Pricing Parisian Options: The Extended Binomial Method vs. Monte-Carlo Simulation

Abstract

I extend the Cox, Ross, Rubinstein binomial model to price Parisian options and compare it with Monte-Carlo simulation. The CRR tree is extended to solve the path-dependence of Parisian options by keeping track of a vector of prices that the Parisian option may take at each tree node under different scenarios. The extended model can be applied to price a class of path-dependent options with minimal modifications. I also incorporate the method for choosing the number of time-steps that will yield more precise price estimates. The results are then compared to those given by closed-form formulas in the limiting cases by setting time-below the barrier (in a knock-out option) to be zero or longer than the option maturity. The extended binomial model requires less computing time to produce accurate results when compared with the Monte-Carlo approach. Moreover, with a small modification, the extended binomial model can price American style Parisian options. On the other hand, Monte-Carlo simulation is superior to account for discrete price monitoring and to provide likely error in the pricing estimates.