Title: Pricing Parisian option with adaptive Monte Carlo method
Authors: Sercan Gur - Vienna University of Economics and Business (Austria) [presenting]
Klaus Poetzelberger - WU Vienna (Austria)
Abstract: Parisian option is a type of barrier option, which can only be exercised if the underlying value process not only reaches a barrier level but remains a certain prescribed time (so-called window period) below (or above) this level. Closed form solutions for the value of these contracts do not exist. In order to price Parisian options, we use Monte Carlo simulation instead of partial differential equations, inverse Laplace transform or lattices. We propose a new Monte Carlo method which can be used to price Parisian options not only with constant boundary but with more general boundary. The advantage of this approach is that it can easily be adapted to compute the price of an option with more complicated path-dependent pay-off. We use adaptive control variable to improve the efficiency of the Monte Carlo estimator. At last, we provide a numerical example to illustrate our method and a comparison of previous Monte Carlo methods with our technique.