1. Consider an asset which follows a geometric Brownian motion (GBM) with drift µ = 10% and volatiltiy σ = 20%. Assume that the risk free rate is r = 5%. The initial asset price at time t = 0 is S(0) = 100. Simulate 10 different paths of the asset price making use of the GBM, in both the real and the risk-neutral worlds.
Now compute the price of a six month fixed-strike Asian option with a strike price of 105 (using arithmetic average). Do the pricing for both call and put options, using Monte Carlo simulation.
Repeat the above exercise with strike price K = 110 and K = 90. How do your results compare ?
Now do a sensitivity analysis of the option prices.
2. Compute the prices of the Asian options given above by employing variance reduction techniques also and compare your results.
