Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
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 sto...
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| Hlavní autoři: | , , , |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge ; Tokyo
Cambridge University Press
2011
Cambridge Univ. Press |
| Vydání: | 1 |
| Témata: | |
| ISBN: | 0521843588, 9780521843584 |
| On-line přístup: | Získat plný text |
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Obsah:
- 7.2 Stochastic Volatility Correction for American Put -- 7.3 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 Effect -- 9.6 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 -- 12.4 The CIR Model -- 12.5 Options on Bonds -- 13 Credit Risk I: Structural Models with Stochastic Volatility -- 13.1 Single-Name Credit Derivatives -- 13.2 Multiname Credit Derivatives -- 14 Credit Risk II: Multiscale Intensity-Based Models -- 14.1 Background on Stochastic Intensity Models -- 14.2 Multiname Credit Derivatives -- 14.3 Symmetric Vasicek Model -- 14.4 Homogeneous Group Structure -- 15 Epilogue -- References -- Index
- 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 Models -- 2.1 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 Analysis -- 4.3 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