Calibration of stochastic volatility models via second order approximation: the Heston model case
Using a suitable Hull and White type formula we develop a methodology to obtain a second order approximation to the implied volatility for very short maturities. Using this approximation we accurately calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short maturities so accurate is that we also take into account the term-structure for large maturities. We may say that calibration is not "memoryless", in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla options that can then be used to price exotic derivatives. The methodology is simple, accurate, fast, and it requires a minimal computational cost.
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- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
- Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010.
"FX Smile in the Heston Model,"
25491, University Library of Munich, Germany.
- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
- Agnieszka Janek & Tino Kluge & RafaÅ‚ Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," SFB 649 Discussion Papers SFB649DP2010-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," Papers 1010.1617, arXiv.org.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. Full references (including those not matched with items on IDEAS)
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