The arbitrage-free Multivariate Mixture Dynamics Model: Consistent single-assets and index volatility smiles
AbstractWe introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each underlying shows a volatility smile and is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows to reconcile single name and index/basket volatility smiles in a consistent framework. Rather than simply correlating one-dimensional local volatility models for each asset, our approach could be dubbed a multidimensional local volatility approach with state dependent diffusion matrix. The model is quite tractable, leading to a complete market and not requiring Fourier techniques, contrary to multivariate stochastic volatility models such as Wishart. We provide a semi-analytic formula for the price of European options on a basket/index of securities. A comparison with the standard approach consisting in using Monte Carlo simulation that samples simply-correlated suitably discretized one-dimensional paths is made. Our results show that our approach is promising in terms of basket option pricing. We also introduce a multivariate uncertain volatility model of which our multivariate local volatilities model is a multivariate markovian projection and analyze the dependence structure induced by our multivariate dynamics in detail. A few numerical examples on simple contracts conclude the paper.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.7010.
Date of creation: Feb 2013
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Web page: http://arxiv.org/
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- NEP-ALL-2013-03-02 (All new papers)
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