1. Consider a stock currently priced at $40 with expected rate of return 8% p.a., volatility 25% p.a. and continuous dividend yield 6% p.a. The risk-free rate is 3% p.a. An American call is written on this stock with strike $45 and maturity in 1 year. (a) Using Hull's approximation verify that the critical stock price at t = 0) is $61.43735 and compute the critical stock price at the time points t = 0.2,0.4, 0.6, 0.8,0.99. (4 marks] (b) Using (a), plot and label the continuation region and the stopping region for this option. [2 marks] (c) Using Hull's approximation, price the option. [3 marks] (d) Find the probability that the stock price exceeds the critical price at time t=0.5. [3 marks] 1. Consider a stock currently priced at $40 with expected rate of return 8% p.a., volatility 25% p.a. and continuous dividend yield 6% p.a. The risk-free rate is 3% p.a. An American call is written on this stock with strike $45 and maturity in 1 year. (a) Using Hull's approximation verify that the critical stock price at t = 0) is $61.43735 and compute the critical stock price at the time points t = 0.2,0.4, 0.6, 0.8,0.99. (4 marks] (b) Using (a), plot and label the continuation region and the stopping region for this option. [2 marks] (c) Using Hull's approximation, price the option. [3 marks] (d) Find the probability that the stock price exceeds the critical price at time t=0.5. [3 marks]