Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.
Accompanying CD-ROM contains ... "all pricing formulas, with VBA code and ready-to-use Excel spreadsheets and 3D charts for Greeks (or Option Sensitivities)."--Jacket.
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This classroom-tested text provides a deep understanding of derivative contracts. Unlike much of the existing literature, the book treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quanto, and Asian options. With many examples and exercises, the text relies on intuition and basic principles, rather than technical computations.
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
New Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research-including Risk magazine's 2013 Quant of the Year-Nonlinear Option Pricing compares various numerical methods for solving hi
This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous Heath-Jarrow-Morton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.
Measuring and Controlling Interest Rate and Credit Risk provides keys to using derivatives to control interest rate risk and credit risk, and controlling interest rate risk in a mortgage-backed securities derivative portfolio. This book includes information on measuring yield curve risk, swaps and exchange-traded options, TC options and related products, and describes how to measure and control the interest rate of risk of a bond portfolio or trading position. Measuring and Controlling Interest Rate and Credit Risk is a systematic evaluation of how to measure and control the interest rate risk and credit risk of a bond portfolio or trading position, defining key points in the process of risk management as related to financial situations. The authors construct a verbal flow chart, defining and illustrating interest rate risk and credit risk in regards to valuation, probability distributions, forecasting yield volatility, correlation and regression analyses. Hedging instruments discussed include futures contracts, interest rate swaps, exchange traded options, OTC options, and credit derivatives. The text includes calculated examples and readers will learn how to measure and control the interest rate risk and credit risk of a bond portfolio or trading position. They will discover value at risk approaches, valuation, probability distributions, yield volatility, futures, interest rate swaps, exchange traded funds; and find in-depth, up-to-date information on measuring interest rate with derivatives, quantifying the results of positions, and hedging. Frank J. Fabozzi (New Hope, PA) is a financial consultant, the Editor of the Journal of Portfolio Management, and an Adjunct Professor of Finance at Yale University?s School of Management. Steven V. Mann (Columbia, SC) is Professor of Finance at the Moore School of Business, University of South Carolina. Moorad Choudhry (Surrey, UK) is a Vice President with JPMorgan Chase structured finance services in London. Moorad Choudhry (Surrey, England) is a senior Fellow at the Centre for Mathematical Trading and Finance, CASS Business School, London, and is Editor of the Journal of Bond Trading and Management. He has authored a number of books on fixed income analysis and the capital markets. Moorad began his City career with ABN Amro Hoare Govett Sterling Bonds Limited, where he worked as a gilt-edged market maker, and Hambros Bank Limited where he was a sterling proprietary trader. He is currently a vice-president in Structured Finance Services with JPMorgan Chase Bank in London.
