摘要(英) |
Along with the rapid development of financial instruments, pricing options correctly and efficiently remains a critical issue both in industry and in academy. However, closedform
formulas for exotic or complicated options price rarely exist even under the standard Black-Scholes assumptions, and consequently additional numerical techniques are required. Among them, Monte Carlo approaches are invaluable tools and are easy to implement, but Monte Carlo estimators usually suffer from large variances. To tackle this problem, we propose an importance sampling procedure with an exponentially tilted measure to minimize the variance of Monte Carlo estimators. We apply our method to calculate both the price and the Greek letters for several popular options, such as spread and maximum options.
|
參考文獻 |
Boyle, P., M. Broadie, and P. Glasserman (1997). Monte carlo methods for security
pricing. Journal of Economic Dynamics and Control 21, 1267–1321.
Boyle, P. P. (1977). Options: A monte carlo approach. Journal of Financial Economics 4,
323–338.
Dupuis, P. and H. Wang (2004). Importance sampling, large deviations, and differential
games. Stochastics and Stochastics Reports 76 (6), 481–508.
Dupuis, P. and H. Wang (2005). Dynamic importance sampling for uniformly recurrent
markov chains. The Annals of Applied Probability 15 (1), 1–38.
Fu, M. C., D. B. Madan, and T. Wang (1999). Pricing continuous asian options a comparison
of monte carlo and laplace trandform inversion methods. Journal of Computational
Finance 2 (2), 49–74.
Glasserman, P., P. Heidelberger, and P. Shahabuddin (1999, April). Asymptotically optimal
importance sampling and stratification for pricing path-dependent options. Math-
ematical Finance 9, 117–152.
Glasserman, P. and Y. Wang (1997). Counterexamples in importance sampling for large
deviations probabilities. The Annals of Statistics 7 (3), 731–746.
Hull, J. and A. White (1988). The use of the control variate technique in option pricing.
Journal of Financial and Quantitative Analysis 23, 237–251.
Lyuu, Y.-D. and H.-W. Teng (2011). Unbiased and efficient greeks of financial options.
Finance and Stochastics, 141–181.
Pellizzari, P. (2001). Efficient monte carlo pricing of European options using mean value
control variates. In Proceedings of Decisions in Economics and Finance.
Ross, S. M. (2006). Simulation. ELSEVIER.
Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential test.
The Annals of Statistics 4 (4), 673–684.
Su, Y. and M. C. Fu (2000). Importance sampling in derivative securities pricing. In
Proceedings of the 2000 Winter Simulation Conference.
Vazquez-Abad, F. J. and D. Dufresne (1998). Accelerated simulation for pricing asian
options. In Proceedings of the 1998 Winter Simulation Conference.
|