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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. repec:cup:cbooks:9780521843584 is not listed on IDEAS
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    JEL classification:

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

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