Dynamic term structure modeling: the fixed income valuation course
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ [u.a.]
Wiley
2007
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| Schriftenreihe: | Wiley finance series
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| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Contributor biographical information Inhaltsverzeichnis |
| Beschreibung: | XXXVI, 683 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 9780471737148 0471737143 |
Internformat
MARC
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| 100 | 1 | |a Nawalkha, Sanjay K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamic term structure modeling |b the fixed income valuation course |c Sanjay K. Nawalkha ; Natalia A. Beliaeva ; Gloria M. Soto |
| 264 | 1 | |a Hoboken, NJ [u.a.] |b Wiley |c 2007 | |
| 300 | |a XXXVI, 683 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley finance series | |
| 650 | 4 | |a Finances | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Finance | |
| 650 | 4 | |a Stochastic processes | |
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| 700 | 1 | |a Beliaeva, Natalia A. |e Verfasser |4 aut | |
| 700 | 1 | |a Soto, Gloria M. |e Verfasser |4 aut | |
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0740/2006037555-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0740/2006037555-b.html |3 Contributor biographical information | |
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Datensatz im Suchindex
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| adam_text | Contents
Ust of figures xxxi
list of Tables xxxv
CHAPTBU
ASbnpletatrodiM^toCoiiUn^ 1
Continuous Time Diffusion Processes 3
Wiener Process 3
Ito Process 5
Ito s Lemma 7
Simple Rules of Stochastic Differentiation
and Integration 9
Obtaining Unconditional Mean and Variance of
Stochastic Integrals under Gaussian Processes 9
Examples of Gaussian Stochastic Integrals 11
Mixed Jump Diffusion Processes 14
The Jump Diffusion Process 14
Ito s Lemma for the Jump Diffusion Process 15
CHAPTB12
Artttrage Free Valuation 17
Arbitrage Free Valuation: Some Basic Results 18
A Simple Relationship between Zero Coupon Bond
Prices and Arrow Debreu Prices 20
The Bayes Rule for Conditional Probabilities of Events 20
The Relationship between Current and Future
AD Prices 21
The Relationship between Cross Sectional AD Prices
and Intertemporal Term Structure Dynamics 22
Existence of the Risk Neutral Probability Measure 23
Stochastic Discount Factor 28
Radon Nikodym Derivative 30
Arbitrage Free Valuation in Continuous Time 31
Change of Probability Measure under a Continuous
Probability Density 32
The Girsanov Theorem and the Radon Nikodym
Derivative 34
Equivalent Martingale Measures 35
Stochastic Discount Factor and Risk Premiums 43
The Feynman Kac Theorem 45
CHAPTH(3
Valuing Interest Rate and Credit Derivatives:
Basic Pricing Frameworks 49
Eurodollar and Other Time Deposit Futures 54
Valuing Futures on a Time Deposit 58
Convexity Bias 60
Treasury Bill Futures 61
Valuing T Bill Futures 62
Convexity Bias 3
Treasury Bond Futures 64
Conversion Factor 65
Cheapest to Deliver Bond 67
Options Embedded in T Bond Futures 68
Valuing T Bond Futures 68
Treasury Note Futures ^
Forward Rate Agreements ^3
Interest Rate Swaps ^4
Day Count Conventions °
The Financial Intermediary 77
Motivations for Interest Rate Swaps °
Pricing Interest Rate Swaps 82
Interest Rate Swaptions 8.5
Caps and Floors °°
Caplet 90
Floorlet 91
Collarlet 92
Caps, Floors, and Collars 92
Black Implied Volatilities for Caps and Swaptions 93
Black Implied Volatilities: Swaptions
Black Implied Volatilities: Caplet 96
Black Implied Volatilities: Caps 9/
Black Implied Volatilities: Difference Caps 98
Pricing Credit Derivatives Using the
Reduced Form Approach 9»
Default Intensity and Survival Probability 10^
Recovery Assumptions 101
Risk Neutral Valuation under the
RMV Assumption 102
Risk Neutral Valuation under the RFV Assumption 103
Valuing Credit Default Swaps Using the
RFV Assumption 104
A New Taxonomy of Term Structure Models 106
CHAPTBM
Fundamental and Preference free Single Factor
Gaussian Models 113
The Arbitrage Free Pricing Framework of Vasicek 115
The Term Structure Equation 116
Risk Neutral Valuation 118
The Fundamental Vasicek Model 120
Bond Price Solution 124
Preference Free Vasicek+, Vasicek++, and
Vasicek+++ Models 128
The Vasicek+ Model 128
The Vasicek++, or the Extended Vasicek Model 136
The Vasicek+++, or the Fully Extended
Vasicek Model 140
Valuing Futures 144
Valuing Futures under the Vasicek, Vasicek+, and
Vasicek++ Models 145
Valuing Futures under the Vasicek+ f+ Model 150
Valuing Options 153
Options on Zero Coupon Bonds 153
Options on Coupon Bonds 157
Valuing Interest Rate Contingent Claims Using Trees 161
Binomial Trees 163
Trinomial Trees 165
Trinomial Tree under the Vasicek+4 Model:
An Example 171
Trinomial Tree under the Vasicek+++ Model:
An Example 178
Appendix 4.1. Bond Price Solution Using the Risk Neutral
Valuation Approach under the Fundamental Vasicek
Model and the Preference Free Vasicek f Model 181
Appendix 4.2. Hull s Approximation to Convexity Bias
under the Ho and Lee Model 184
CHAPTQ15
Fundamental and Ppelerence Free Jump Extended Gaussian Models 187
Fundamental Vasicek GJ Model 188
Bond Price Solution 191
Jump Diffusion Tree 194
Preference Free Vasicek GJ+ and Vasicek GJ f~f Models 201
The Vasicek GJ+ Model 202
The Vasicek GJ++ Model 203
Jump Diffusion Tree 205
Fundamental Vasicek EJ Model 206
Bond Price Solution 207
Jump Diffusion Tree 209
Preference Free Vasicek EJ++ Model 216
Jump Diffusion Tree 218
Valuing Futures and Options 218
Valuing Futures 219
Valuing Options: The Fourier Inversion Method 222
Appendix 5.1 Probability Transformations with a
Damping Constant 233
CHAPTERS
The Fundamental Cox, tagersoD, and Ross Model wltli Exponential
and Lognormal Jumps 237
The Fundamental Cox, Ingersoll, and Ross Model 239
Solution to Riccati Equation with Constant Coefficients 242
CIR Bond Price Solution 243
General Specifications of Market Prices of Risk 244
Valuing Futures 245
Valuing Options 248
Interest Rate Trees for the Cox, Ingersoll, and Ross Model 250
Binomial Tree for the CIR Model 250
Trinomial Tree for the CIR Model 263
Pricing Bond Options and Interest Rate Options with
Trinomial Trees 273
The CIR Model Extended with Jumps 279
Valuing Futures 283
Futures on a Time Deposit 284
Valuing Options 285
Jump Diffusion Trees for the CIR Model Extended
with Jumps 287
Exponential Jumps 287
Lognormal Jumps 295
CHAPTK7
Preference Free Cffi and CEV Models with Jumps 305
Mean Calibrated CIR Model 307
Preference Free CIR+ and CIR++ Models 309
A Common Notational Framework 312
Probability Density and the Unconditional Moments 313
Bond Price Solution 315
Expected Bond Returns 317
Constant Infinite Maturity Forward Rate under
Explosive CIR+ and CIR++ Models 318
A Comparison with Other Markovian
Preference Free Models 321
Calibration to the Market Prices of Bonds and
Interest Rate Derivatives 322
Valuing Futures 323
Valuing Options 325
Interest Rate Trees 327
The CIR f and CIR++ Models Extended with Jumps 328
Preference Free CIR EJ+ and CIR EJ++ Models 329
Jump Diffusion Trees 331
Fundamental and Preference Free Constant Elasticity of
Variance Models 331
Forward Rate and Bond Return Volatilities under the
CEV++ Models 333
Valuing Interest Rate Derivatives Using
Trinomial Trees 336
Fundamental and Preference Free Constant Elasticity of
Variance Models with Lognormal Jumps 341
CH/UTER8
Fundamental and Preference Free Two Factor Afflne Models 345
Two Factor Gaussian Models 348
The Canonical, or the Ac, Form: The Dai and Singleton
[2002] Approach 349
The Ar Form: The Hull and White [1996] Approach 353
The Ay Form: The Brigo and Mercurio [2001, 2006]
Approach 356
Relationship between the AQc(2)++ Model and the
A0y(2)++ Model 358
Relationship between the A0r{2)++ Model and the
A0y{2)++ Model 360
Bond Price Process and Forward Rate Process 361
Probability Density of the Short Rate 362
Valuing Options 363
Two Factor Gaussian Trees 364
Two Factor Hybrid Models 373
Bond Price Process and Forward Rate Process 377
Valuing Futures 377
Valuing Options 380
Two Factor Stochastic Volatility Trees 382
Two Factor Square Root Models 393
The Ay Form 393
The Ar Form 399
Relationship between the Canonical Form and
the Ar Form 402
Two Factor Square Root Trees 403
Appendix 8.1 Hull and White Solution of j (t, T) 410
CHAPTHtS
Fundamental and Prefepence freeMultflactopAfflnelVKMJels 413
Three Factor Affine Term Structure Models 416
The Alr(3), Alr(3)+, and Alr(3)++ Models 416
The A2r(3), A2r(3)+, and A2r(3)++ Models 421
Simple Multifactor Affine Models with
Analytical Solutions 425
The Simple AM(N) Models 425
The Simple AM{N)+ and AM(N)++ Models 427
The Nested ATSMs 429
Valuing Futures 429
Valuing Options on Zero Coupon Bonds or Caplets:
The Fourier Inversion Method 433
Valuing Options on Coupon Bonds or Swaptions: The
Cumulant Expansion Approximation 435
Calibration to Interest Rate Caps Data 448
Unspanned Stochastic Volatility 455
Multifactor ATSMs for Pricing Credit Derivatives 45 /
Simple Reduced Form ATSMs under the
RMV Assumption 458
Simple Reduced Form ATSMs under the
RFV Assumption 468
Appendix 9.1 The Solution of r (t, T, $ ) for CDS Pricing
Using Simple Am(N) Models under the RFV Assumption 476
Appendix 9.2 Stochastic Volatility Jump Based Mixed Sign
AN(N) EJ++ Model and A,(3) EJ++ Model 477
The Mixed Sign AN{N) EJ++ Model 478
The At(3) EJ++ Model 479
CHAPTER 10
Fundamental and Preference Free Quadratic Models 483
Single Factor Quadratic Term Structure Model 484
Duration and Convexity 488
Preference Free Single Factor Quadratic Model 492
Forward Rate Volatility 495
Model Implementation Using Trees 497
Extension to Jumps 498
Fundamental Multifactor QTSMs 501
Bond Price Formulas under Q}{N) and Q4(N) Models 505
Parameter Estimates 506
Preference Free Multifactor QTSMs 508
Forward Rate Volatility and Correlation Matrix 515
Valuing Futures 518
Valuing Options on Zero Coupon Bonds or Caplets:
The Fourier Inversion Method 524
Valuing Options on Coupon Bonds or Swaptions: The
Cumulant Expansion Approximation 527
Calibration to Interest Rate Caps Data 531
Multifactor QTSMs for Valuing Credit Derivatives 537
Reduced Form Q^N), Qj(N)+, and Qi(N)++ Models
under the RMV Assumption 537
Reduced Form Qi(N) and Qi(N)+ Models under the
RFV Assumption 543
Appendix 10.1 The Solution of r (t, T, ( ) for CDS Pricing
Using the Qi(N) Model under the RFV Assumption 547
CHAPTER 11
The HJM Forward Rate Model 551
The HJM Forward Rate Model 552
Numerical Implementation Using Nonrecombining Trees 556
A One Factor Nonrecombining Binomial Tree 557
A Two Factor Nonrecombining Trinomial Tree 565
Recursive Programming 569
A Recombining Tree for the Proportional Volatility
HJM Model 572
Forward Price Dynamics under the Forward Measure 573
A Markovian Forward Price Process under the
Proportional Volatility Model 575
A Recombining Tree for the Proportional
Volatility Model Using the Nelson and
Ramaswamy Transform 576
CHAPTER 12
The UBOR Market Model 583
The Lognormal Forward LIBOR Model (LFM) 585
Multifactor LFM under a Single Numeraire 588
The Lognormal Forward Swap Model (LSM) 591
A Joint Framework for Using Black s Formulas for Pricing
Caps and Swaptions 595
The Relationship between the Forward Swap Rate and
Discrete Forward Rates 596
Approximating the Black Implied Volatility of a
Swaption under the LFM 597
Specifying Volatilities and Correlations 600
Forward Rate Volatilities: Some General Results 600
Forward Rate Volatilities: Specific Functional Forms 604
Instantaneous Correlations and Terminal Correlations 60s
Full Rank Instantaneous Correlations 612
Reduced Rank Correlation Structures 61
Terminal Correlations 623
Explaining the Smile: The First Approach 623
The CEV Extension of the LFM 624
Displaced Diffusion Extension of the LFM 626
Unspanned Stochastic Volatility Jump Models 629
Joshi and Rebonato [2003] Model 630
Jarrow, Li, and Zhao [2007] Model 631
An Extension of the JLZ Model 636
Empirical Performance of the JLZ [2007] Model 637
References 647
About the CD ROM 658
index 661
List of Figures
Figure 2.1 Information Structure 19
Figure 2.2 Transformation of Probability Distribution 34
Figure 3.1 Interest Rate Swap with a Financial Intermediary 77
Figure 3.2 Issuance of Fixed Coupon Debt and Floating Rate
Debt with a Simultaneous Execution of a Swap 79
Figure 3.3 The Usefulness of Fundamental versus
Preference Free Models 109
Figure 4.1 The Effect of Mean Reversion 121
Figure 4.2 Sample Paths for Vasicek s Model 122
Figure 4.3 The Distribution of the Future Short Rate in
Vasicek s Model 124
Figure 4.4 The Term Structure of Zero Coupon Yields in
Vasicek s Model 127
Figure 4.5 Volatilities Structures in the Vasicek and
Merton Models 128
Figure 4.6 One Period Binomial Tree 163
Figure 4.7 Two Period Binomial Tree 164
Figure 4.8 One Period Trinomial Tree 165
Figure 4.9 Tree for a Bond for the Vasicek+ Model 167
Figure 4.10 Convergence of the Tree Solution 169
Figure 4.11 Tree for a European Call Option for the
Vasicek+ Model 170
Figure 4.12 Tree for an American Put Option for the
Vasicek+ Model 1 72
Figure 4.13 Tree for the 0.5 Year Zero Coupon Bond for the
Vasicek++ Model 1 ~4
Figure 4.14 Tree for the 1 Year Zero Coupon Bond for the
Vasicek++ Model 1 75
Figure 4.15 Tree for the 1.5 Year Zero Coupon Bond for the
Vasicek++ Model 176
Figure 4.16 Time Dependent Drift Related Functions of the
Short Rate Process for the Vasicek+++ Model 179
Figure 4.17 Tree for an American Call Option for the
Vasicek+++ Model 180
Figure 5.1 The Poisson Process over an Infinitesimally Small
Interval dt 189
Figure 5.2 Jump Diffusion Interest Rate Tree 195
Figure 5.3 Approximation of the Jump Distribution 196
Figure 5.4 Inerest Rate Tree 199
Figure 5.5 Bond Value Calculation 201
Figure 5.6 Approximation of the Jump Distribution Using
Two Exponential Curves 211
Figure 5.7 Interest Rate Tree 214
Figure 5.8 Bond Value Calculation 215
Figure 6.1 X Process Tree 253
Figure 6.2 X(t) Tree with Multiple Node Jumps—
NR Approach 254
Figure 6.3 X(t) Tree with Multiple Node Jumps—
NB Approach 256
Figure 6.4 X(t) Tree with Multiple Node Jumps Truncated
above Zero—NB Approach 256
Figure 6.5 Binomial Tree for the CIR Model 260
Figure 6.6 X Process Trinomial Tree 264
Figure 6.7 Truncated X Process Trinomial Tree 264
Figure 6.8 Trinomial Tree Contraction 266
Figure 6.9 Trinomial Tree Expansion 266
Figure 6.10 Multiple Jumps in a Trinomial Tree 267
Figure 6.11 Trinomial Tree for the CIR Model 270
Figure 6.12 Trinomial Tree for the CIR Model for Pricing an
American Call Option on a Coupon Bond 277
Figure 6.13 General Jump Diffusion Tree 288
Figure 6.14 Approximation of the Jump Distribution Using an
Exponential Curve 290
Figure 6.15 Approximation of the Jump Distribution Using an
Exponential Curve 292
Figure 6.16 Exponential Jump Diffusion Tree Truncation 292
Figure 6.17 Tree for the CIR Model Extended with
Exponential Jumps 294
Figure 6.18 Three Step Jump Diffusion Tree with M — 9 296
Figure 6.19 Approximation of the Lognormal Jump
Distribution Using a Normal Curve 29/
Figure 6.20 Lognormal Jump Diffusion Tree Truncation 300
Figure 6.21 Tree for the CIR Model Extended with
Lognormal Jumps 301
Figure 8.1 Trinomial Tree for the Y^t) Process 366
Figure 8.2 Trinomial Tree for the Y2(t) Process ^
Figure 8.3 Two Dimensional Short Rate Tree 367
Figure 8.4 One Dimensional Tree for the Y](t) Process 369
Figure 8.5 Two Dimensional Short Rate Tree 370
Figure 8.6 Two Dimensional Bond Tree 371
Figure 8.7 Trinomial Tree for the Transform Xi(t) 383
Figure 8.8 The Trinomial Tree for the X2(t) Process at Time 0 385
Figure 8.9 Node Span of X2(t) as a Function of k(t) 386
Figure 8.10 The Trinomial Tree for X2(t) Conditional on the
Occurrence of YJ1 at Time 1 387
Figure 8.11 The Trinomial Tree for X2(t) Conditional on the
Occurrence of Y]1 at Time 1 387
Figure 8.12 One Dimensional Trinomial Tree for the
Y,(f) Process 389
Figure 8.13 One Dimensional Tree for the X2(t) Process 390
Figure 8.14 One Dimensional Trinomial Tree for the
Y2(t) Process 390
Figure 8.15 Two Dimensional Short Rate Tree 391
Figure 8.16 Two Dimensional Bond Tree 392
Figure 8.17 Two Dimensional Short Rate Tree 404
Figure 8.18 One Dimensional Trinomial Tree for the
Yi(t) Process 405
Figure 8.19 One Dimensional Trinomial Tree for the
Y2(t) Process 406
Figure 8.20 Two Dimensional Short Rate Tree 408
Figure 8.21 Two Dimensional Bond Tree 409
Figure 9.1 Average Black Implied Volatilities of
Difference Caps 449
Figure 9.2 Root Mean Square Pricing Errors in Pooled Data 452
Figure 10.1 Five and Ten Year Bond Prices versus r(t), with
Default Parameters 8 = 0, % = 0.5, jx = 0.125,
and a = 0.04 490
Figure 10.2 The Deterministic Functions afx (t, T) and o 2 (r, T)
and the Forward Rate Volatility Function at (t, T)
+afl (t, T) Y(t) 496
Figure 10.3 Trinomial Tree for the Y(t) Process 497
Figure 10.4 Trinomial Tree for the Quadratic Model 499
Figure 10.5 Root Mean Square Pricing Errors in Pooled Data 534
Figure 11.1 The Evolution of a One Factor Forward Rate Curve 558
Figure 11.2 Forward Rate Evolution at Each Node of the Tree 559
Figure 11.3 Evolution of the Tree from Time 0 to Time 1
(where h = ) 562
Figure 11.4 The One Period Forward Rate Tree 564
Figure 11.5 Evolution of the Tree from Time 1 to Time 2,
Starting from the Up State at Time 1 564
Figure 11.6 Evolution of the Forward Rates over Two Periods 566
Figure 11.7 Valuation of a European Call Option on the
Four Period Zero Coupon Bond with Exercise Date
2 and Exercise Price K = 0.84 567
Figure 11.8 Evolution of the Forward Rate in the Discretized
Two Factor HJM Model Using a Trinomial Tree 568
Figure 11.9 A Recursive Program 570
Figure 11.10 Pseudocode to Solve the Price of a Call Option
under the HJM Model 571
Figure 11.11 The X Process Tree 577
List of Tables
Table 3.1 Total Outstanding Notional Amounts of
Single Currency Interest Rate Derivatives (in millions
of U.S. dollars) 50
Table 3.2 Notional Amounts Outstanding at End of June 2006
of Interest Rate Derivatives by Instrument,
Counterparty, and Currency (in millions
of U.S. dollars) 51
Table 3.3 Credit Default Swaps Market Notional Amounts
Outstanding at End of June 2006 (in millions
of U.S. dollars) 53
Table 3.4 Interest Rate Futures 55
Table 3.5 Deliverable Bonds for the T Bond Futures Contract 67
Table 3.6 Cost of Delivery 68
Table 3.7 Cash Flows Exchanged by Firm A 75
Table 3.8 Cost of Debt in Fixed and Floating Debt Markets 78
Table 3.9 Cost of Financing and Savings for Firm A and Firm B 81
Table 4.1 Calculations for Separate Zero Coupon
European Calls 161
Table 4.2 Volatilities of Zero Coupon Bonds for the
Vasicek+ ) +Model 179
Table 6.1 Prices of Zero Coupon Bonds for the CIR Term
Structure Model, Using the NB Approach versus the
NR Approach (see Nelson and Ramaswamy, Table 2) 262
Table 6.2 Prices of Zero Coupon Bonds for the CIR Term
Structure Model, Using the Trinomial Tree versus the
Binomial Tree, Using the NB Approach 272
Table 6.3 Prices of Zero Coupon Bond Options under the CIR
Term Structure Model, Using the NB Truncated Tree
Approach (with in = 0.08)a 275
Table 6.4 Prices of Coupon Bond Options under the CIR Term
Structure Model with 8 Percent Coupon, Using NB
Truncated Tree Approach (with m — 0.08
and K = 100)a 276
Table 7.1 Parameter Restrictions Imposed by Alternative
Models of Short Term Interest Rates 332
Table 8.1 Joint Probabilities Given as a Product of Marginal
Probabilities, Conditional on the Occurrence of Y}1
and X l at Time 1 388
Table 9.1 Overall Goodness of Fit, Chi Square Tests 419
Table 9.2 Overall Goodness of Fit, Chi Square Tests 422
Table 9.3 The ATSMs Nested in the Simple AM(N) and
AM(N)++ Models 430
Table 9.4 Descriptive Statistics of Difference Cap Prices 449
Table 9.5 Estimated Parameter Values Averaged over the
Sample Period 451
Table 9.6 Average Percentage Pricing Errors 453
Table 10.1 EMM Estimates of the Parameters for Fundamental
Three Factor QTSMs 507
Table 10.2 Estimated Risk Neutral Parameter Values and
Initial State Variable Values Averaged over
the Sample Period 5
Table 10.3 Average Percentage Pricing Errors j
Table 11.1 European Call Option Prices for the Proportional
Volatility HJM Model (in dollars) 578
Table 11.2 European Put Option Prices for the Proportional
Volatility HJM Model (in dollars) 579
Table 11.3 Recombining Trees to Price Caps and Floors for
the Proportional Volatility HJM Model (prices are
in dollars) 581
Table 12.1 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.75), with
p^ =0.613 and P = 0.1 614
Table 12.2 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.84), with
Poo =0.77, ri = 0.1,andra= 10 6l8
Table 12.3 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.88), with
f x = 0.77, n = 0.1, and « = 10 62°
Table 12.4 Parameter Estimates of Unspanned Stochastic
Volatility Models ^
Table 12.5 Average Percentage Pricing Errors of Unspanned
Stochastic Volatility Models 640
Table 12.6 Parameter Estimates of Unspanned Stochastic
Volatility Jump Models ^
Table 12.7 Average Percentage Pricing Errors of Unspanned
Stochastic Volatility Jump Models ^4
|
| adam_txt |
Contents
Ust of figures xxxi
list of Tables xxxv
CHAPTBU
ASbnpletatrodiM^toCoiiUn^ 1
Continuous Time Diffusion Processes 3
Wiener Process 3
Ito Process 5
Ito's Lemma 7
Simple Rules of Stochastic Differentiation
and Integration 9
Obtaining Unconditional Mean and Variance of
Stochastic Integrals under Gaussian Processes 9
Examples of Gaussian Stochastic Integrals 11
Mixed Jump Diffusion Processes 14
The Jump Diffusion Process 14
Ito's Lemma for the Jump Diffusion Process 15
CHAPTB12
Artttrage Free Valuation 17
Arbitrage Free Valuation: Some Basic Results 18
A Simple Relationship between Zero Coupon Bond
Prices and Arrow Debreu Prices 20
The Bayes Rule for Conditional Probabilities of Events 20
The Relationship between Current and Future
AD Prices 21
The Relationship between Cross Sectional AD Prices
and Intertemporal Term Structure Dynamics 22
Existence of the Risk Neutral Probability Measure 23
Stochastic Discount Factor 28
Radon Nikodym Derivative 30
Arbitrage Free Valuation in Continuous Time 31
Change of Probability Measure under a Continuous
Probability Density 32
The Girsanov Theorem and the Radon Nikodym
Derivative 34
Equivalent Martingale Measures 35
Stochastic Discount Factor and Risk Premiums 43
The Feynman Kac Theorem 45
CHAPTH(3
Valuing Interest Rate and Credit Derivatives:
Basic Pricing Frameworks 49
Eurodollar and Other Time Deposit Futures 54
Valuing Futures on a Time Deposit 58
Convexity Bias 60
Treasury Bill Futures 61
Valuing T Bill Futures 62
Convexity Bias "3
Treasury Bond Futures 64
Conversion Factor 65
Cheapest to Deliver Bond 67
Options Embedded in T Bond Futures 68
Valuing T Bond Futures 68
Treasury Note Futures '^
Forward Rate Agreements ^3
Interest Rate Swaps ^4
Day Count Conventions ' °
The Financial Intermediary 77
Motivations for Interest Rate Swaps '°
Pricing Interest Rate Swaps 82
Interest Rate Swaptions 8.5
Caps and Floors °°
Caplet 90
Floorlet 91
Collarlet 92
Caps, Floors, and Collars 92
Black Implied Volatilities for Caps and Swaptions 93
Black Implied Volatilities: Swaptions "
Black Implied Volatilities: Caplet 96
Black Implied Volatilities: Caps 9/
Black Implied Volatilities: Difference Caps 98
Pricing Credit Derivatives Using the
Reduced Form Approach 9»
Default Intensity and Survival Probability 10^
Recovery Assumptions 101
Risk Neutral Valuation under the
RMV Assumption 102
Risk Neutral Valuation under the RFV Assumption 103
Valuing Credit Default Swaps Using the
RFV Assumption 104
A New Taxonomy of Term Structure Models 106
CHAPTBM
Fundamental and Preference free Single Factor
Gaussian Models 113
The Arbitrage Free Pricing Framework of Vasicek 115
The Term Structure Equation 116
Risk Neutral Valuation 118
The Fundamental Vasicek Model 120
Bond Price Solution 124
Preference Free Vasicek+, Vasicek++, and
Vasicek+++ Models 128
The Vasicek+ Model 128
The Vasicek++, or the Extended Vasicek Model 136
The Vasicek+++, or the Fully Extended
Vasicek Model 140
Valuing Futures 144
Valuing Futures under the Vasicek, Vasicek+, and
Vasicek++ Models 145
Valuing Futures under the Vasicek+ f+ Model 150
Valuing Options 153
Options on Zero Coupon Bonds 153
Options on Coupon Bonds 157
Valuing Interest Rate Contingent Claims Using Trees 161
Binomial Trees 163
Trinomial Trees 165
Trinomial Tree under the Vasicek+4 Model:
An Example 171
Trinomial Tree under the Vasicek+++ Model:
An Example 178
Appendix 4.1. Bond Price Solution Using the Risk Neutral
Valuation Approach under the Fundamental Vasicek
Model and the Preference Free Vasicek f Model 181
Appendix 4.2. Hull's Approximation to Convexity Bias
under the Ho and Lee Model 184
CHAPTQ15
Fundamental and Ppelerence Free Jump Extended Gaussian Models 187
Fundamental Vasicek GJ Model 188
Bond Price Solution 191
Jump Diffusion Tree 194
Preference Free Vasicek GJ+ and Vasicek GJ f~f Models 201
The Vasicek GJ+ Model 202
The Vasicek GJ++ Model 203
Jump Diffusion Tree 205
Fundamental Vasicek EJ Model 206
Bond Price Solution 207
Jump Diffusion Tree 209
Preference Free Vasicek EJ++ Model 216
Jump Diffusion Tree 218
Valuing Futures and Options 218
Valuing Futures 219
Valuing Options: The Fourier Inversion Method 222
Appendix 5.1 Probability Transformations with a
Damping Constant 233
CHAPTERS
The Fundamental Cox, tagersoD, and Ross Model wltli Exponential
and Lognormal Jumps 237
The Fundamental Cox, Ingersoll, and Ross Model 239
Solution to Riccati Equation with Constant Coefficients 242
CIR Bond Price Solution 243
General Specifications of Market Prices of Risk 244
Valuing Futures 245
Valuing Options 248
Interest Rate Trees for the Cox, Ingersoll, and Ross Model 250
Binomial Tree for the CIR Model 250
Trinomial Tree for the CIR Model 263
Pricing Bond Options and Interest Rate Options with
Trinomial Trees 273
The CIR Model Extended with Jumps 279
Valuing Futures 283
Futures on a Time Deposit 284
Valuing Options 285
Jump Diffusion Trees for the CIR Model Extended
with Jumps 287
Exponential Jumps 287
Lognormal Jumps 295
CHAPTK7
Preference Free Cffi and CEV Models with Jumps 305
Mean Calibrated CIR Model 307
Preference Free CIR+ and CIR++ Models 309
A Common Notational Framework 312
Probability Density and the Unconditional Moments 313
Bond Price Solution 315
Expected Bond Returns 317
Constant Infinite Maturity Forward Rate under
Explosive CIR+ and CIR++ Models 318
A Comparison with Other Markovian
Preference Free Models 321
Calibration to the Market Prices of Bonds and
Interest Rate Derivatives 322
Valuing Futures 323
Valuing Options 325
Interest Rate Trees 327
The CIR f and CIR++ Models Extended with Jumps 328
Preference Free CIR EJ+ and CIR EJ++ Models 329
Jump Diffusion Trees 331
Fundamental and Preference Free Constant Elasticity of
Variance Models 331
Forward Rate and Bond Return Volatilities under the
CEV++ Models 333
Valuing Interest Rate Derivatives Using
Trinomial Trees 336
Fundamental and Preference Free Constant Elasticity of
Variance Models with Lognormal Jumps 341
CH/UTER8
Fundamental and Preference Free Two Factor Afflne Models 345
Two Factor Gaussian Models 348
The Canonical, or the Ac, Form: The Dai and Singleton
[2002] Approach 349
The Ar Form: The Hull and White [1996] Approach 353
The Ay Form: The Brigo and Mercurio [2001, 2006]
Approach 356
Relationship between the AQc(2)++ Model and the
A0y(2)++ Model 358
Relationship between the A0r{2)++ Model and the
A0y{2)++ Model 360
Bond Price Process and Forward Rate Process 361
Probability Density of the Short Rate 362
Valuing Options 363
Two Factor Gaussian Trees 364
Two Factor Hybrid Models 373
Bond Price Process and Forward Rate Process 377
Valuing Futures 377
Valuing Options 380
Two Factor Stochastic Volatility Trees 382
Two Factor Square Root Models 393
The Ay Form 393
The Ar Form 399
Relationship between the Canonical Form and
the Ar Form 402
Two Factor "Square Root" Trees 403
Appendix 8.1 Hull and White Solution of j\(t, T) 410
CHAPTHtS
Fundamental and Prefepence freeMultflactopAfflnelVKMJels 413
Three Factor Affine Term Structure Models 416
The Alr(3), Alr(3)+, and Alr(3)++ Models 416
The A2r(3), A2r(3)+, and A2r(3)++ Models 421
Simple Multifactor Affine Models with
Analytical Solutions 425
The Simple AM(N) Models 425
The Simple AM{N)+ and AM(N)++ Models 427
The Nested ATSMs 429
Valuing Futures 429
Valuing Options on Zero Coupon Bonds or Caplets:
The Fourier Inversion Method 433
Valuing Options on Coupon Bonds or Swaptions: The
Cumulant Expansion Approximation 435
Calibration to Interest Rate Caps Data 448
Unspanned Stochastic Volatility 455
Multifactor ATSMs for Pricing Credit Derivatives 45 /
Simple Reduced Form ATSMs under the
RMV Assumption 458
Simple Reduced Form ATSMs under the
RFV Assumption 468
Appendix 9.1 The Solution of r\(t, T, $ ) for CDS Pricing
Using Simple Am(N) Models under the RFV Assumption 476
Appendix 9.2 Stochastic Volatility Jump Based Mixed Sign
AN(N) EJ++ Model and A,(3) EJ++ Model 477
The Mixed Sign AN{N) EJ++ Model 478
The At(3) EJ++ Model 479
CHAPTER 10
Fundamental and Preference Free Quadratic Models 483
Single Factor Quadratic Term Structure Model 484
Duration and Convexity 488
Preference Free Single Factor Quadratic Model 492
Forward Rate Volatility 495
Model Implementation Using Trees 497
Extension to Jumps 498
Fundamental Multifactor QTSMs 501
Bond Price Formulas under Q}{N) and Q4(N) Models 505
Parameter Estimates 506
Preference Free Multifactor QTSMs 508
Forward Rate Volatility and Correlation Matrix 515
Valuing Futures 518
Valuing Options on Zero Coupon Bonds or Caplets:
The Fourier Inversion Method 524
Valuing Options on Coupon Bonds or Swaptions: The
Cumulant Expansion Approximation 527
Calibration to Interest Rate Caps Data 531
Multifactor QTSMs for Valuing Credit Derivatives 537
Reduced Form Q^N), Qj(N)+, and Qi(N)++ Models
under the RMV Assumption 537
Reduced Form Qi(N) and Qi(N)+ Models under the
RFV Assumption 543
Appendix 10.1 The Solution of r\(t, T, ( ) for CDS Pricing
Using the Qi(N) Model under the RFV Assumption 547
CHAPTER 11
The HJM Forward Rate Model 551
The HJM Forward Rate Model 552
Numerical Implementation Using Nonrecombining Trees 556
A One Factor Nonrecombining Binomial Tree 557
A Two Factor Nonrecombining Trinomial Tree 565
Recursive Programming 569
A Recombining Tree for the Proportional Volatility
HJM Model 572
Forward Price Dynamics under the Forward Measure 573
A Markovian Forward Price Process under the
Proportional Volatility Model 575
A Recombining Tree for the Proportional
Volatility Model Using the Nelson and
Ramaswamy Transform 576
CHAPTER 12
The UBOR Market Model 583
The Lognormal Forward LIBOR Model (LFM) 585
Multifactor LFM under a Single Numeraire 588
The Lognormal Forward Swap Model (LSM) 591
A Joint Framework for Using Black's Formulas for Pricing
Caps and Swaptions 595
The Relationship between the Forward Swap Rate and
Discrete Forward Rates 596
Approximating the Black Implied Volatility of a
Swaption under the LFM 597
Specifying Volatilities and Correlations 600
Forward Rate Volatilities: Some General Results 600
Forward Rate Volatilities: Specific Functional Forms 604
Instantaneous Correlations and Terminal Correlations 60s
Full Rank Instantaneous Correlations 612
Reduced Rank Correlation Structures 61"
Terminal Correlations 623
Explaining the Smile: The First Approach 623
The CEV Extension of the LFM 624
Displaced Diffusion Extension of the LFM 626
Unspanned Stochastic Volatility Jump Models 629
Joshi and Rebonato [2003] Model 630
Jarrow, Li, and Zhao [2007] Model 631
An Extension of the JLZ Model 636
Empirical Performance of the JLZ [2007] Model 637
References 647
About the CD ROM 658
index 661
List of Figures
Figure 2.1 Information Structure 19
Figure 2.2 Transformation of Probability Distribution 34
Figure 3.1 Interest Rate Swap with a Financial Intermediary 77
Figure 3.2 Issuance of Fixed Coupon Debt and Floating Rate
Debt with a Simultaneous Execution of a Swap 79
Figure 3.3 The Usefulness of Fundamental versus
Preference Free Models 109
Figure 4.1 The Effect of Mean Reversion 121
Figure 4.2 Sample Paths for Vasicek's Model 122
Figure 4.3 The Distribution of the Future Short Rate in
Vasicek's Model 124
Figure 4.4 The Term Structure of Zero Coupon Yields in
Vasicek's Model 127
Figure 4.5 Volatilities Structures in the Vasicek and
Merton Models 128
Figure 4.6 One Period Binomial Tree 163
Figure 4.7 Two Period Binomial Tree 164
Figure 4.8 One Period Trinomial Tree 165
Figure 4.9 Tree for a Bond for the Vasicek+ Model 167
Figure 4.10 Convergence of the Tree Solution 169
Figure 4.11 Tree for a European Call Option for the
Vasicek+ Model 170
Figure 4.12 Tree for an American Put Option for the
Vasicek+ Model 1 72
Figure 4.13 Tree for the 0.5 Year Zero Coupon Bond for the
Vasicek++ Model 1 ~4
Figure 4.14 Tree for the 1 Year Zero Coupon Bond for the
Vasicek++ Model 1 75
Figure 4.15 Tree for the 1.5 Year Zero Coupon Bond for the
Vasicek++ Model 176
Figure 4.16 Time Dependent Drift Related Functions of the
Short Rate Process for the Vasicek+++ Model 179
Figure 4.17 Tree for an American Call Option for the
Vasicek+++ Model 180
Figure 5.1 The Poisson Process over an Infinitesimally Small
Interval dt 189
Figure 5.2 Jump Diffusion Interest Rate Tree 195
Figure 5.3 Approximation of the Jump Distribution 196
Figure 5.4 Inerest Rate Tree 199
Figure 5.5 Bond Value Calculation 201
Figure 5.6 Approximation of the Jump Distribution Using
Two Exponential Curves 211
Figure 5.7 Interest Rate Tree 214
Figure 5.8 Bond Value Calculation 215
Figure 6.1 X Process Tree 253
Figure 6.2 X(t) Tree with Multiple Node Jumps—
NR Approach 254
Figure 6.3 X(t) Tree with Multiple Node Jumps—
NB Approach 256
Figure 6.4 X(t) Tree with Multiple Node Jumps Truncated
above Zero—NB Approach 256
Figure 6.5 Binomial Tree for the CIR Model 260
Figure 6.6 X Process Trinomial Tree 264
Figure 6.7 Truncated X Process Trinomial Tree 264
Figure 6.8 Trinomial Tree Contraction 266
Figure 6.9 Trinomial Tree Expansion 266
Figure 6.10 Multiple Jumps in a Trinomial Tree 267
Figure 6.11 Trinomial Tree for the CIR Model 270
Figure 6.12 Trinomial Tree for the CIR Model for Pricing an
American Call Option on a Coupon Bond 277
Figure 6.13 General Jump Diffusion Tree 288
Figure 6.14 Approximation of the Jump Distribution Using an
Exponential Curve 290
Figure 6.15 Approximation of the Jump Distribution Using an
Exponential Curve 292
Figure 6.16 Exponential Jump Diffusion Tree Truncation 292
Figure 6.17 Tree for the CIR Model Extended with
Exponential Jumps 294
Figure 6.18 Three Step Jump Diffusion Tree with M — 9 296
Figure 6.19 Approximation of the Lognormal Jump
Distribution Using a Normal Curve 29/
Figure 6.20 Lognormal Jump Diffusion Tree Truncation 300
Figure 6.21 Tree for the CIR Model Extended with
Lognormal Jumps 301
Figure 8.1 Trinomial Tree for the Y^t) Process 366
Figure 8.2 Trinomial Tree for the Y2(t) Process ^
Figure 8.3 Two Dimensional Short Rate Tree 367
Figure 8.4 One Dimensional Tree for the Y](t) Process 369
Figure 8.5 Two Dimensional Short Rate Tree 370
Figure 8.6 Two Dimensional Bond Tree 371
Figure 8.7 Trinomial Tree for the Transform Xi(t) 383
Figure 8.8 The Trinomial Tree for the X2(t) Process at Time 0 385
Figure 8.9 Node Span of X2(t) as a Function of k(t) 386
Figure 8.10 The Trinomial Tree for X2(t) Conditional on the
Occurrence of YJ1 at Time 1 387
Figure 8.11 The Trinomial Tree for X2(t) Conditional on the
Occurrence of Y]1 at Time 1 387
Figure 8.12 One Dimensional Trinomial Tree for the
Y,(f) Process 389
Figure 8.13 One Dimensional Tree for the X2(t) Process 390
Figure 8.14 One Dimensional Trinomial Tree for the
Y2(t) Process 390
Figure 8.15 Two Dimensional Short Rate Tree 391
Figure 8.16 Two Dimensional Bond Tree 392
Figure 8.17 Two Dimensional Short Rate Tree 404
Figure 8.18 One Dimensional Trinomial Tree for the
Yi(t) Process 405
Figure 8.19 One Dimensional Trinomial Tree for the
Y2(t) Process 406
Figure 8.20 Two Dimensional Short Rate Tree 408
Figure 8.21 Two Dimensional Bond Tree 409
Figure 9.1 Average Black Implied Volatilities of
Difference Caps 449
Figure 9.2 Root Mean Square Pricing Errors in Pooled Data 452
Figure 10.1 Five and Ten Year Bond Prices versus r(t), with
Default Parameters 8 = 0, % = 0.5, jx = 0.125,
and a = 0.04 490
Figure 10.2 The Deterministic Functions afx (t, T) and o 2 (r, T)
and the Forward Rate Volatility Function at\ (t, T)
+afl (t, T) Y(t) 496
Figure 10.3 Trinomial Tree for the Y(t) Process 497
Figure 10.4 Trinomial Tree for the Quadratic Model 499
Figure 10.5 Root Mean Square Pricing Errors in Pooled Data 534
Figure 11.1 The Evolution of a One Factor Forward Rate Curve 558
Figure 11.2 Forward Rate Evolution at Each Node of the Tree 559
Figure 11.3 Evolution of the Tree from Time 0 to Time 1
(where h = \) 562
Figure 11.4 The One Period Forward Rate Tree 564
Figure 11.5 Evolution of the Tree from Time 1 to Time 2,
Starting from the Up State at Time 1 564
Figure 11.6 Evolution of the Forward Rates over Two Periods 566
Figure 11.7 Valuation of a European Call Option on the
Four Period Zero Coupon Bond with Exercise Date
2 and Exercise Price K = 0.84 567
Figure 11.8 Evolution of the Forward Rate in the Discretized
Two Factor HJM Model Using a Trinomial Tree 568
Figure 11.9 A Recursive Program 570
Figure 11.10 Pseudocode to Solve the Price of a Call Option
under the HJM Model 571
Figure 11.11 The X Process Tree 577
List of Tables
Table 3.1 Total Outstanding Notional Amounts of
Single Currency Interest Rate Derivatives (in millions
of U.S. dollars) 50
Table 3.2 Notional Amounts Outstanding at End of June 2006
of Interest Rate Derivatives by Instrument,
Counterparty, and Currency (in millions
of U.S. dollars) 51
Table 3.3 Credit Default Swaps Market Notional Amounts
Outstanding at End of June 2006 (in millions
of U.S. dollars) 53
Table 3.4 Interest Rate Futures 55
Table 3.5 Deliverable Bonds for the T Bond Futures Contract 67
Table 3.6 Cost of Delivery 68
Table 3.7 Cash Flows Exchanged by Firm A 75
Table 3.8 Cost of Debt in Fixed and Floating Debt Markets 78
Table 3.9 Cost of Financing and Savings for Firm A and Firm B 81
Table 4.1 Calculations for Separate Zero Coupon
European Calls 161
Table 4.2 Volatilities of Zero Coupon Bonds for the
Vasicek+ ) +Model 179
Table 6.1 Prices of Zero Coupon Bonds for the CIR Term
Structure Model, Using the NB Approach versus the
NR Approach (see Nelson and Ramaswamy, Table 2) 262
Table 6.2 Prices of Zero Coupon Bonds for the CIR Term
Structure Model, Using the Trinomial Tree versus the
Binomial Tree, Using the NB Approach 272
Table 6.3 Prices of Zero Coupon Bond Options under the CIR
Term Structure Model, Using the NB Truncated Tree
Approach (with in = 0.08)a 275
Table 6.4 Prices of Coupon Bond Options under the CIR Term
Structure Model with 8 Percent Coupon, Using NB
Truncated Tree Approach (with m — 0.08
and K = 100)a 276
Table 7.1 Parameter Restrictions Imposed by Alternative
Models of Short Term Interest Rates 332
Table 8.1 Joint Probabilities Given as a Product of Marginal
Probabilities, Conditional on the Occurrence of Y}1
and X\l at Time 1 388
Table 9.1 Overall Goodness of Fit, Chi Square Tests 419
Table 9.2 Overall Goodness of Fit, Chi Square Tests 422
Table 9.3 The ATSMs Nested in the Simple AM(N) and
AM(N)++ Models 430
Table 9.4 Descriptive Statistics of Difference Cap Prices 449
Table 9.5 Estimated Parameter Values Averaged over the
Sample Period 451
Table 9.6 Average Percentage Pricing Errors 453
Table 10.1 EMM Estimates of the Parameters for Fundamental
Three Factor QTSMs 507
Table 10.2 Estimated Risk Neutral Parameter Values and
Initial State Variable Values Averaged over
the Sample Period 5"
Table 10.3 Average Percentage Pricing Errors "j
Table 11.1 European Call Option Prices for the Proportional
Volatility HJM Model (in dollars) 578
Table 11.2 European Put Option Prices for the Proportional
Volatility HJM Model (in dollars) 579
Table 11.3 Recombining Trees to Price Caps and Floors for
the Proportional Volatility HJM Model (prices are
in dollars) 581
Table 12.1 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.75), with
p^ =0.613 and P = 0.1 614
Table 12.2 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.84), with
Poo =0.77, ri = 0.1,andra= 10 6l8
Table 12.3 Correlations among Ten Forward Rates Generated
Using the Function in Equation (12.88), with
f x = 0.77, n = 0.1, and « = 10 62°
Table 12.4 Parameter Estimates of Unspanned Stochastic
Volatility Models ^
Table 12.5 Average Percentage Pricing Errors of Unspanned
Stochastic Volatility Models 640
Table 12.6 Parameter Estimates of Unspanned Stochastic
Volatility Jump Models ^
Table 12.7 Average Percentage Pricing Errors of Unspanned
Stochastic Volatility Jump Models ^4 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nawalkha, Sanjay K. Beliaeva, Natalia A. Soto, Gloria M. |
| author_facet | Nawalkha, Sanjay K. Beliaeva, Natalia A. Soto, Gloria M. |
| author_role | aut aut aut |
| author_sort | Nawalkha, Sanjay K. |
| author_variant | s k n sk skn n a b na nab g m s gm gms |
| building | Verbundindex |
| bvnumber | BV022949132 |
| callnumber-first | H - Social Science |
| callnumber-label | HG101 |
| callnumber-raw | HG101 |
| callnumber-search | HG101 |
| callnumber-sort | HG 3101 |
| callnumber-subject | HG - Finance |
| classification_rvk | QH 237 QK 660 |
| ctrlnum | (OCoLC)76871380 (DE-599)BVBBV022949132 |
| dewey-full | 332.01/51923 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.01/51923 |
| dewey-search | 332.01/51923 |
| dewey-sort | 3332.01 551923 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV022949132 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:01:22Z |
| indexdate | 2024-07-09T21:08:22Z |
| institution | BVB |
| isbn | 9780471737148 0471737143 |
| language | English |
| lccn | 2006037555 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016153631 |
| oclc_num | 76871380 |
| open_access_boolean | |
| owner | DE-945 DE-355 DE-BY-UBR DE-523 |
| owner_facet | DE-945 DE-355 DE-BY-UBR DE-523 |
| physical | XXXVI, 683 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley finance series |
| spelling | Nawalkha, Sanjay K. Verfasser aut Dynamic term structure modeling the fixed income valuation course Sanjay K. Nawalkha ; Natalia A. Beliaeva ; Gloria M. Soto Hoboken, NJ [u.a.] Wiley 2007 XXXVI, 683 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Wiley finance series Finances Processus stochastiques Finance Stochastic processes Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Festverzinsliches Wertpapier (DE-588)4121262-9 gnd rswk-swf Wertpapieranalyse (DE-588)4124458-8 gnd rswk-swf Zinsstruktur (DE-588)4067855-6 gnd rswk-swf Zinsstruktur (DE-588)4067855-6 s Derivat Wertpapier (DE-588)4381572-8 s Festverzinsliches Wertpapier (DE-588)4121262-9 s Wertpapieranalyse (DE-588)4124458-8 s b DE-604 Beliaeva, Natalia A. Verfasser aut Soto, Gloria M. Verfasser aut http://www.loc.gov/catdir/toc/ecip075/2006037555.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0740/2006037555-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0740/2006037555-b.html Contributor biographical information HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016153631&sequence=000012&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nawalkha, Sanjay K. Beliaeva, Natalia A. Soto, Gloria M. Dynamic term structure modeling the fixed income valuation course Finances Processus stochastiques Finance Stochastic processes Derivat Wertpapier (DE-588)4381572-8 gnd Festverzinsliches Wertpapier (DE-588)4121262-9 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4121262-9 (DE-588)4124458-8 (DE-588)4067855-6 |
| title | Dynamic term structure modeling the fixed income valuation course |
| title_auth | Dynamic term structure modeling the fixed income valuation course |
| title_exact_search | Dynamic term structure modeling the fixed income valuation course |
| title_exact_search_txtP | Dynamic term structure modeling the fixed income valuation course |
| title_full | Dynamic term structure modeling the fixed income valuation course Sanjay K. Nawalkha ; Natalia A. Beliaeva ; Gloria M. Soto |
| title_fullStr | Dynamic term structure modeling the fixed income valuation course Sanjay K. Nawalkha ; Natalia A. Beliaeva ; Gloria M. Soto |
| title_full_unstemmed | Dynamic term structure modeling the fixed income valuation course Sanjay K. Nawalkha ; Natalia A. Beliaeva ; Gloria M. Soto |
| title_short | Dynamic term structure modeling |
| title_sort | dynamic term structure modeling the fixed income valuation course |
| title_sub | the fixed income valuation course |
| topic | Finances Processus stochastiques Finance Stochastic processes Derivat Wertpapier (DE-588)4381572-8 gnd Festverzinsliches Wertpapier (DE-588)4121262-9 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| topic_facet | Finances Processus stochastiques Finance Stochastic processes Derivat Wertpapier Festverzinsliches Wertpapier Wertpapieranalyse Zinsstruktur |
| url | http://www.loc.gov/catdir/toc/ecip075/2006037555.html http://www.loc.gov/catdir/enhancements/fy0740/2006037555-d.html http://www.loc.gov/catdir/enhancements/fy0740/2006037555-b.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016153631&sequence=000012&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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