We value an Asian call option in lognormal stock price model using Monte Carlo simulation. Stock price today is $100. Annual continuously compounded risk-free rate is r = 0.06, annual standard deviation (volatility) of return σ = 0.30. An Asian call with strike price K = $90 that expires in T = 3 months is written on this stock. Option payment is based on the arithmetic average of the stock price at the end of months 1, 2, and 3.

Table 1 gives the simulation results of standard normal shocks in the lognormal stock price model in month 1, 2, and 3.

Finish the table by computing stock prices at the end of month 1, 2, 3; arithmetic average of stock prices A(S k ), and terminal call option payoff V k in each trial. And then compute the Monte Carlo price of this Asian option based on 5 trials. 

Write down the calculation details of the 1st trial, and Monte Carlo price. To show the details for trial 2-4.

 

TABLE 1 - Simulating an Asian call option terminal payoffs in a lognormal stock price model. Trial (k) Zk (1) Zk (2) Zk (3) S(0) Sk (1) Sk (2) Sk (3) A(Sk) Vk 1 -0.096 0.593 -0.725 100 2 -1.677 0.755 - 1.300 100 3 1.342 -1.230 0.562 100 4 1.822 -0.807 -1.426 100 5 -1.062 0.655 -0.612 100