An Asymptotic Expansion with Push-Down of Malliavin Weights
AbstractThis paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in a stochastic volatility model. In particular, the integration-by-parts formula in Malliavin calculus and the push-down of Malliavin weights are effectively applied. It provides an expansion formula for generalized Wiener functionals and closed-form approximation formulas in stochastic volatility environment. In addition, it presents applications of the general formula to a local volatility expansion as well as to expansions of option prices for the shifted log-normal model with stochastic volatility. Moreover, with some result of Malliavin calculus in jump-type models, this paper derives an approximation formula for the jump-diffusion model in stochastic volatility environment. Some numerical examples are also shown.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-695.
Date of creation: Dec 2009
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-10 (All new papers)
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- Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
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