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Geometrical Considerations on Heston's Market Model

Dell'Era, Mario (2010): Geometrical Considerations on Heston's Market Model. Forthcoming in: Quantitative Finanace

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Abstract

We propose to discuss a new technique to derive an good approximated solution for the price of a European call and put options, in a market model with stochastic volatility. In particular, the model that we have considered is the Heston's model. This allows arbitrary correlation between volatility and spot asset returns. We are able to write the price of European call and put, in the same form in which one can see in the Black-Scholes model. The solution technique is based upon coordinate transformations that reduce the initial PDE in a straightforward one-dimensional heat equation.

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