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.


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


[1] Bertoin, J. (1996). Lévy Processes. Cambridge Univ. Press. · Zbl 0861.60003
[2] Daniels, H. E. (1987). Tail probability approximations. Internat. Statistical Rev. 55 37-48. JSTOR: · Zbl 0614.62016
[3] Eberlein, E. and Keller, U. (1995). Hy perbolic distributions in finance. Bernoulli 1 281- 299. · Zbl 0836.62107
[4] Gerber, H. U. and Shiu, E. S. W. (1994). Option pricing by Esscher-transforms. Trans. Soc. Actuaries 46 99-140.
[5] Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Studies 6 327-343. · Zbl 1384.35131
[6] Heston, S. (1993). Invisible parameters in option prices. J. Finance 48 933-947.
[7] Hurst, S. R., Platen, E. and Rachev, S. T. (1995). A comparison of subordinated asset price models.
[8] Jensen, J. L. (1995). Saddlepoint Approximations. Oxford Univ. Press. · Zbl 1274.62008
[9] Lugannani, R. and Rice, S. (1980). Saddlepoint approximations for the distribution of the sum of independent random variables. Adv. Appl. Probab. 12 475-490. JSTOR: · Zbl 0425.60042
[10] Rogers, L. C. G. and Williams, D. (1987). Diffusions, Markov Processes, and Martingales 2. Wiley, Chichester. · Zbl 0977.60005
[11] Scott, L. O. (1997). Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: applications of Fourier inversion methods. Math. Finance 7 413- 426. · Zbl 1020.91030
[12] Wood, A. T. A., Booth, J. G. and Butler, W. (1993). Saddlepoint approximations to the CDF of some statistics with nonnormal limit distributions. J. Amer. Statist. Assoc. 88 680-686. JSTOR: · Zbl 0773.62008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.