Geometrical Approximation method and stochastic volatility market models
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.
|Date of creation:||05 May 2010|
|Date of revision:|
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- Roger Lord & Remmert Koekkoek & Dick van Dijk, 2006.
"A Comparison of Biased Simulation Schemes for Stochastic Volatility Models,"
Tinbergen Institute Discussion Papers
06-046/4, Tinbergen Institute, revised 07 Jun 2007.
- Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
- Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
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