Path-Dependent Option Pricing via Monte Carlo Simulation
Consider an economy, with a stock
S
, that has the following parameters:
(S_(0),\sigma ,\delta ,r)=(1,0.20,0,0.02)
, and
over the subsequent two years, a pair of uniform random numbers
U_(1),U_(2)
will be simulated three times, with outcomes
Simulation 1:
(U_(1),U_(2))=(0.50,0.16)
, and
Simulation 2:
(U_(1),U_(2))=(0.32,0.36)
, and
Simulation 3:
(U_(1),U_(2))=(0.27,0.70)
, respectively.
Consider a geometric average strike Asian call option with time to maturity of 2 years, where we define the payoff at time 2 as
V_(2):=max{S_(2)-(S_(1)S_(2))^((1)/(2)),0}.
Estimate the Monte Carlo valuation of this path-dependent call option. (50 pts)