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Saddlepoint methods for option pricing. (English) Zbl 1178.91192

Summary: A single saddlepoint approximation for call prices seen as complementary probabilities that log price exceeds log strike by an independent exponential under the share measure is developed using a non-Gaussian base. The suggested base is that of a Gaussian random variable less an exponential with parameter \(\lambda\). It is suggested that \(\lambda\) be chosen to match the volatility under the share measure. The method is implemented and observed to be exact for the Black-Scholes model. Six other models with closed forms for the cumulant generating function are also investigated.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
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