Asset Pricing

by Kariya, Takeaki; Liu, Regina Y.

• ISBN13: 9781402072437
• ISBN10: 1402072430
• Format: Hardcover
• Copyright: 2002-11-01
• Publisher: Kluwer Academic Pub

Summary

The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of Asset Pricing -Discrete Time Approach- is to provide a systematic exposition, with practical applications, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. Useful as a textbook on financial asset pricing, this book will also appeal to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science.

Table of Contents

Introduction	1	(8)
Main Goals	1	(1)
The Importance of The No-Arbitrage Theory	2	(1)
The Discrete Time Approach and Some Key Features of This Book	3	(1)
Comparisons with Other Textbooks	4	(2)
A Brief Summary of the Contents	6	(3)
Options, Futures and Other Derivatives	9	(18)
Overview	9	(1)
No-Arbitrage and Put-Call Parity	10	(9)
Exotic Options	19	(3)
Forward Contracts and Futures	22	(5)
Basic Probability Theory	27	(16)
Overview	27	(1)
Conditional Distributions and Conditional Expectations	28	(7)
Multivariate Normal Distribution and Normal Mixture Distribution	35	(4)
Nonlinear Time Series Model	39	(4)
Pricing Models for Financial Assets	43	(22)
Overview	43	(2)
Stochastic Processes and Brownian Motion	45	(6)
Martingale and Product Process	51	(5)
log-DD Process and Change of Probability Measures	56	(9)
General No-Arbitrage Asset Price Theory	65	(32)
Overview	65	(2)
Basic Framework of No-Arbitrage Price Theory	67	(3)
Condition for No-Arbitrage	70	(4)
Price Theory for Derivatives and the Black-Scholes Formula	74	(6)
No-Arbitrage Binomial Process and Replicability of an Option	80	(8)
Martingale Condition for log-DD Process	88	(9)
Model Specifications in Applications	97	(14)
Overview	97	(3)
Self-Consistency Tests for Models	100	(5)
Multi-Factor Model -- Identifiability and Estimation	105	(2)
Model under Original Measure Q vs Risk Neutral Model under Equivalent Measure Q*	107	(4)
Valuation of Derivatives Via Monte Carlo Methods	111	(28)
Overview	111	(1)
Monte Carlo Method	112	(5)
Variance Reduction Methods	117	(16)
General Theory for CV Methods	133	(6)
Stock Option Theory and its Applications	139	(28)
Overview	139	(1)
General Price Theory for a Stock Option	140	(3)
Black-Scholes (BS) Formula	143	(6)
BS Option Portfolios	149	(4)
Valuation of Exotic Options	153	(4)
Garch Model and Stochastic Volatility Model	157	(5)
Valuation of an American Put	162	(5)
Currency Options	167	(14)
Overview	167	(1)
Pricing Currency Options	168	(4)
Currency Options Containing Stocks	172	(3)
A Condition for No-Arbitrage	175	(6)
The Term Structure of Spot Rates	181	(20)
Overview	181	(1)
Spot Rate and No-Arbitrage Price of a Discount Bond	182	(6)
One Factor Term Structure Model for Spot Rates	188	(6)
Empirical Viewpoint on CIR Type Model	194	(2)
Interest Swaps	196	(5)
The HJM Model For Bonds and its Applications	201	(28)
Overview	201	(1)
Forward Rates	202	(4)
The K-Factor HJM Model for Discount Bond Price	206	(7)
Specification Problems of HJM Model	213	(4)
Specification of Volatility Functions	217	(5)
Empirical Analyses of Interest Futures	222	(7)
Pricing Defaultable Bonds	229	(10)
Overview	229	(1)
Recovery Rate and Default Probability	230	(1)
Valuation of Corporate Discount Bond	231	(6)
Pricing a Coupon Bond	237	(2)
Valuation of CD with Transfer Option	239	(12)
Overview	239	(1)
Valuation of a CD with Transfer Option	239	(4)
Valuation of the Transfer Option	243	(2)
Valuation of the Closing Option	245	(1)
Ex Post Multiplier and Risk of the Bank	246	(5)
Pricing Mortgage-Backed Securities	251	(18)
Overview	251	(2)
Cashflow Function of an MBS	253	(1)
Valuation Formula for an MBS	254	(4)
Interest Incentive Function	258	(3)
Monte Carlo (MC) Valuation of an MBS	261	(6)
Estimation Procedure	267	(2)
References	269	(4)
Index	273