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Saddlepoint approximations to option prices. (English) Zbl 0963.91054

Summary: The use of saddle-point approximations in statistics is a well-established technique for computing the distribution of a random variables whose moment generating function is known. In this paper, we apply the methodology to computing the prices of various European-style options, whose returns processes are not the Brownian motion with drift assumed in the Black-Scholes paradigm. Through a number of examples, we show that the methodology is generally accurate and fast.

MSC:

91B28 Finance etc. (MSC2000)
62E17 Approximations to statistical distributions (nonasymptotic)
60J99 Markov processes
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