Monte Carlo methods for pricing discrete Parisian options

Abstract

The paper develops an efficient Monte Carlo method to price discretely monitored Parisian options based on a control variate approach. The paper also modifies the Parisian option design by assuming the option is exercised when the barrier condition is met rather than at maturity. We obtain formulas for this new design when the underlying is continuously monitored and develop an efficient Monte Carlo method for the discrete case. Our method can also be used for the case of multiple barriers. We use numerical examples to illustrate the approach and reveal important features of the different types of options considered. Some performance-based executive stock options include different tranches of discretely monitored Parisian options and we illustrate this with a practical example.