Pricing parisian options using modified monte carlo simulation - Ramos, Aaron J.; Escaner, Jose Maria L. IV (Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman, 2016)
Parisian options are financial contracts that give the holder the right to buy or sell an underlying asset, say a stock, for a specified strike price and a specified maturity. However, the right to buy or sell can only be obtained or it may be lost under the condition that the stock price remains below (or above) a certain level, called the barrier, for a certain time period before maturity. Because of this path dependence,pricing parisian options (and exotic options in general) is done numerically.For this thesis we shall be pricing a Parisian down-and-out call, where the holder obtains the right to buy a stock for the strike price if the stock price stays below the barrier for a given time period before maturity. We will be modifying the usual Monte Carlo method by first using a change of measure to express the option price in terms of a Brownian motion. Then we will be using the concept of a Brownian bridge to obtain more precise measurements of the lengths of the Brownian motion excursions. We then compare the convergence of the standard Monte Carlo method to the modified version with respect to the number of subintervals used and computation time.
Thesis (M.S.-Applied Mathematics) --University of the Philippines Diliman
Keywords: Monte Carlo method