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Sensitivity Analysis for Monte Carlo Simulation of Option Pricing

Published online by Cambridge University Press:  27 July 2009

Michael C. Fu  and
Jian-Qlang Hu
Michael C. Fu
Affiliation:
College of Business and Management, University of Maryland, College Park, Maryland 20742
Jian-Qlang Hu
Affiliation:
Department of Manufacturing Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215
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Abstract

Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing, which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 3 , July 1995 , pp. 417 - 446
Copyright
Copyright © Cambridge University Press 1995

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References

1.Boyle, P.P. (1977).Options: A Monte Carlo approach. Journal of Financial Economics 4: 323–338.CrossRefGoogle Scholar
2.Broadie, M. & Glasserman, P. (1993). Estimating security price derivatives using simulation (submitted for publication).Google Scholar
3.Cox, J.C. & Ross, S.A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics 3: 145–166.CrossRefGoogle Scholar
4.Duffie, D. & Glynn, P. (1993). Efficient Monte Carlo simulation of security prices. Working Paper, Stanford University, Stanford, CA.Google Scholar
5.Figlewski, S. (1989). Options arbitrage in imperfect markets. Journal of Finance XLIV: 1289–1311.CrossRefGoogle Scholar
6.Fu, M.C. (1994). Optimization via simulation: A review. Annals of Operations Research 53: 199–248.CrossRefGoogle Scholar
7.Fu, M.C. & Hu, J.Q. (1992). Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework. IEEE Transactions on Automatic Control 37: 1483–1500.CrossRefGoogle Scholar
8.Fu, M.C. & Hu, J.Q. (1993). Sensitivity analysis for Monte Carlo simulation of option pricing. Working Paper, University of Maryland, College of Business and Management, College Park.Google Scholar
9.Glasserman, P. (1991). Gradient estimation via perturbation analysis. Amsterdam: Kluwer Academic.Google Scholar
10.Gong, W.B. & Ho, Y.C. (1987). Smoothed perturbation analysis of discrete-event dynamic system's. IEEE Transactions on Automatic Control 32: 858–867.CrossRefGoogle Scholar
11.Grant, D., Vora, G. & Weeks, D. (1993). Path-dependent options: Extending the Monte Carlo simulation approach. Working Paper, University of New Mexico, Albuquerque.Google Scholar
12.Harrison, J.M. & Pliska, S. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications 11: 215–260.CrossRefGoogle Scholar
13.Ho, Y.C. & Cao, X.R. (1991). Discrete event dynamic systems and perturbation analysis. Amsterdam: Kluwer Academic.CrossRefGoogle Scholar
14.Hull, J.C. (1993). Options, futures, and other derivative securities, 2nd ed.. New York: Prentice-Hall.Google Scholar
15.Hull, J.C. & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance 42: 281–300.CrossRefGoogle Scholar
16.Johnson, H. & Shanno, D. (1987). Option pricing when the variance is changing. Journal of Financial and Quantitative Analysis 22: 143–151.CrossRefGoogle Scholar
17.Kushner, H.J. & Clark, D.C. (1978). Stochastic approximation methods for constrained and unconstrained systems. New York: Springer-Verlag.CrossRefGoogle Scholar
18.Rubinstein, R.Y. & Shapiro, A. (1993). Discrete event systems: Sensitivity analysis and stochastic optimization by the score function method. New York: John Wiley & Sons.Google Scholar
19.Scott, L.O. (1987). Option pricing when the variance changes randomly: Theory, estimation, and an application. Journal of Financial and Quantitative Analysi 22: 419–438.CrossRefGoogle Scholar
20.Stoll, H.R. & Whaley, R.E. (1993). Futures and Options. South-Western.Google Scholar
21.Tilley, J. (1993).Valuing American options in a path simulation model. Morgan Stanley Working Paper; also, Transactions of the Society of Actuaries 45: 83–104.Google Scholar
22.Welch, R.L. & Chen, D.M. (1991). Static optimization of American contingent claims. Advances in Futures and Options Research 5: 175–184Google Scholar