6. Black-Scholes Formula (Application). Suppose that a stock price obeys a geometric Brownian motion with current price $60. Consider a European call option with maturity 1 year and the strike price $68. The risk-free interest rate is 6% per annum, and the volatility is 10% per annum. (a) In the risk-neutral world, what is the probability that the stock price will be greater than $68 at the end 1 year? (b) Construct a 95% confidence interval for the stock price at the end of 1 year? (c) Find the fair premium for the call option. (d) Consider a European put option with the same expiration time T = 1 and same strike price K = $68, what is the fair premium for the corresponding put? 6. Black-Scholes Formula (Application). Suppose that a stock price obeys a geometric Brownian motion with current price $60. Consider a European call option with maturity 1 year and the strike price $68. The risk-free interest rate is 6% per annum, and the volatility is 10% per annum. (a) In the risk-neutral world, what is the probability that the stock price will be greater than $68 at the end 1 year? (b) Construct a 95% confidence interval for the stock price at the end of 1 year? (c) Find the fair premium for the call option. (d) Consider a European put option with the same expiration time T = 1 and same strike price K = $68, what is the fair premium for the corresponding put