A Finite Element Platform For Pricing Path-Dependent Exotic Options

For many path-dependent options, such as Asian options, lookbacks, Parisian options, using partial differentiation equation (PDE) approach to price these exotic options can be straightforward and flexible. In addition, modified versions of the standard exotic path-dependent options can be easily accommodated in the same pricing algorithms. For example, American early exercise features, barriers (both constant or time dependent) on the underlying or the path-dependent parameters, and any pay-off functions can be readily implemented in an extended version of the same pricing scheme. Most importantly, the methods is simple and easy to understand, and it is fast to implement. Of course, volatility surfaces and interest-rate term structures are natural part of any PDE solutions.