 331
7.1.3.3.
A known discrete dividend
........ 332
7.1.4.
Examples
....................... 332
7.1.4.1.
The European put price with dividends
333
7.1.4.2.
The American put price with dividends
333
7.2.
A Simple Extension to Account for Information Uncertainty
in the Valuation of Futures and Options
........... 338
Contents xxvii
7.2.1.
On the valuation of derivatives and information
costs
.......................... 338
7.2.2.
The valuation of forward and futures contracts in
the presence of information costs
.......... 340
7.2.2.1.
Forward, futures, and arbitrage
..... 340
7.2.2.2.
The valuation of forward contracts in the
absence of distributions to the underlying
asset
.................... 340
7.2.2.3.
The valuation of forward contracts in the
presence of a known cash income to the
underlying asset
.............. 341
7.2.2.4.
The valuation of forward contracts in the
presence of a known dividend yield to the
underlying asset
.............. 341
7.2.2.5.
The valuation of stock index futures
. . 342
7.2.2.6.
The valuation of Forward and futures
contracts on currencies
.......... 342
7.2.2.7.
The valuation of futures contracts on
silver and gold
.............. 343
7.2.2.8.
The valuation of Futures on other
commodities
................ 343
7.2.3.
Arbitrage and information costs in the lattice
approach
....................... 343
7.2.4.
The binomial model for options in the presence of a
continuous dividend stream and information costs
346
7.2.5.
The binomial model for options in the presence of a
known dividend yield and information costs
.... 347
7.2.6.
The binomial model for options in the presence of a
discrete dividend stream and information costs
. . 347
7.2.7.
The binomial model for futures options in the
presence of information costs
............ 347
7.2.8.
The lattice approach for American options with
information costs and several cash distributions
. . 348
7.2.8.1.
The model
................. 348
7.3.
The Binomial Model and the Risk Neutrality: Some
Important Details
........................ 349
7.3.1.
The binomial parameters and risk neutrality
. . . 349
7.3.2.
The convergence argument
............. 352
xxviii Derivatives,
Risk
Management
and Value
7.4.
The Hull and White Trinomial Model for Interest Rate
Options
............................. 353
7.5.
Pricing Path-Dependent Interest Rate Contingent Claims
Using a Lattice
......................... 355
7.5.1.
The framework
.................... 355
7.5.2.
Valuation of the path-dependent security
..... 358
7.5.2.1.
Fixed-coupon rate security
........ 358
7.5.2.2.
Floating-coupon security
......... 359
7.5.3.
Options on path-dependent securities
....... 359
7.5.3.1.
Short-dated options
............ 359
7.5.3.2.
Long-dated options
............ 359
Summary
................................ 360
Questions
................................ 362
References
................................ 362
PART III. OPTION PRICING IN A
CONTINUOUS-TIME SETTING: BASIC
MODELS, EXTENSIONS AND APPLICATIONS
365
CHAPTER
8.
EUROPEAN OPTION PRICING
MODELS: THE PRECURSORS OF THE BLACK-
SCHOLES-MERTON THEORY AND HOLES
DURING MARKET TURBULENCE
367
Chapter Outline
............................ 367
Introduction
.............................. 368
8.1.
Precursors to the Black-Scholes Model
............ 369
8.1.1.
Bachelier
formula
................... 369
8.1.2. Sprenkle
formula
................... 370
8.1.3.
Boness formula
.................... 371
8.1.4.
Samuelson
formula
.................. 371
8.2.
How the Black-Scholes Option Formula is Obtained
.... 372
8.2.1.
The short story
.................... 372
8.2.2.
The differential equation
............... 373
8.2.3.
The derivation of the formula
............ 373
8.2.4.
Publication of the formula
.............. 374
8.2.5.
Testing the formula
................. 374
8.3.
Financial Theory and the Black-Scholes-Merton Theory
. . 375
8.3.1.
The Black-Scholes-Merton theory
......... 375
8.3.2.
Analytical formulas
................. 376
Contents xxix
8.4. The Black-Scholes Model................... 377
8.4.1. The Black-Scholes
model and CAPM
....... 377
8.4.2. An alternative
derivation of the
Black-Scholes
model
......................... 380
8.4.3.
The put-call parity relationship
........... 382
8.4.4.
Examples
....................... 383
8.5.
The Black Model for Commodity Contracts
......... 386
8.5.1.
The model for forward, futures, and option contracts
386
8.5.2.
The put-call relationship
............... 388
8.6.
Application of the CAPM Model to Forward and Futures
Contracts
............................ 389
8.6.1.
An application of the model to forward and futures
contracts
....................... 389
8.6.2.
An application to the derivation of the commodity
option valuation
................... 390
8.6.3.
An application to commodity options and
commodity futures options
............. 393
8.7.
The Holes in the Black Scholes-Merton Theory and the
Financial Crisis
......................... 394
8.7.1.
Volatility changes
................... 394
8.7.2.
Interest rate changes
................. 395
8.7.3.
Borrowing penalties
................. 396
8.7.4.
Short-selling penalties
................ 396
8.7.5.
Transaction costs
................... 396
8.7.6.
Taxes
......................... 396
8.7.7.
Dividends
....................... 396
8.7.8.
Takeovers
....................... 397
Summary
................................ 397
Questions
................................ 398
Appendix A. The Cumulative Normal Distribution Function
. . . 399
Appendix B. The
Divariate
Normai
Density Function
....... 400
References
................................ 401
CHAPTER
9.
SIMPLE EXTENSIONS AND
APPLICATIONS OF THE BLACK-SCHOLES TYPE
MODELS IN VALUATION AND RISK MANAGEMENT
403
Chapter Outline
............................ 403
Introduction
.............................. 403
xxx Derivatives.
Risk
Management
and Value
9.1.
Applications of the Black-Scholes Model
........... 404
9.1.1.
Valuation and the role of equity options
...... 404
9.1.2.
Valuation and the role of index options
...... 405
9.1.2.1.
Analysis and valuation
.......... 405
9.1.2.2.
Arbitrage between index options and
futures
................... 406
9.1.3.
Valuation of options on zero-coupon bonds
.... 407
9.1.4.
Valuation and the role of short-term options on
long-term bonds
................... 408
9.1.5.
Valuation of interest rate options
.......... 409
9.1.6.
Valuation and the role of bond options: the case of
coupon-paying bonds
................. 410
9.1.7.
The valuation of a swaption
............. 411
9.2.
Applications of the Black s Model
............... 413
9.2.1.
Options on equity index futures
.......... 413
9.2.2.
Options on currency forwards and options
on currency futures
.................. 414
9.2.2.1.
Options on currency forwards
...... 414
9.2.2.2.
Options on currency futures
....... 414
9.2.3.
The Black s model and valuation of interest
rate caps
....................... 415
9.3.
The Extension to Foreign Currencies: The Garman and
Kohlhagen Model and its Applications
............ 416
9.3.1.
The currency call formula
.............. 416
9.3.2.
The currency put formula
.............. 416
9.3.3.
The interest-rate theorem and the pricing of
forward currency options
.............. 417
9.4.
The Extension to Other Commodities: The Merton,
Barone-
Adesi and Whaley Model, and Its Applications
. . . 420
9.4.1.
The model
...................... 420
9.4.2.
An application to portfolio insurance
........ 421
9.5.
The Real World and the Black-Scholes Type Models
.... 422
9.5.1.
Volatility
....................... 422
9.5.2.
The hedging strategy
................. 422
9.5.3.
The log-normal assumption
............. 422
9.5.4.
A world of finite trading
.............. 423
9.5.5.
Total variance
.................... 423
9.5.6.
Black-Scholes as the limiting case
......... 423
9.5.7.
Using the model to optimize hedging
........ 424
Contents xxxi
Summary
................................ 424
Questions
................................ 426
Appendix
................................ 427
References
................................ 437
CHAPTER
10.
APPLICATIONS OF OPTION PRICING
MODELS TO THE MONITORING AND THE
MANAGEMENT OF PORTFOLIOS OF DERIVATIVES
IN THE REAL WORLD
439
Chapter Outline
............................ 439
Introduction
.............................. 440
10.1.
Option-Price Sensitivities: Some Specific Examples
..... 441
10.1.1.
Delta
......................... 441
10.1.2.
Gamma
........................ 442
10.1.3.
Theta
......................... 443
10.1.4. Vega.......................... 444
10.1.5.
Rho
.......................... 444
10.1.6.
Elasticity
....................... 445
10.2.
Monitoring and Managing an Option Position in Real Time
445
10.2.1.
Simulations and analysis of option price sensitivities
using
Barone-
Adesi and Whaley model
....... 446
10.2.2.
Monitoring and adjusting the option position
in real time
...................... 451
10.2.2.1.
Monitoring and managing the delta
. . . 451
10.2.2.2.
Monitoring and managing the gamma
. 454
10.2.2.3.
Monitoring and managing the theta
. . . 457
10.2.2.4.
Monitoring and managing the
vega . . . 458
10.3.
The Characteristics of Volatility Spreads
........... 459
Summary
................................ 460
Appendix A: Greek-Letter Risk Measures in Analytical Models
. . 461
A.I. B-S model
...................... 461
A.2. Black s Model
..................... 462
A.3. Garman and Kohlhagen s model
.......... 463
A.4. Merton s and Barone-Adesi and Whaley s model
. 463
Appendix B: The Relationship Between Hedging Parameters
. . . 464
Appendix C: The Generalized Relationship Between the Hedging
Parameters
........................... 465
Appendix D: A Detailed Derivation of the Greek Letters
...... 479
Questions
................................ 478
References
................................ 489
xxxii
Derivatives, Risk Management and Value
PART IV. MATHEMATICAL FOUNDATIONS
OF OPTION PRICING MODELS IN A
CONTINUOUS-TIME SETTING: BASIC
CONCEPTS AND EXTENSIONS
491
CHAPTER
11.
THE DYNAMICS OF ASSET PRICES
AND THE ROLE OF INFORMATION: ANALYSIS AND
APPLICATIONS IN ASSET AND RISK MANAGEMENT
493
Chapter Outline
............................ 493
Introduction
.............................. 494
11.1.
Continuous Time Processes for Asset Price Dynamics
. . . 495
11.1.1.
Asset price dynamics and Wiener process
..... 495
11.1.2.
Asset price dynamics and the generalized Wiener
process
........................ 497
11.1.3.
Asset price dynamics and the
Ito
process
..... 497
11.1.4.
The log-normal property
............... 499
11.1.5.
Distribution of the rate of return
.......... 500
11.2.
Ito s Lemma and Its Applications
............... 501
11.2.1.
Intuitive form
..................... 501
11.2.2.
Applications to stock prices
............. 505
11.2.3.
Mathematical form
.................. 505
11.2.4.
The generalized Ito s formula
............ 508
11.2.5.
Other applications of Ito s formula
......... 510
11.3.
Taylor Series, Ito s Theorem and the Replication Argument
513
11.3.1.
The relationship between Taylor series and Ito s
differential
...................... 513
11.3.2.
Ito s differential and the replication portfolio
. . . 514
11.3.3.
Ito s differential and the arbitrage portfolio
.... 515
11.3.4.
Why are error terms neglected?
........... 517
11.4.
Forward and Backward Equations
.............. 518
11.5.
The Main Concepts in Bond Markets and the General
Arbitrage Principle
....................... 519
11.5.1.
The main concepts in bond pricing
......... 519
11.5.2.
Time-dependent interest rates and information
uncertainty
...................... 521
11.5.3.
The general arbitrage principle
........... 522
11.6.
Discrete Hedging and Option Pricing
............. 523
11.6.1.
Discrete hedging
................... 523
Contents xxxiii
11.6.2.
Pricing the option
.................. 525
11.6.3.
The real distribution of returns and the
hedging error
..................... 526
Summary
................................ 526
Questions
................................ 527
Appendix A: Introduction to Diffusion Processes
.......... 528
Appendix B: The Conditional Expectation
............. 529
Appendix C: Taylor Series
....................... 529
Exercises
................................ 530
References
................................ 532
CHAPTER
12.
RISK MANAGEMENT: APPLICATIONS
TO THE PRICING OF ASSETS AND DERIVATIVES IN
COMPLETE MARKETS
535
Chapter Outline
............................ 535
Introduction
.............................. 536
12.1.
Characterization of Complete Markets
............ 536
12.2.
Pricing Derivative Assets: The Case of Stock Options
. . . . 538
12.2.1.
The problem
..................... 538
12.2.2.
The PDE method
.................. 539
12.2.3.
The martingale method
............... 541
12.3.
Pricing Derivative Assets: The Case of Bond Options and
Interest Rate Options
..................... 546
12.3.1.
Arbitrage-free family of bond prices
........ 546
12.3.2.
Time-homogeneous models
............. 547
12.3.3.
Time-inhomogeneous models
............ 550
12.4.
Asset Pricing in Complete Markets: Changing Numeraire
and Time
............................ 551
12.4.1.
Assumptions and the valuation context
...... 551
12.4.2.
Valuation of derivatives in a standard
Black-Scholes-Merton economy
........... 552
12.4.3.
Changing numeraire and time: The martingale
approach and the PDE approach
.......... 554
12.5.
Valuation in an Extended Black and Scholes Economy
in the Presence of Information Costs
............. 560
Summary
................................ 563
Questions
................................ 564
Appendix A: The Change in Probability and the Girsanov Theorem
564
xxxiv Derivatives,
Risk
Management
and Value
Appendix
В:
Resolution of the Partial Differential Equation for
a European Call Option on a Non-Dividend Paying Stock
in the Standard Context
.................... 565
Appendix C: Approximation of the Cumulative Normal Distribution
571
Appendix D: Leibniz s Rule for Integral Differentiation
....... 572
Appendix E: Pricing Bonds: Mathematical Foundations
...... 573
Exercises
................................ 575
References
................................ 580
CHAPTER
13.
SIMPLE EXTENSIONS AND
GENERALIZATIONS OF THE BLACK-SCHOLES TYPE
MODELS IN THE PRESENCE OF INFORMATION COSTS
583
Chapter Outline
............................ 583
Introduction
.............................. 583
13.1.
Differential Equation for a Derivative Security on a Spot
Asset in the Presence of a Continuous Dividend Yield and
Information Costs
....................... 584
13.2.
The Valuation of Securities Dependent on Several Variables
in the Presence
of Incomplete Information: A General Method
........ 585
13.3.
The General Differential Equation for the Pricing of
Derivatives
........................... 588
13.4.
Extension of the Risk-Neutral Argument in the Presence of
Information Costs
....................... 589
13.5.
Extension to Commodity Futures Prices within Incomplete
Information
........................... 590
13.5.1.
Differential equation for a derivative security
dependent on a futures price in the presence
of information costs
................. 590
13.5.2.
Commodity futures prices
.............. 592
13.5.3.
Convenience yields
................. 592
Summary
................................ 593
Questions
................................ 593
Appendix A: A General Equation for Derivative Securities
..... 594
Appendix B: Extension to the Risk-Neutral Valuation Argument
. 596
Exercises
................................ 596
References
................................ 612
Contents xxxv
PART V. EXTENSIONS OF OPTION PRICING
THEORY TO AMERICAN OPTIONS AND
INTEREST RATE INSTRUMENTS IN A
CONTINUOUS-TIME SETTING: DIVIDENDS,
COUPONS AND STOCHASTIC INTEREST RATES
613
CHAPTER
14.
EXTENSION OF ASSET AND RISK
MANAGEMENT IN THE PRESENCE OF
AMERICAN OPTIONS: DIVIDENDS, EARLY EXERCISE,
AND INFORMATION UNCERTAINTY
615
Chapter Outline
............................ 615
Introduction
.............................. 616
14.1.
The Valuation of American Options: The General Problem
618
14.1.1.
Early exercise of American calls
........... 618
14.1.2.
Early exercise of American puts
........... 620
14.1.3.
The American put option and its critical stock price
623
14.2.
Valuation of American Commodity Options and Futures
Options with Continuous Distributions
............ 627
14.2.1.
Valuation of American commodity options
..... 627
14.2.2.
Examples and applications
............. 630
14.2.3.
Valuation of American futures options
....... 632
14.2.4.
Examples and applications
............. 634
14.3.
Valuation of American Commodity and Futures Options with
Continuous Distributions within Information Uncertainty
. 634
14.3.1.
Commodity option valuation with information costs
634
14.3.2.
Simulation results
.................. 638
14.4.
Valuation of American Options with Discrete
Cash-Distributions
....................... 640
14.4.1.
Early exercise of American options
........ 641
14.4.2.
Valuation of American options with dividends
. . . 642
14.5.
Valuation of American Options with Discrete Cash
Distributions within Information Uncertainty
........ 645
14.5.1.
The model
...................... 645
14.5.2.
Simulation results
.................. 647
14.6.
The Valuation Equations for Standard and Compound
Options with Information Costs
................ 648
14.6.1.
The pricing of assets under incomplete information
650
14.6.2.
The valuation of equity as a compound option
. . 650
xxxvi
Derivatives, Risk Management and Value
Summary
................................ 654
Questions
................................ 656
Appendix A: An Alternative Derivation of the Compound Option s
Formula Using the Martingale Approach
........... 656
Exercises
................................ 657
References
................................ 664
CHAPTER
15.
RISK MANAGEMENT OF BONDS AND
INTEREST RATE SENSITIVE INSTRUMENTS IN THE
PRESENCE OF STOCHASTIC INTEREST RATES AND
INFORMATION UNCERTAINTY: THEORY AND TESTS
667
Chapter Outline
............................ 667
Introduction
.............................. 668
15.1.
The Valuation of Bond Options and Interest Rate Options
. 669
15.1.1.
The problems in using the B-S model for
interest-rate options
................. 669
15.1.2.
Sensitivity of the theoretical option prices to
changes in factors
.................. 670
15.2.
A Simple Non-Parametric Approach to Bond Futures
Option Pricing
......................... 670
15.2.1.
Canonical modeling and option pricing theory
. . . 671
15.2.2.
Assessing the distribution of the underlying futures
price
.......................... 672
15.2.3.
Transforming actual probabilities into risk-neutral
probabilities
...................... 672
15.2.4.
Qualitative comparison of Black and canonical
model values
..................... 673
15.3.
One-Factor Interest Rate Modeling and the Pricing of Bonds:
The General Case
........................ 673
15.3.1.
Bond pricing in the general case: The arbitrage
argument and information costs
........... 673
15.3.2.
Pricing callable bonds within information
uncertainty
...................... 676
15.4.
Fixed Income Instruments as a Weighted Portfolio of
Power Options
......................... 676
15.5.
Merton s Model for Equity Options in the Presence
of Stochastic Interest Rates: Two-Factor Models
...... 678
Contents xxxvii
15.5.1.
The model in the presence of stochastic interest
rates
.......................... 679
15.5.2.
Applications of Merton s model
........... 680
15.6.
Some Models for the Pricing of Bond Options
........ 681
15.6.1.
An extension of the
Но
-Lee
model for bond options
681
15.6.2.
The Schaefer and Schwartz model
......... 683
15.6.3.
The Vasicek
(1977)
model
.............. 683
15.6.4.
The Ho and Lee model
................ 684
15.6.5.
The Hull and White model
............. 685
Summary
................................ 686
Questions
................................ 687
Appendix A: Government Bond Futures and Implicit Embedded
Options
............................. 687
A.I. Criteria for the CTD
.................
A.2. Yield changes
.....................
A.3. The value for a futures position
........... 690
A.4. Parallel yield shift
.................. 691
A.5. Relative yield shift
.................. 692
Appendix B: One-Factor Fallacies for Interest Rate Models
.... 692
B.I. The models in practice
................ 693
B.2. Spreads between rates
................ 693
Appendix C: Merton s Model in the Presence of Stochastic
Interest Rates
.......................... 694
References
................................ 701
CHAPTER
16.
MODELS OF INTEREST RATES,
INTEREST-RATE SENSITIVE INSTRUMENTS, AND
THE PRICING OF BONDS: THEORY AND TESTS
703
Chapter Outline
............................ 703
Introduction
.............................. 704
16.1.
Interest Rates and Interest-Rate Sensitive Instruments
. . . 705
16.1.1.
Zero-coupon bonds
.................. 705
16.1.2.
Term structure of interest rates
........... 705
16.1.3.
Forward interest rates
................ 706
16.1.4.
Short-term interest rate
............... 707
16.1.5.
Coupon-bearing bonds
................ 707
16.1.6.
Yield-to-Maturity (YTM)
.............. 708
16.1.7.
Market conventions
.................. 709
xxxviii
Derivatives, Risk Management and Value
16.2.
Interest Rates and the Pricing of Bonds
........... 710
16.2.1.
The instantaneous interest rates under certainty
. 710
16.2.2.
The instantaneous interest rate under uncertainty
711
16.3.
Interest Rate Processes and the Pricing of Bonds and Options
712
16.3.1.
The Vasicek model
.................. 713
16.3.2.
The Brennan and Schwartz model
......... 713
16.3.3.
The
CIR
model
.................... 713
16.3.4.
The Ho and Lee model
................ 714
16.3.5.
The HJM model
................... 714
16.3.6.
The BDT model
................... 716
16.3.7.
The Hull and White model
............. 717
16.3.8.
Fong and Vasicek model
............... 718
16.3.9.
Longstaff and Schwartz model
............ 718
16.4.
The Relative Merits of the Competing Models
........ 718
16.5.
A Comparative Analysis of Term Structure Estimation
Models
.............................. 721
16.5.1.
The construction of the term structure and coupon
bonds
......................... 721
16.5.2.
Fitting functions and estimation procedure
.... 722
16.6.
Term Premium Estimates From Zero-Coupon Bonds: New
Evidence on the Expectations Hypothesis
.......... 724
16.7.
Distributional Properties of Spot and Forward Interest Rates:
USD, DEM, GBP, and
JPY
.................. 726
16.7.1.
Interest rate levels
.................. 728
16.7.2.
Interest rate differences and log differences
.... 728
Summary
................................ 731
Appendix A: An Application of Interest Rate Models to Account for
Information Costs: An Exercise
................ 732
A.I. An application of the HJM model in the presence of
information costs
................... 732
A.I.I. The forward rate equation
........ 732
A.1.2. The spot rate process
........... 733
A.
1.3.
The market price of risk
......... 734
A.
1.4.
Relationship between risk-neutral forward
rate drift and volatility
.......... 735
A.
1.5.
Pricing derivatives
............ 735
A.2. An application of the Ho and Lee model in the
presence of information cost
............. 736
Contents xxxix
Appendix
В:
Implementation
of the BDT
Model
with Different
Volatility Estimators
...................... 737
B.I. The BDT model
................... 737
B.2. Estimation results
.................. 738
Questions
................................ 739
References
................................ 740
PART VI. GENERALIZATION OF OPTION
PRICING MODELS AND STOCHASTIC VOLATILITY
743
CHAPTER
17.
EXTREME MARKET MOVEMENTS,
RISK AND ASSET MANAGEMENT: GENERALIZATION
TO JUMP PROCESSES, STOCHASTIC VOLATILITIES,
AND INFORMATION COSTS
745
Chapter Outline
............................ 745
Introduction
.............................. 745
17.1.
The Jump-Diffusion and the Constant Elasticity of Variance
Models
.............................. 747
17.1.1.
The jump-diffusion model
.............. 747
17.1.2.
The constant elasticity of variance diffusion (CEV)
process
........................ 748
17.2.
On Jumps, Hedging and Information Costs
......... 749
17.2.1.
Hedging in the presence of jumps
.......... 750
17.2.2.
Hedging the jumps
.................. 752
17.2.3.
Jump volatility
.................... 753
17.3.
On the Smile Effect and Market Imperfections in the
Presence of Jumps and Incomplete Information
....... 754
17.3.1.
On smiles and jumps
................. 754
17.3.2.
On smiles, jumps, and incomplete information
. . 759
17.3.3.
Empirical results in the presence of jumps and
incomplete information
............... 760
17.4.
Implied Volatility and Option Pricing Models: The Model
and Simulation Results
..................... 763
ПАЛ.
The valuation model
................. 763
17.4.2.
Simulation results
.................. 765
17.4.3.
Model calibration and the smile effect
....... 766
Summary
................................ 767
Questions
................................ 768
References
................................ 768
xl
Derivatives, Risk Management and Value
CHAPTER
18.
RISK MANAGEMENT DURING
ABNORMAL MARKET CONDITIONS: FURTHER
GENERALIZATION TO JUMP PROCESSES,
STOCHASTIC VOLATILITIES, AND INFORMATION COSTS
771
Chapter Outline
............................ 771
Introduction
.............................. 772
18.1.
Option Pricing in the Presence of a Stochastic Volatility
. . 774
18.1.1.
The Hull and White model
............. 774
18.1.2.
Stein and Stein model
................ 775
18.1.3.
The Heston model
.................. 777
18.1.4.
The Hoffman, Platen, and
Schweizer
model
.... 778
18.1.5.
Market price of volatility risk
............ 781
18.1.6.
The market price of risk for traded assets
..... 782
18.2.
Generalization of Some Models with Stochastic Volatility
and Information Costs
..................... 782
18.2.1.
Generalization of the Hull and White
(1987)
model
782
18.2.2.
Generalization of Wiggins s model
......... 784
18.2.3.
Generalization of Stein and Stein s model
..... 785
18.2.4.
Generalization of Heston s model
.......... 786
18.2.5.
Generalization of Johnson and Shanno s model
. . 788
18.3.
The Volatility Smiles: Some Standard Results
........ 788
18.3.1.
The smile effect in stock options and index options
788
18.3.2.
The smile effect for bond and currency options
. . 789
18.3.3.
Volatility smiles: Empirical evidence
........ 790
18.4.
Empirical Results Regarding Information Costs and Option
Pricing
.............................. 791
18.4.1.
Information costs and option pricing:
The estimation method
............... 791
18.4.2.
The asymmetric distortion of the smile
....... 792
18.4.3.
Asymmetric Smiles and information costs in
a stochastic volatility model
............. 793
Summary
................................ 795
Questions
................................ 796
References
................................ 796
Contents xli
PART
VII.
OPTION
PRICING
MODELS AND
NUMERICAL ANALYSIS
799
CHAPTER
19.
RISK MANAGEMENT, NUMERICAL
METHODS AND OPTION PRICING
801
Chapter Outline
............................ 801
Introduction
.............................. 801
19.1.
Numerical Analysis and Simulation Techniques: An
Introduction to Finite Difference Methods
.......... 803
19.1.1.
The implicit difference scheme
........... 804
19.1.2.
Explicit difference scheme
.............. 806
19.1.3.
An extension to account for information costs
. . . 807
19.2.
Application to European Options on Non-Dividend Paying
Stocks
.............................. 807
19.2.1.
The analytic solution
................. 808
19.2.2.
The numerical solution
................ 808
19.2.3.
An application to European calls on non-dividend
paying stocks in the presence of information costs
810
19.3.
Valuation of American Options with a Composite Volatility
811
19.3.1.
The effect of interest rate volatility on the index
volatility
....................... 811
19.3.2.
Valuation of index options with a composite
volatility
....................... 812
19.3.3.
Numerical solutions and simulations
........ 813
19.4.
Simulation Methods: Monte-Carlo Method
......... 817
19.4.1.
Simulation of Gaussian variables
.......... 818
19.4.2.
Relationship between option values and simulation
methods
....................... 818
Summary
................................ 819
Questions
................................ 820
Appendix A: Simple Concepts in Numerical Analysis
........ 820
Appendix B: An Algorithm for a European Call
.......... 822
Appendix C: The Algorithm for the Valuation of American
Long-term Index Options with a Composite Volatility
. . . 823
xlii Derivatives,
Risk
Management
and Value
Exercises
................................ 826
Appendix
D:
The Monte-Carlo Method and the Dynamics of
Asset Prices
........................... 829
References
................................ 830
CHAPTER
20.
NUMERICAL METHODS AND PARTIAL
DIFFERENTIAL EQUATIONS FOR EUROPEAN AND
AMERICAN DERIVATIVES WITH COMPLETE AND
INCOMPLETE INFORMATION
833
Chapter Outline
............................ 833
Introduction
.............................. 834
20.1.
Valuation of American Calls on Dividend-Paying Stocks
. . 835
20.1.1.
The Schwartz model
................. 835
20.1.2.
The numerical solution
................ 836
20.2.
American Puts on Dividend-Paying Stocks
.......... 837
20.2.1.
The Brennan and Schwartz model
......... 837
20.2.2.
The numerical solution
................ 838
20.3.
Numerical Procedures in the Presence of Information Costs:
Applications
........................... 839
20.3.1.
Finite difference methods in the presence of
information costs
................... 839
20.3.2.
An application to the American put using explicit
or implicit finite difference methods
........ 841
20.4.
Convertible Bonds
....................... 842
20.4.1.
Specific features of CB
................ 842
20.4.2.
The valuation equations
............... 843
20.4.3.
The numerical solution
................ 845
20.4.4.
Simulations
...................... 847
20.5.
Two-Factor Interest Rate Models and Bond Pricing within
Information Uncertainty
.................... 847
20.6.
CBs Pricing within Information Uncertainty
......... 850
20.6.1.
The pricing of CBs
.................. 850
20.6.2.
Specific call and put features
............ 851
20.6.3.
The pricing of CBs in two-factor models within
information uncertainty
............... 851
Summary
................................ 852
Appendix A: A Discretizing Strategy for Mean-Reverting Models
. 853
Appendix B: An Algorithm for the American Call with Dividends
861
Contents xliii
Appendix C: The Algorithm for the American Put with Dividends
862
Appendix D: The Algorithm for CBs with Call and Put Prices
. . 864
Questions
................................ 867
Exercises
................................ 867
References
................................ 872
PART
VIII.
EXOTIC DERIVATIVES
875
CHAPTER
21.
RISK MANAGEMENT: EXOTICS AND
SECOND-GENERATION OPTIONS
877
Chapter Outline
............................ 877
Introduction
.............................. 877
21.1.
Exchange Options
....................... 879
21.2.
Forward-Start Options
...................... 880
21.3.
Pay-Later Options
....................... 882
21.4.
Simple Chooser Options
.................... 884
21.5.
Complex Choosers
....................... 885
21.6.
Compound Options
....................... 886
21.6.1.
The call on a call in the presence of a cost of carry
887
21.6.2.
The put on a call in the presence of a cost of carry
21.6.3.
The formula for a call on a put in the presence of a
cost of carry
.....................
21.6.4.
The put on a put in the presence of a cost of carry
889
21.7.
Options on the Maximum (Minimum)
............ 889
21.7.1.
The call on the minimum of two assets
....... 891
21.7.2.
The call on the maximum of two assets
...... 892
21.7.3.
The put on the minimum (maximum) of two assets
892
21.8.
Extendible Options
....................... 893
21.8.1.
The valuation context
................ 893
21.8.2.
Extendible calls
.................... 894
21.9.
Equity-Linked Foreign Exchange Options and
Quantos
. . . 896
21.9.1.
The foreign equity call struck in foreign currency
. 898
21.9.2.
The foreign equity call struck in domestic currency
898
21.9.3.
Fixed exchange rate foreign equity call
....... 899
21.9.4.
An equity-linked foreign exchange call
....... 900
21.10.
Binary Barrier Options
..................... 901
21.10.1.
Path-independent binary options
.......... 902
xliv Derivatives,
Risk
Management
and Value
21.10.1.1.
Standard cash-or-nothing options
.... 902
21.10.1.2.
Cash-or-nothing options with shadow
costs
.................... 903
21.10.1.3.
Standard asset-or-nothing options
.... 904
21.10.1.4.
Asset-or-nothing options with shadow
costs
.................... 905
21.10.1.5.
Standard gap options
........... 906
21.10.1.6.
Gap options with shadow costs
..... 908
21.10.1.7.
Supershares
................ 908
21.11.
Lookback
Options
....................... 908
21.11.1.
Standard
lookback
options
............. 909
21.11.2.
Options on
extrema
................. 909
21.11.2.1.
On the maximum
............. 909
21.11.2.2.
On the minimum
............. 910
21.11.3.
Limited risk options
................. 910
21.11.4.
Partial
lookback
options
............... 911
Summary
................................ 913
Questions
................................ 914
References
................................ 914
CHAPTER
22.
VALUE AT RISK, CREDIT RISK,
AND CREDIT DERIVATIVES
917
Chapter Outline
............................ 917
Introduction
.............................. 917
22.1.
VaR and Riskmetrics: Definitions and Basic Concepts
. . . 919
22.1.1.
The definition of risk
................. 920
22.1.2.
VaR: Definition
.................... 920
22.2.
Statistical and Probability Foundation of VaR
........ 921
22.2.1.
Using percentiles or quantiles to measure market
risk
.......................... 922
22.2.2.
The choice of the horizon
.............. 922
22.3.
A More Advanced Approach to VaR
............. 923
22.4.
Credit Valuation and the Creditmetrics Approach
...... 927
22.4.1.
The portfolio context of credit
........... 927
22.4.2.
Different credit risk measures
............ 927
22.4.3.
Stand alone or single exposure risk calculation
. . 928
22.4.4.
Differing exposure type
............... 928
Contents xlv
22.5.
Default and Credit-Quality Migration in the Creditmetrics
Approach
............................ 929
22.5.1.
Default
........................ 929
22.5.2.
Credit-quality migration
............... 929
22.5.3.
Historical tabulation and recovery rates
...... 930
22.6.
Credit-Quality Correlations
.................. 930
22.7.
Portfolio Management of Default Risk in the Kealhofer,
McQuown and Vasicek (KMV) Approach
.......... 932
22.7.1.
The model of default risk
.............. 932
22.7.2.
Asset market value and volatility
.......... 933
22.8.
Credit Derivatives: Definitions and Main Concepts
..... 933
22.8.1.
Forward contracts
.................. 933
22.8.2.
The structure of credit-default instruments
.... 934
22.8.2.1.
Total return swaps
............ 934
22.8.2.2.
Credit-default swaps
........... 934
22.8.2.3.
Basket default swaps
........... 935
22.8.2.4.
Credit-defaxilt exchange swap
...... 935
22.8.2.5.
Credit-linked notes (CLNs)
....... 936
22.9.
The Rating Agencies Models and the Proprietary Models
. 936
22.9.1.
The rating agencies models
............. 936
22.9.2.
The proprietary models
............... 938
Summary
................................ 940
References
................................ 941
Index
.................................. 943
|
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| id | DE-604.BV035797522 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:48Z |
| institution | BVB |
| isbn | 9789812838629 9812838627 |
| language | English |
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| spelling | Bellalah, Mondher Verfasser aut Derivates, risk management & value Mondher Bellalah Singapore [u.a.] World Scientific 2010 XLV, 949 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Angekündigt u.d.T.: Bellalah, Mondher: Options Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Risikomanagement (DE-588)4121590-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018656718&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bellalah, Mondher Derivates, risk management & value Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd Risikomanagement (DE-588)4121590-4 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4121590-4 |
| title | Derivates, risk management & value |
| title_auth | Derivates, risk management & value |
| title_exact_search | Derivates, risk management & value |
| title_full | Derivates, risk management & value Mondher Bellalah |
| title_fullStr | Derivates, risk management & value Mondher Bellalah |
| title_full_unstemmed | Derivates, risk management & value Mondher Bellalah |
| title_short | Derivates, risk management & value |
| title_sort | derivates risk management value |
| topic | Derivative securities Risk management Derivat Wertpapier (DE-588)4381572-8 gnd Risikomanagement (DE-588)4121590-4 gnd |
| topic_facet | Derivative securities Risk management Derivat Wertpapier Risikomanagement |
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