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Calibration of stochastic volatility models via second order approximation: the Heston model case

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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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  • Elisa Alòs & Rafael De Santiago & Josep Vives, 2012. "Calibration of stochastic volatility models via second order approximation: the Heston model case," Economics Working Papers 1346, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1346
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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
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    4. Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010. "FX Smile in the Heston Model," MPRA Paper 25491, University Library of Munich, Germany.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    7. Fabio Antonelli & Sergio Scarlatti, 2009. "Pricing options under stochastic volatility: a power series approach," Finance and Stochastics, Springer, vol. 13(2), pages 269-303, April.
    8. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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