论文信息 - EFFICIENT MONTE CARLO ALGORITHM FOR PRICING BARRIER OPTIONS

EFFICIENT MONTE CARLO ALGORITHM FOR PRICING BARRIER OPTIONS

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.

Kyoung-Sook Moon

[1] Raul Tempone,et al. Adaptive Monte Carlo Algorithms for Stopped Diffusion , 2005 .

[2] Riccardo Mannella,et al. Absorbing boundaries and optimal stopping in a stochastic differential equation , 1999 .

[3] Ioannis Karatzas,et al. Brownian Motion and Stochastic Calculus , 1987 .

[4] Grant Lythe,et al. Efficient Numerical Solution of Stochastic Differential Equations Using Exponential Timestepping , 2000 .

[5] P. Wilmott,et al. The Mathematics of Financial Derivatives: Preface , 1995 .

[6] F. Black,et al. The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[7] E. Gobet. Weak approximation of killed diffusion using Euler schemes , 2000 .

[8] A. Atiya,et al. Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options , 2002 .

[9] A Gu,et al. Breaking down barriers , 2018, Nature Astronomy.

[10] Paolo Baldi,et al. Exact asymptotics for the probability of exit from a domain and applications to simulation , 1995 .

[11] J. Emanuel,et al. Breaking down the barriers , 2002, Nature.

[12] E. Haug. The complete guide to option pricing formulas , 1997 .

[13] Noelle Foreshaw. Options… , 2010 .

[14] N. Kunitomo,et al. Pricing Options With Curved Boundaries , 1992 .

[15] R. C. Merton,et al. Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.