| Description |
1 online resource (458 pages) |
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data file |
| Contents |
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. |
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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. |
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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. |
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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. |
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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. |
| Note |
12.3 The Quadratic Model. |
| Summary |
The authors consolidate and extend ideas from their previous book. Ideal for practitioners and as a graduate-level textbook. |
| Bibliography |
Includes bibliographical references (pages 430-438) and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Derivative securities -- Econometric models.
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Derivative securities -- Econometric models. |
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Derivative securities. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Author |
Papanicolaou, George.
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Sircar, Ronnie.
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Solna, Knut.
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| Other Form: |
Print version: Fouque, Jean-Pierre. Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives. Cambridge : Cambridge University Press, ©2011 9780521843584 |
| ISBN |
9781139158770 |
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1139158775 |
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9781139160827 (electronic book) |
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1139160826 (electronic book) |
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9781139020534 (electronic book) |
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1139020536 (electronic book) |
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9781139157018 (e-book) |
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1139157019 |
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9781139157018 |
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9780521843584 |
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0521843588 |
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