Geometrical Approximation method and stochastic volatility market models

Dell'Era, Mario (2010): Geometrical Approximation method and stochastic volatility market models. Forthcoming in: Wilmott Magazine

Abstract

We propose to discuss a new technique to derive an good approximated solution for the price of a European Vanilla options, in a market model with stochastic volatility. In particular, the models that we have considered are the Heston and SABR(for beta=1). These models allow 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Financial pricing method
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; I - Health, Education, and Welfare > I2 - Education and Research Institutions > I22 - Educational Finance ; Financial Aid

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