Pricing of financial derivatives via simulation

ABSTRACT

The word "derivative" has led a ubiquitous existence in the news in recent years. This paper gives a tutorial on financial derivatives and the use of Monte Carlo simulation techniques for their pricing. We provide the basic financial terminology and key concepts in the field, focusing on options pricing, in particular. Although no prior knowledge of finance is assumed in the exposition, previous experience with stochastic simulations-generation of random inputs and basic statistical output analysis-is requisite.

REFERENCES

• 1: Boyle, P.P. 1977. Options: a Monte Carlo approach. Journal of Financial Economics 4: 323-338.
• 2: Broadie, M. and Glasserman, P. 1993. Estimating security price derivatives using simulation, submitted for publication.
• 3: Broadie, M. and Glasserman, P. 1995. Pricing American-style options. Working paper. Columbia University.
• 4: Cox, John C. and Rubinstein, Mark. 1985. Optzons markets. Englewood Cliffs, N.J.: Prentice-Hall.
• 5: Cox, J.C. and Ross, S.A. 1976. The valuation of options for alternative stochastic processes," Journal of Financial Economics 3: 145-166.
• 6: Fu, M.C. 1994a. Optimization using simulation: a review. Annals of Operations Research 53: 199- 248.
• 7: Michael C. Fu, A tutorial review of techniques for simulation optimization, Proceedings of the 26th conference on Winter simulation, p.149-156, December 11-14, 1994, Orlando, Florida, United States
• 8: Fu, M.C. and J.Q. Hu. 1995. Sensitivity analysis for Monte Carlo simulation of option pricing, Probability in the Engineemng and Informational Sciences, Vol.9, No.3.
• 9: Fu, M.C, Madan, D.B., and T.Wang. 1995. Pricing continuous time Asian options: a comparison of analytical and Monte Carlo methods, presented at the 12th International Conference in Finance, June 1995, Bordeaux, France. also, submitted for publication.
• 10: Geman, H. and Kydeland, A. 1995. Domino effect. Risk Volume 8, No. 4.
• 11: Geman, H. and Yor, M. 1993. Bessel processes, Asian options and perpetuities. Mathematical F~nance 3, No.4: 349-375.
• 12: Gibson, Rajna. 1991. Option valuation: analyzzng and pricing standardized options contracts. New York: McGraw-Hill.
• 13: Glasserman, P. 1991. Gradient Estimation Via Perturbation Analysis. Kluwer Academic.
• 14: Harrison, J.M. and Pliska, S. 1981. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applicat,erie 11: 215-260.
• 15: Ho, Y.C. and X.R. Cao. 1991. Perturbation Analysis and Discrete Event Dynamic Systems. Kluwer Academic.
• 16: Hull, J.C. 1993. Options, Futures, and Other Derivative Securities, 2nd edition. Prentice Hall.
• 17: Hull, J.C. and White, A. 1987. The pricing of options on assets with stochastic volatilities, Journal of Finance 42: 281-300.
• 18: Johnson, H. and Shanno, D. 1987. Option pricing when the variance is changing. Journal of Financial and Quantitative Analysis 22: 143-151.
• 19: Stoll, Hans R., and Whaley, Robert E. 1993. Futures and options : theory and applications. Cincinnati, Ohio: South-Western Pub. Co.
• 20: Tilley, J. 1993. Valuing American options in a path simulation model. Transactzons of the Society of Actuaries 45: 83-104.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation
          Subjects: Monte Carlo

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

  J. Computer Applications
  J.1 ADMINISTRATIVE DATA PROCESSING
      Subjects: Business
  J.4 SOCIAL AND BEHAVIORAL SCIENCES
      Subjects: Economics

General Terms:
Economics, Theory