Grzelak, Lech and Oosterlee, Kees
(2010):
*An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile.*

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## Abstract

We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the dimension of the corresponding pricing PDE can be greatly reduced. We place by a number of approximations the model in the class of affine processes [DPS00], for which we then provide the corresponding forward characteristic function. We discuss in detail the accuracy of the approximations and the efficient calibration. Finally, by experiments, we show the effect of the correlations and interest rate smile/skew on typical equity-interest rate hybrid product prices. For a whole strip of strikes this approximate hybrid model can be evaluated for equity plain vanilla options in just milliseconds.

Item Type: | MPRA Paper |
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Original Title: | An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile |

Language: | English |

Keywords: | hybrid models; Heston equity model; Libor Market Model with stochastic volatility; displaced diffusion; affine diffusion; fast calibration. |

Subjects: | G - Financial Economics > G1 - General Financial Markets F - International Economics > F3 - International Finance G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing |

Item ID: | 20574 |

Depositing User: | Lech A. Grzelak |

Date Deposited: | 09 Feb 2010 14:13 |

Last Modified: | 27 Sep 2019 13:13 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/20574 |