Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
Saddlepoint methods for option pricing
Peter Carr, Dilip Madan
Abstract
ABSTRACT
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 λ. It is suggested that λ 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.
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