On the short-maturity behaviour of the implied volatility skew for random strike options and applications to option pricing approximation |
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Authors: | Elisa Alòs Jorge A León |
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Institution: | 1. Dpt. d’Economia i Empresa and Barcelona Graduate School of Economics, Universitat Pompeu Fabra, c/Ramon Trias Fargas, 25-27, 08005 Barcelona, Spain.;2. Control Automático, CINVESTAV-IPN, Apartado Postal 14-740, 07000 México, DF, Mexico. |
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Abstract: | In this paper, we propose a general technique to develop first- and second-order closed-form approximation formulas for short-maturity options with random strikes. Our method is based on a change of numeraire and on Malliavin calculus techniques, which allow us to study the corresponding short-maturity implied volatility skew and to obtain simple closed-form approximation formulas depending on the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches for two-asset and three-asset spread options such as Kirk’s formula or the decomposition method presented in Alòs et al. Energy Risk, 2011, 9, 52–57]. This methodology is not model-dependent, and it can be applied to the case of random interest rates and volatilities. |
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Keywords: | Spread options Girsanov’s Theorem Kirk’s formula Malliavin calculus Derivative operator in the Malliavin calculus sense Skorohod integral |
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