Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models
Heath, Jarrow and Morton Implied Volatility Functions and Conditional Heteroskedasticity Models

Author: Kaushik I. Amin

Publisher:

Published: 1998

Total Pages:

ISBN-13:

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We evaluate various popular models of interest rate volatility and the Heath-Jarrow-Morton (HJM) approach to value interest rate derivatives by studying the information content and the forecast ability of HJM implied volatility in the Eurodollar futures options market. Implied volatility corresponding to the Ho-Lee, Courtadon, Cox-Ingersoll-Ross, Vasicek, and a linear proportional volatility model are examined within the HJM framework. The exercise compares these implied volatilities to a number of historical volatility benchmarks based on the GARCH model, the Glosten-Jagannathan-Runkle model, and several hybrid models combining the Cox-Ingersoll-Ross and Courtadon spot rate models and the GARCH and GJR approaches to model interest rate volatility. Our results show that there is a strong interaction effect between return shocks and the level of the interest rates in the volatility dynamics that none of the existing HJM volatility models and none of the GARCH type models can fully capture. Specifically, the impact of a shock to interest rate volatility is higher under a high interest rate than a low interest rate. The importance of implied volatility from the Ho-Lee, Courtadon, and Cox-Ingersoll-Ross models is significantly reduced after a term capturing the interaction effect is added to the volatility specification. The importance of implied volatility from the linear proportional and the Vasicek models is reduced but they can still explain a reasonably large portion of the time-variation in volatility.

Stochastic Calculus for Finance II
Stochastic Calculus for Finance II

Author: Steven E. Shreve

Publisher: Springer Science & Business Media

Published: 2004-06-03

Total Pages: 586

ISBN-13: 9780387401010

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"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Interest Rate Models Theory and Practice
Interest Rate Models Theory and Practice

Author: Damiano Brigo

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 544

ISBN-13: 3662045532

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The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.

The Volatility Smile
The Volatility Smile

Author: Emanuel Derman

Publisher: John Wiley & Sons

Published: 2016-08-15

Total Pages: 532

ISBN-13: 1118959175

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The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.

Advances in Investment Analysis and Portfolio Management
Advances in Investment Analysis and Portfolio Management

Author: Cheng-Few Lee

Publisher: Elsevier

Published: 2001-09-14

Total Pages: 345

ISBN-13: 0080543979

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This research annual publication intends to bring together investment analysis and portfolio theory and their implementation to portfolio management. It seeks theoretical and empirical research manuscripts with high quality in the area of investment and portfolio analysis. The contents will consist of original research on: The principles of portfolio management of equities and fixed-income securities. The evaluation of portfolios (or mutual funds) of common stocks, bonds, international assets, and options. The dynamic process of portfolio management. Strategies of international investments and portfolio management. The applications of useful and important analytical techniques such as mathematics, econometrics, statistics, and computers in the field of investment and portfolio management. Theoretical research related to options and futures. In addition, it also contains articles that present and examine new and important accounting, financial, and economic data for managing and evaluating portfolios of risky assets.