Asymptotic analysis for stochastic volatility: martingale expansion |
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Authors: | Masaaki Fukasawa |
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Institution: | 1.Center for the Study of Finance and Insurance,Osaka University,Osaka,Japan |
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Abstract: | A general class of stochastic volatility models with jumps is considered and an asymptotic expansion for European option prices
around the Black–Scholes prices is validated in the light of Yoshida’s martingale expansion theory. Several known formulas
of regular and singular perturbation expansions are obtained as corollaries. An expansion formula for the Black–Scholes implied
volatility is given which explains the volatility skew and term structure. The leading term of the expansion is always an
affine function of log moneyness, while the term structure of the coefficients depends on the details of the underlying stochastic
volatility model. Several specific models which represent various types of term structure are studied. |
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Keywords: | |
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