An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 20574.
Date of creation: 27 Jan 2010
Date of revision:
hybrid models; Heston equity model; Libor Market Model with stochastic volatility; displaced diffusion; affine diffusion; fast calibration.;
Find related papers by JEL classification:
- G1 - Financial Economics - - General Financial Markets
- F3 - International Economics - - International Finance
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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