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: http://hal.archives-ouvertes.fr/|
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- 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.
- Eric Benhamou & Emmanuel Gobet & Mohammed Miri, 2009. "Smart expansion and fast calibration for jump diffusion," Post-Print hal-00200395, HAL.
- Vladimir Piterbarg, 2005. "Stochastic Volatility Model with Time-dependent Skew," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 147-185.
- Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480.
- Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
- E. Benhamou & E. Gobet & M. Miri, 2010. "Expansion Formulas For European Options In A Local Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 603-634.
- Eric Benhamou & Emmanuel Gobet & Mohammed Miri, 2010. "Expansion formulas for European options in a local volatility model," Post-Print hal-00325939, HAL.
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