Please show me the specific calculations how to get this right.
Question 3 The table below shows the simulated values of the underlying at times t = 6m and t = lyr. Use the Least-Squares Monte-Carlo method to calculate time Path 1 t = 6m 29.2533 t=lyr 31.1637 Path 2 42.7788 51.4520 Path 3 27.6238 24.2960 Path 4 49.5507 44.0307 Path 5 36.1251 33.6701 the price of an American put option expiring in 1 year, struck at $40 and paying zero dividend. The spot price of the underlying stock is $36 and the risk-free rate is 6%. Tabulate or show all intermediate calculations. The fitted regression coefficients for a model with two Laguerre basis functions, Lo(x) = 1 and L1(x) = 1 - x, are o = 28.9798 and u 0.6457 [20] Solution 3 Answer is 5.6802. Paths 2 and 4 are out-of-the-money. It is optimal to exercise at maturity along path 5. It is optimal to exercise at t = 6m for paths 1 and 3. 5 The table below shows the estimated expecting holding values of the put option at t = 6m (5 marks] Path 2 time t = 6m Path 1 10.7366 Path 3 11.7888 Path 4 0 Path 5 6.2996 0 The table below shows the intrinsic put option values at t= 6m time t=6m Path 1 10.7467 Path 2 0 Path 3 12.3762 Path 4 0 Path 5 3.8749 Now compare the expected holding values with the intrinsic. If the estimated is less than the intrinsic, then exercise at time t= 6m otherwise discount the payoff at time t = lyr as follows: (10 marks) time t=6m Path 1 10.7467 Path 2 0 Path 3 12.3762 Path 4 0 Path 5 6.1428 = (40 - 33.6701) -TAt Now discount all values at t = 6m to t = 0 in the above table and compute the average over all five paths. Finally since 5.6802 > (40 - 36) we do not exercise at t = 0. (5 marks) Question 3 The table below shows the simulated values of the underlying at times t = 6m and t = lyr. Use the Least-Squares Monte-Carlo method to calculate time Path 1 t = 6m 29.2533 t=lyr 31.1637 Path 2 42.7788 51.4520 Path 3 27.6238 24.2960 Path 4 49.5507 44.0307 Path 5 36.1251 33.6701 the price of an American put option expiring in 1 year, struck at $40 and paying zero dividend. The spot price of the underlying stock is $36 and the risk-free rate is 6%. Tabulate or show all intermediate calculations. The fitted regression coefficients for a model with two Laguerre basis functions, Lo(x) = 1 and L1(x) = 1 - x, are o = 28.9798 and u 0.6457 [20] Solution 3 Answer is 5.6802. Paths 2 and 4 are out-of-the-money. It is optimal to exercise at maturity along path 5. It is optimal to exercise at t = 6m for paths 1 and 3. 5 The table below shows the estimated expecting holding values of the put option at t = 6m (5 marks] Path 2 time t = 6m Path 1 10.7366 Path 3 11.7888 Path 4 0 Path 5 6.2996 0 The table below shows the intrinsic put option values at t= 6m time t=6m Path 1 10.7467 Path 2 0 Path 3 12.3762 Path 4 0 Path 5 3.8749 Now compare the expected holding values with the intrinsic. If the estimated is less than the intrinsic, then exercise at time t= 6m otherwise discount the payoff at time t = lyr as follows: (10 marks) time t=6m Path 1 10.7467 Path 2 0 Path 3 12.3762 Path 4 0 Path 5 6.1428 = (40 - 33.6701) -TAt Now discount all values at t = 6m to t = 0 in the above table and compute the average over all five paths. Finally since 5.6802 > (40 - 36) we do not exercise at t = 0
