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Efficient Monte Carlo algorithm for pricing Barrier options

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A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

Abstract

A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

참고문헌 (14)

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  9. I. Karatzas, "Brownian Motion and Stochastic Calculus" (1991), Springer-Verlag
  10. R. Mannella, "Absorbing boundaries and optimal stopping in a stochastic differential equation", Physics Letters A, 254, pp.257~262 (1999)
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  12. S. A. K. Metwally, "Using Brownian bridge for fast simulation of jumpdiffusion processes and barrier options", J. Derivatives Fall, pp.43~54 (2002)
  13. E. Reiner, "Breaking down the barriers", Risk, 4(8), pp.28~35 (1991)
  14. P. Wilmott, "The Mathematics of Financial Derivatives" (1995), Cambridge University Press

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