Arbitrage theory in continuous time

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Arbitrage theory in continuous time / Tomas Björk

版:: 2nd ed
資料種別:: 図書
出版情報:: Oxford : Oxford University Press, 2004
形態:: xviii, 466 p. ; 24 cm
著者名:: Björk, Tomas <DA11882433>
ISBN:: 9780199271269 [0199271267] (: hbk)
書誌ID:: BA66508939

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Arbitrage theory in continuous time. 3rd ed (: hbk)
Tomas Björk , Oxford University Press , 2009

書誌詳細

注記:

Includes bibliographical references (p. [453]-460) and index

主題:

Arbitrage; Arbitrage--Mathematical models

言語:

英語

目次情報:

Introduction / 1：

Problem Formulation / 1.1：

The Binomial Model / 2：

The One Period Model / 2.1：

Model Description / 2.1.1：

Portfolios and Arbitrage / 2.1.2：

Contingent Claims / 2.1.3：

Risk Neutral Valuation / 2.1.4：

The Multiperiod Model / 2.2：

Exercises / 2.2.1：

Notes / 2.4：

A More General One Period Model / 3：

The Model / 3.1：

Absence of Arbitrage / 3.2：

Martingale Pricing / 3.3：

Completeness / 3.4：

Stochastic Discount Factors / 3.5：

Stochastic Integrals / 3.6：

Information / 4.1：

Martingales / 4.3：

Stochastic Calculus and the Ito Formula / 4.5：

Examples / 4.6：

The Multidimensional Ito Formula / 4.7：

Correlated Wiener Processes / 4.8：

Differential Equations / 4.9：

Stochastic Differential Equations / 5.1：

Geometric Brownian Motion / 5.2：

The Linear SDE / 5.3：

The Infinitesimal Operator / 5.4：

Partial Differential Equations / 5.5：

The Kolmogorov Equations / 5.6：

Portfolio Dynamics / 5.7：

Self-financing Portfolios / 6.1：

Dividends / 6.3：

Exercise / 6.4：

Arbitrage Pricing / 7：

Contingent Claims and Arbitrage / 7.1：

The Black-Scholes Equation / 7.3：

The Black-Scholes Formula / 7.4：

Options on Futures / 7.6：

Forward Contracts / 7.6.1：

Futures Contracts and the Black Formula / 7.6.2：

Volatility / 7.7：

Historic Volatility / 7.7.1：

Implied Volatility / 7.7.2：

American options / 7.8：

Completeness and Hedging / 7.9：

Completeness in the Black-Scholes Model / 8.1：

Completeness-Absence of Arbitrage / 8.3：

Parity Relations and Delta Hedging / 8.4：

Parity Relations / 9.1：

The Greeks / 9.2：

Delta and Gamma Hedging / 9.3：

The Martingale Approach to Arbitrage Theory / 9.4：

The Case with Zero Interest Rate / 10.1：

A Rough Sketch of the Proof / 10.2：

Precise Results / 10.2.2：

The General Case / 10.3：

Summary for the Working Economist / 10.4：

The Mathematics of the Martingale Approach / 10.8：

Stochastic Integral Representations / 11.1：

The Girsanov Theorem: Heuristics / 11.2：

The Girsanov Theorem / 11.3：

The Converse of the Girsanov Theorem / 11.4：

Girsanov Transformations and Stochastic Differentials / 11.5：

Maximum Likelihood Estimation / 11.6：

Black-Scholes from a Martingale Point of View / 11.7：

Pricing / 12.1：

Multidimensional Models: Classical Approach / 12.3：

Reducing the State Space / 13.1：

Hedging / 13.5：

Multidimensional Models: Martingale Approach / 13.6：

Markovian Models and PDEs / 14.1：

Market Prices of Risk / 14.6：

The Hansen-Jagannathan Bounds / 14.7：

Incomplete Markets / 14.9：

A Scalar Nonpriced Underlying Asset / 15.1：

The Multidimensional Case / 15.3：

A Stochastic Short Rate / 15.4：

The Martingale Approach / 15.5：

Summing Up / 15.6：

Discrete Dividends / 15.7：

Price Dynamics and Dividend Structure / 16.1.1：

Pricing Contingent Claims / 16.1.2：

Continuous Dividends / 16.2：

Continuous Dividend Yield / 16.2.1：

Currency Derivatives / 16.2.2：

Pure Currency Contracts / 17.1：

Domestic and Foreign Equity Markets / 17.2：

Domestic and Foreign Market Prices of Risk / 17.3：

Barrier Options / 17.4：

Mathematical Background / 18.1：

Out Contracts / 18.2：

Down-and-Out Contracts / 18.2.1：

Up-and-Out Contracts / 18.2.2：

In Contracts / 18.2.3：

Ladders / 18.4：

Lookbacks / 18.5：

Stochastic Optimal Control / 18.6：

An Example / 19.1：

The Formal Problem / 19.2：

The Hamilton-Jacobi-Bellman Equation / 19.3：

Handling the HJB Equation / 19.4：

The Linear Regulator / 19.5：

Optimal Consumption and Investment / 19.6：

A Generalization / 19.6.1：

Optimal Consumption / 19.6.2：

The Mutual Fund Theorems / 19.7：

The Case with No Risk Free Asset / 19.7.1：

The Case with a Risk Free Asset / 19.7.2：

Bonds and Interest Rates / 19.8：

Zero Coupon Bonds / 20.1：

Interest Rates / 20.2：

Definitions / 20.2.1：

Relations between df(t,T), dp(t,T), and dr(t) / 20.2.2：

An Alternative View of the Money Account / 20.2.3：

Coupon Bonds, Swaps, and Yields / 20.3：

Fixed Coupon Bonds / 20.3.1：

Floating Rate Bonds / 20.3.2：

Interest Rate Swaps / 20.3.3：

Yield and Duration / 20.3.4：

Short Rate Models / 20.4：

Generalities / 21.1：

The Term Structure Equation / 21.2：

Martingale Models for the Short Rate / 21.3：

Q-dynamics / 22.1：

Inversion of the Yield Curve / 22.2：

Affine Term Structures / 22.3：

Definition and Existence / 22.3.1：

A Probabilistic Discussion / 22.3.2：

Some Standard Models / 22.4：

The Vasicek Model / 22.4.1：

The Ho-Lee Model / 22.4.2：

The CIR Model / 22.4.3：

The Hull-White Model / 22.4.4：

Forward Rate Models / 22.5：

The Heath-Jarrow-Morton Framework / 23.1：

Martingale Modeling / 23.2：

The Musiela Parameterization / 23.3：

Change of Numeraire / 23.4：

Changing the Numeraire / 24.1：

Forward Measures / 24.4：

Using the T-bond as Numeraire / 24.4.1：

An Expectation Hypothesis / 24.4.2：

A General Option Pricing Formula / 24.5：

The General Gaussian Model / 24.6：

Caps and Floors / 24.8：

LIBOR and Swap Market Models / 24.9：

Caps: Definition and Market Practice / 25.1：

The LIBOR Market Model / 25.2：

Pricing Caps in the LIBOR Model / 25.3：

Terminal Measure Dynamics and Existence / 25.4：

Calibration and Simulation / 25.5：

The Discrete Savings Account / 25.6：

Swaps / 25.7：

Swaptions: Definition and Market Practice / 25.8：

The Swap Market Models / 25.9：

Pricing Swaptions in the Swap Market Model / 25.10：

Drift Conditions for the Regular Swap Market Model / 25.11：

Concluding Comment / 25.12：

Forwards and Futures / 25.13：

Futures Contracts / 26.1：

Measure and Integration / 26.3：

Sets and Mappings / A.1：

Measures and Sigma Algebras / A.2：

Integration / A.3：

Sigma-Algebras and Partitions / A.4：

Sets of Measure Zero / A.5：

The L[superscript p] Spaces / A.6：

Hilbert Spaces / A.7：

Sigma-Algebras and Generators / A.8：

Product measures / A.9：

The Lebesgue Integral / A.10：

The Radon-Nikodym Theorem / A.11：

Probability Theory / A.12：

Random Variables and Processes / B.1：

Partitions and Information / B.2：

Sigma-algebras and Information / B.3：

Independence / B.4：

Conditional Expectations / B.5：

Equivalent Probability Measures / B.6：

Martingales and Stopping Times / B.7：

Discrete Stochastic Integrals / C.1：

Likelihood Processes / C.3：

Stopping Times / C.4：

References / C.5：

Index

Introduction / 1：

Problem Formulation / 1.1：

The Binomial Model / 2：

The One Period Model / 2.1：

Model Description / 2.1.1：

Portfolios and Arbitrage / 2.1.2：

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