## Fourier Transform Methods in FinanceIn recent years, Fourier transform methods have emerged as one ofthe major methodologies for the evaluation of derivative contracts,largely due to the need to strike a balance between the extensionof existing pricing models beyond the traditionalBlack-Scholes setting and a need to evaluate pricesconsistently with the market quotes.
Readers will learn how to: - compute the Hilbert transform of the pricing kernel under aFast Fourier Transform (FFT) technique
- characterise the price dynamics on a market in terms of thecharacteristic function, allowing for both diffusive processes andjumps
- apply the concept of characteristic function to non-stationaryprocesses, in particular in the presence of stochastic volatilityand more generally time change techniques
- perform a change of measure on the characteristic function inorder to make the price process a martingale
- recover a general representation of the pricing kernel of theeconomy in terms of Hilbert transform using the theory ofgeneralised functions
- apply the pricing formula to the most famous pricing models,with stochastic volatility and jumps.
Junior and senior practitioners alike will benefit from thisquick reference guide to state of the art models and marketcalibration techniques. Not only will it enable them to write analgorithm for option pricing using the most advanced models,calibrate a pricing model on options data, and extract the impliedprobability distribution in market data, they will also understandthe most advanced models and techniques and discover how thesetechniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9 |

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### Contents

The Dynamics of Asset Prices | 29 |

vi | 39 |

ArbitrageFree Pricing | 79 |

Generalized Functions | 95 |

The Fourier Transform | 113 |

Fourier Transforms at Work | 129 |

xiii | 144 |

Appendices | 153 |

12 | 177 |

Complex Integration | 185 |

Vector Spaces and Function Spaces | 201 |

E The Fast Fourier Transform | 207 |

14 | 210 |

F The Fractional Fast Fourier Transform | 215 |

The Path Integral Approach | 225 |

230 | |

### Other editions - View all

Fourier Transform Methods in Finance Umberto Cherubini,Giovanni Della Lunga,Sabrina Mulinacci,Pietro Rossi No preview available - 2010 |

Fourier Transform Methods in Finance Umberto Cherubini,Giovanni Della Lunga,Sabrina Mulinacci,Pietro Rossi No preview available - 2010 |

Fourier Transform Methods in Finance Umberto Cherubini,Giovanni Della Lunga,Sabrina Mulinacci,Pietro Rossi No preview available - 2010 |