Multiscale stochastic volatility for equity, interest rate, and credit derivatives / / Jean-Pierre Fouque [and others] [[electronic resource]]

• Record Nr.: UNINA9910457520303321
• Autore: Fouque Jean-Pierre
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2011
• ISBN: 1-107-22565-5; 1-283-34216-2; 1-139-15982-8; 9786613342164; 1-139-16082-6; 1-139-15526-1; 1-139-15701-9; 1-139-15877-5; 1-139-02053-6
• Descrizione fisica: 1 online resource (xiii, 441 pages) : digital, PDF file(s)
• Disciplina: 332.642015195
• Soggetti: Derivative securities - Econometric models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; MULTISCALE STOCHASTIC VOLATILITY FOR EQUITY, INTEREST RATE, AND CREDIT DERIVATIVES; Title; Copyright; To our families and students; Contents; Introduction; 1 The Black-Scholes Theory of Derivative Pricing; 1.1 Market Model; 1.2 Derivative Contracts; 1.3 Replicating Strategies; 1.4 Risk-Neutral Pricing; 1.5 Risk-Neutral Expectations and Partial Differential Equations; 1.6 American Options and Free Boundary Problems; 1.7 Path-Dependent Derivatives; 1.8 First-Passage Structural Approach to Default; 1.9 Multidimensional Stochastic Calculus; 1.10 Complete Market; 2 Introduction to Stochastic Volatility Models2.1 Implied Volatility Surface; 2.2 Local Volatility; 2.3 Stochastic Volatility Models; 2.4 Derivative Pricing; 2.5 General Results on Stochastic Volatility Models; 2.6 Summary and Conclusions; 3 Volatility Time Scales; 3.1 A Simple Picture of Fast and Slow Time Scales; 3.2 Ergodicity and Mean-Reversion; 3.3 Examples of Mean-Reverting Processes; 3.4 Time Scales ; in Synthetic Returns Data; 3.5 Time Scales in Market Data; 3.6 Multiscale Models; 4 First-Order Perturbation Theory; 4.1 Option Pricing under Multiscale Stochastic Volatility; 4.2 Formal Regular and Singular Perturbation Analysis4.3 Parameter Reduction; 4.4 First-Order Approximation: Summary and Discussion; 4.5 Accuracy of First-Order Approximation; 5 Implied Volatility Formulas and Calibration; 5.1 Approximate Call Prices and Implied Volatilities; 5.2 Calibration Procedure; 5.3 Illustration with S&P 500 Data; 5.4 Maturity Cycles; 5.5 Higher-Order Corrections; 6 Application to Exotic Derivatives; 6.1 European Binary Options; 6.2 Barrier Options; 6.3 Asian Options; 7 Application to American Derivatives; 7.1 American Options Valuation under Stochastic Volatility; 7.2 Stochastic Volatility Correction for American Put7.3 Parameter Reduction; 7.4 Summary; 8 Hedging Strategies; 8.1 Black-Scholes Delta Hedging; 8.2 The Strategy and its Cost; 8.3 Mean Self-Financing Hedging Strategy; 8.4 A Strategy with Frozen Parameters; 8.5 Strategies Based on Implied Volatilities; 8.6 Martingale Approach to Pricing; 8.7 Non-Markovian Models of Volatility; 9 Extensions; 9.1 Dividends and Varying Interest Rates; 9.2 Probabilistic Representation of the Approximate Prices; 9.3 Second-Order Correction from Fast Scale; 9.4 Second-Order Corrections from Slow and Fast Scales; 9.5 Periodic Day Effect9.6 Markovian Jump Volatility Models; 9.7 Multidimensional Models; 10 Around the Heston Model; 10.1 The Heston Model; 10.2 Approximations to the Heston Model; 10.3 A Fast Mean-Reverting Correction to the Heston Model; 10.4 Large Deviations and Short Maturity Asymptotics; 11 Other Applications; 11.1 Application to Variance Reduction in Monte Carlo Computations; 11.2 Portfolio Optimization under Stochastic Volatility; 11.3 Application to CAPM Forward-Looking Beta Estimation; 12 Interest Rate Models; 12.1 The Vasicek Model; 12.2 The Bond Price and its Expansion; 12.3 The Quadratic Model
• Sommario/riassunto: Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.