"An Asymptotic Expansion with Push-Down of Malliavin Weights"
This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin weights are effectively applied. We provide an expansion formula for generalized Wiener functionals and closed-form approximation formulas in stochastic volatility environment. In addition, we present applications of the general formula to expansions of option prices for the shifted log-normal model with stochastic volatility. Moreover, with some results of Malliavin calculus in jump-type models, we derive an approximation formula for the jump-diffusion model in stochastic volatility environment. Some numerical examples are also shown.
Year of publication: |
2011-11
|
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Authors: | Takahashi, Akihiko ; Yajima, Yoshihiro |
Institutions: | Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics |
Saved in:
freely available
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