FE545 Homework Assignment #1 Due Date: Oct. 4th (Monday). Data: An Asian option is a type of exotic option. Unlike a vanilla European option where the price of the option is depen- dent upon the price of the underlying asset at expiry, an Asian option pay-off is a function of multiple points up to and includ- ing the price at expiry. Thus it is “path-dependent” as the price relies on knowing how the underlying behaved at certain points before expiry. Asian options in particular base their price off the mean average price of these sampled points. To simplify the problem, we will consider equally distributed sample points beginning at time and ending at maturity, In this problem, we will consider Geometirc mean A of the spot prices we use the following formula: A(0, T ) = exp ( 1 N N∑ i=1 log(S(ti)) ) (1) Unlike in the vanilla European option Monte Carlo case we have learned in class, where we only needed to generate mul- tiple spot values at expiry, we now need to generate multiple spot paths, each sampled at the correct points. Thus instead of providing a double value representing spot to our option, we now need to provide a std :: vector < double > (i.e. a vector of 1 double values), each element of which represents a sample of the spot price on a particular path. We will still be modeling our asset price path via a Geometric Brownian Motion (GBM), and we will create each path by adding the correct drift and variance at each step in order to maintain the properties of GBM. Implement PayOff classes according to the following tem- plate: #ifndef __PAY_OFF__ #define __PAY_OFF__ #include
