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

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Abstract
We define an equityinterest 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 displaceddiffusion stochastic volatility Libor Market Model [AA02]. We assume a nonzero 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 equityinterest 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 

Original Title:  An EquityInterest 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:  13. Feb 2013 03:05 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/20574 