New approximations in local volatility models
For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. Averaging both expansions give even more accurate results. Approximations of the implied volatility are provided as well.
|Date of creation:||2013|
|Date of revision:|
|Publication status:||Published, Inspired by Finance. The Musiela Festschrift, Springer (Ed.), 2013, 305--330|
|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00523369|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
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- Eric Benhamou & Emmanuel Gobet & Mohammed Miri, 2010. "Expansion formulas for European options in a local volatility model," Post-Print hal-00325939, HAL.
- 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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