Ebook: Interest Rate Dynamics, Derivatives Pricing, and Risk Management

There are two types of tenn structure models in the literature: the equilibrium models and the no-arbitrage models. And there are, correspondingly, two types of interest rate derivatives pricing fonnulas based on each type of model of the tenn structure. The no-arbitrage models are characterized by the work of Ho and Lee (1986), Heath, Jarrow, and Morton (1992), Hull and White (1990 and 1993), and Black, Dennan and Toy (1990). Ho and Lee (1986) invent the no-arbitrage approach to the tenn structure modeling in the sense that the model tenn structure can fit the initial (observed) tenn structure of interest rates. There are a number of disadvantages with their model. First, the model describes the whole volatility structure by a sin­ gle parameter, implying a number of unrealistic features. Furthennore, the model does not incorporate mean reversion. Black-Dennan-Toy (1990) develop a model along tbe lines of Ho and Lee. They eliminate some of the problems of Ho and Lee (1986) but create a new one: for a certain specification of the volatility function, the short rate can be mean-fteeting rather than mean-reverting. Heath, Jarrow and Morton (1992) (HJM) construct a family of continuous models of the term struc­ ture consistent with the initial tenn structure data.

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This book presents a three-factor model of the term structure of interest rates in which the short mean and volatility of the short rate are stochastic. By this specification, this model has nested many of the term structure models in the existing literature. Based on this rather realistic and sophisticated model, the book further shows how to price interest rate derivatives and to formulate risk management scheme. The model is potentially useful for practical purposes such as pricing bonds, hedging bond portfolios, and formulating dynamic trading strategies. The model could also be used to perform other types of security analyses, such as the valuation of mortgage-backed securities, synthetic security construction, immunization, portfolio indexing, asset/liability management, etc.

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This book presents a three-factor model of the term structure of interest rates in which the short mean and volatility of the short rate are stochastic. By this specification, this model has nested many of the term structure models in the existing literature. Based on this rather realistic and sophisticated model, the book further shows how to price interest rate derivatives and to formulate risk management scheme. The model is potentially useful for practical purposes such as pricing bonds, hedging bond portfolios, and formulating dynamic trading strategies. The model could also be used to perform other types of security analyses, such as the valuation of mortgage-backed securities, synthetic security construction, immunization, portfolio indexing, asset/liability management, etc.
Content:
Front Matter....Pages i-xii
A Three-Factor Model of the Term Structure of Interest Rates....Pages 1-36
Pricing Interest Rate Derivatives....Pages 37-60
Pricing Exotic Options....Pages 61-70
Fitting to a Given Term Structure....Pages 71-75
A Discrete-Time Version of the Model....Pages 77-94
Estimation of the Model....Pages 95-103
Managing Interest Rate Risk....Pages 105-117
Extensions of the Model....Pages 119-124
Concluding Remarks....Pages 125-126
Back Matter....Pages 127-152

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This book presents a three-factor model of the term structure of interest rates in which the short mean and volatility of the short rate are stochastic. By this specification, this model has nested many of the term structure models in the existing literature. Based on this rather realistic and sophisticated model, the book further shows how to price interest rate derivatives and to formulate risk management scheme. The model is potentially useful for practical purposes such as pricing bonds, hedging bond portfolios, and formulating dynamic trading strategies. The model could also be used to perform other types of security analyses, such as the valuation of mortgage-backed securities, synthetic security construction, immunization, portfolio indexing, asset/liability management, etc.
Content:
Front Matter....Pages i-xii
A Three-Factor Model of the Term Structure of Interest Rates....Pages 1-36
Pricing Interest Rate Derivatives....Pages 37-60
Pricing Exotic Options....Pages 61-70
Fitting to a Given Term Structure....Pages 71-75
A Discrete-Time Version of the Model....Pages 77-94
Estimation of the Model....Pages 95-103
Managing Interest Rate Risk....Pages 105-117
Extensions of the Model....Pages 119-124
Concluding Remarks....Pages 125-126
Back Matter....Pages 127-152
....