デリバティブの理論と実務(改訂版)<br>Financial Derivatives in Theory and Practice (Wiley Series in Probability and Statistics) (Revised)

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デリバティブの理論と実務(改訂版)
Financial Derivatives in Theory and Practice (Wiley Series in Probability and Statistics) (Revised)

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  • 製本 Hardcover:ハードカバー版/ページ数 437 p.
  • 言語 ENG
  • 商品コード 9780470863589
  • DDC分類 332.6457

基本説明

A complete, rigorous and yet readable account of the mathematics underlying derivative pricing and a guide to applying these ideas to solve real pricing problems.

Table of Contents

Preface to revised edition                         xv
Preface xvii
Acknowledgements xxi
Part I: Theory 1 (212)
Single-Period Option Pricing 3 (16)
Option pricing in a nutshell 3 (1)
The simplest setting 4 (1)
General one-period economy 5 (10)
Pricing 6 (1)
Conditions for no arbitrage: existence 7 (2)
of Z
Completeness: uniqueness of Z 9 (3)
Probabilistic formulation 12 (3)
Units and numeraires 15 (1)
A two-period example 15 (4)
Brownian Motion 19 (12)
Introduction 19 (1)
Definition and existence 20 (1)
Basic properties of Brownian motion 21 (5)
Limit of a random walk 21 (2)
Deterministic transformations of 23 (1)
Brownian motion
Some basic sample path properties 24 (2)
Strong Markov property 26 (5)
Reflection principle 28 (3)
Martingales 31 (32)
Definition and basic properties 32 (3)
Classes of martingales 35 (6)
Martingales bounded in L1 35 (1)
Uniformly integrable martingales 36 (3)
Square-integrable martingales 39 (2)
Stopping times and the optional sampling 41 (8)
theorem
Stopping times 41 (4)
Optional sampling theorem 45 (4)
Variation, quadratic variation and 49 (7)
integration
Total variation and Stieltjes 49 (2)
integration
Quadratic variation 51 (4)
Quadratic covariation 55 (1)
Local martingales and semimartingales 56 (5)
The space cMloc 56 (3)
Semimartingales 59 (2)
Supermartingales and the Doob--Meyer 61 (2)
decomposition
Stochastic Integration 63 (28)
Outline 63 (2)
Predictable processes 65 (2)
Stochastic integrals: the L2 theory 67 (7)
The simplest integral 68 (1)
The Hilbert space L2(M) 69 (1)
The L2 integral 70 (2)
Modes of convergence to H • M 72 (2)
Properties of the stochastic integral 74 (3)
Extensions via localization 77 (4)
Continuous local martingales as 77 (1)
integrators
Semimartingales as integrators 78 (2)
The end of the road! 80 (1)
Stochastic calculus: Ito's formula 81 (10)
Integration by parts and Ito's formula 81 (2)
Differential notation 83 (2)
Multidimensional version of Ito's 85 (3)
formula
Levy's theorem 88 (3)
Girsanov and Martingale Representation 91 (24)
Equivalent probability measures and the 91 (8)
Randon--Nikodym derivative
Basic results and properties 91 (4)
Equivalent and locally equivalent 95 (2)
measures on a filtered space
Novikov's condition 97 (2)
Girsanov's theorem 99 (6)
Girsanov's theorem for continuous 99 (2)
semimartingales
Girsanov's theorem for Brownian motion 101 (4)
Martingale representation theorem 105 (10)
The space I2(M) and its orthogonal 106 (4)
complement
Martingale measures and the martingale 110 (1)
representation theorem
Extensions and the Brownian case 111 (4)
Stochastic Differential Equations 115 (26)
Introduction 115 (1)
Formal definition of an SDE 116 (1)
An aside on the canonical set-up 117 (2)
Weak and strong solutions 119 (6)
Weak solutions 119 (2)
Strong solutions 121 (3)
Tying together strong and weak 124 (1)
Establishing existence and uniqueness: 125 (9)
Ito theory
Picard--Lindelof iteration and ODEs 126 (1)
A technical lemma 127 (3)
Existence and uniqueness for Lipschitz 130 (4)
coefficients
Strong Markov property 134 (5)
Martingale representation revisited 139 (2)
Option Pricing in Continuous Time 141 (42)
Asset price processes and trading 142 (4)
strategies
A model for asset prices 142 (2)
Self-financing trading strategies 144 (2)
Pricing European options 146 (5)
Option value as a solution to a PDE 147 (2)
Option pricing via an equivalent 149 (2)
martingale measure
Continuous time theory 151 (25)
Information within the economy 152 (1)
Units, numeraires and martingale 153 (5)
measures
Arbitrage and admissible strategies 158 (5)
Derivative pricing in an arbitrage-free 163 (1)
economy
Completeness 164 (9)
Pricing kernels 173 (3)
Extensions 176 (7)
General payout schedules 176 (2)
Controlled derivative payouts 178 (1)
More general asset price processes 179 (1)
Infinite trading horizon 180 (3)
Dynamic Term Structure Models 183 (30)
Introduction 183 (1)
An economy of pure discount bonds 183 (4)
Modelling the term structure 187 (26)
Pure discount bond models 191 (1)
Pricing kernel approach 191 (1)
Numeraire models 192 (2)
Finite variation kernel models 194 (3)
Absolutely continuous (FVK) models 197 (1)
Short-rate models 197 (3)
Heath--Jarrow--Morton models 200 (6)
Flesaker--Hughston models 206 (7)
Part II: Practice 213 (46)
Modelling in Practice 215 (12)
Introduction 215 (1)
The real world is not a martingale measure 215 (3)
Modelling via infinitesimals 216 (1)
Modelling via macro information 217 (1)
Product-based modelling 218 (5)
A warning on dimension reduction 219 (2)
Limit cap valuation 221 (2)
Local versus global calibration 223 (4)
Basic Instruments and Terminology 227 (10)
Introduction 227 (1)
Deposits 227 (2)
Accrual factors and Libor 228 (1)
Forward rate agreements 229 (1)
Interest rate swaps 230 (2)
Zero coupon bonds 232 (1)
Discount factors and valuation 233 (4)
Discount factors 233 (1)
Deposit valuation 233 (1)
FRA valuation 234 (1)
Swap valuation 234 (3)
Pricing Standard Market Derivatives 237 (10)
Introduction 237 (1)
Forward rate agreements and swaps 237 (1)
Caps and floors 238 (4)
Valuation 240 (1)
Put-call parity 241 (1)
Vanilla swaptions 242 (2)
Digital options 244 (3)
Digital caps and floors 244 (1)
Digital swaptions 245 (2)
Futures Contracts 247 (12)
Introduction 247 (1)
Futures contract definition 247 (5)
Contract specification 248 (1)
Market risk without credit risk 249 (2)
Mathematical formulation 251 (1)
Characterizing the futures price process 252 (3)
Discrete resettlement 252 (1)
Continuous resettlement 253 (2)
Recovering the futures price process 255 (1)
Relationship between forwards and futures 256 (3)
Orientation: Pricing Exotic European 259 (56)
Derivatives
Terminal Swap-Rate Models 263 (14)
Introduction 263 (1)
Terminal time modelling 263 (3)
Model requirements 263 (2)
Terminal swap-rate models 265 (1)
Example terminal swap-rate models 266 (3)
The exponential swap-rate model 266 (1)
The geometric swap-rate model 267 (1)
The linear swap-rate model 268 (1)
Arbitrage-free property of terminal 269 (4)
swap-rate models
Existence of calibrating parameters 270 (1)
Extension of model to [0, ∞) 271 (2)
Arbitrage and the linear swap-rate model 273 (1)
Zero coupon swaptions 273 (4)
Convexity Corrections 277 (10)
Introduction 277 (1)
Valuation of `convexity-related' products 278 (4)
Affine decomposition of convexity 278 (2)
products
Convexity corrections using the linear 280 (2)
swap-rate model
Examples and extensions 282 (5)
Constant maturity swaps 283 (1)
Options on constant maturity swaps 284 (1)
Libor-in-arrears swaps 285 (2)
Implied Interest Rate Pricing Models 287 (16)
Introduction 287 (1)
Implying the functional form DTS 288 (4)
Numerical implementation 292 (1)
Irregular swaptions 293 (6)
Numerical comparison of exponential and 299 (4)
implied swap-rate models
Multi-Currency Terminal Swap-Rate Models 303 (12)
Introduction 303 (1)
Model construction 304 (4)
Log-normal case 305 (2)
General case: volatility smiles 307 (1)
Examples 308 (7)
Spread options 308 (3)
Cross-currency swaptions 311 (4)
Orientation: Pricing Exotic American and 315 (102)
Path-Dependent Derivatives
Short-Rate Models 319 (18)
Introduction 319 (1)
Well-known short-rate models 320 (5)
Vasicek--Hull--White model 320 (2)
Log-normal short-rate models 322 (1)
Cox--Ingersoll--Ross model 323 (1)
Multidimensional short-rate models 324 (1)
Parameter fitting within the 325 (4)
Vasicek--Hull--White model
Derivation of φ, Ψ and B.T 326 (1)
Derivation of ξ, ζ and η 327 (1)
Derivation of μ, λ and A.T 328 (1)
Bermudan swaptions via 329 (8)
Vasicek--Hull--White
Model calibration 330 (1)
Specifying the `tree' 330 (2)
Valuation through the tree 332 (1)
Evaluation of expected future value 332 (2)
Error analysis 334 (3)
Market Models 337 (14)
Introduction 337 (1)
Libor market models 338 (5)
Determining the drift 339 (2)
Existence of a consistent 341 (2)
arbitrage-free term structure model
Example application 343 (1)
Regular swap-market models 343 (4)
Determining the drift 344 (2)
Existence of a consistent 346 (1)
arbitrage-free term structure model
Example application 346 (1)
Reverse swap-market models 347 (4)
Determining the drift 348 (1)
Existence of a consistent 349 (1)
arbitrage-free term structure model
Example application 350 (1)
Markov-Functional Modelling 351 (22)
Introduction 351 (1)
Markov-functional models 351 (3)
Fitting a one-dimensional 354 (5)
Markov-functional model to swaption prices
Deriving the numeraire on a grid 355 (3)
Existence of a consistent 358 (1)
arbitrage-free term structure model
Example models 359 (4)
Libor model 359 (2)
Swap model 361 (2)
Multidimensional Markov-functional models 363 (2)
Log-normally driven Markov-functional 364 (1)
models
Relationship to market models 365 (2)
Mean reversion, forward volatilities and 367 (3)
correlation
Mean reversion and correlation 367 (1)
Mean reversion and forward volatilities 368 (1)
Mean reversion within the 369 (1)
Markov-functional Libor model
Some numerical results 370 (3)
Exercises and Solutions 373 (44)
Appendix 1 The Usual Conditions 417 (2)
Appendix 2 L2 Spaces 419 (2)
Appendix 3 Gaussian Calculations 421 (2)
References 423 (4)
Index 427