## Derivatives in Financial Markets with Stochastic VolatilityThis important work addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. The authors present mathematical and statistical tools that exploit the volatile nature of the market. The mathematics is introduced through examples and illustrated with simulations and the modeling approach that is described is validated and tested on market data. The material is suitable for a one-semester course for graduate students with some exposure to methods of stochastic modeling and arbitrage pricing theory in finance. The volume is easily accessible to derivatives practitioners in the financial engineering industry. |

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### Contents

Introduction to Stochastic Volatility Models | 33 |

Scales in MeanReverting Stochastic Volatility | 58 |

Tools for Estimating the Rate of Mean Reversion | 77 |

Asymptotics for Pricing European Derivatives | 87 |

Implementation and Stability | 108 |

Application to Exotic Derivatives | 124 |

Application to American Derivatives | 132 |

Generalizations | 145 |

Applications to InterestRate Models | 174 |

195 | |

### Common terms and phrases

arbitrage asset price asymptotic analysis average Black-Scholes formula Black-Scholes price bond price Chapter coefficients compute constant volatility contract correlation deduce defined denote depend derivative prices discounted equivalent martingale measure ergodic estimated European derivative example exponential fast mean Figure fluctuations free boundary Gaussian geometric Brownian motion given group parameters h(XT implied volatility surface independent infinitesimal invariant distribution Ito's formula lognormal market price Markov process Markovian maturity maximum expected utility mean reversion mean-reverting stochastic volatility no-arbitrage price notation observed obtained Papanicolaou partial differential equation payoff function Poisson equation portfolio price of volatility pricing function problem put option rate of mean respect risky asset satisfies self-financing short rate simulated skew solution solved standard Brownian motion stochastic differential equation stochastic integral stochastic volatility correction stochastic volatility model stock price strike price terminal condition tion variogram Vasicek model volatility process volatility risk yield curve zero

### References to this book

Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |

Stochastic Calculus of Variations in Mathematical Finance Paul Malliavin,Anton Thalmaier No preview available - 2005 |