Question 4 (a) A financial institution has sold a European call option on 10,000 shares on a non-dividend- paying stock that has 4 weeks to run until expiration. The current stock price is $50, the exercise price is $51, the interest rate is 4% p.a. compounded continuously, and stock's volatility is 15% p.a. Assume the distribution of stock price is lognormal. The stock prices in the next 4 weeks are given in the following table. Weeks Price ($) 0 50 51 2 52 3 53 4 52 Determine the total cost of writing this option by Dynamic Delta Hedging when it is rebalancing weekly. [10 marks] (b) Consider an Asian call option on a stock with a dividend rate of 1% p.a. The current stock price is $50, the exercise price is $51, the risk-free interest rate is 3% p.a. compounded continuously, the volatility is 15% p.a. and the time to expiry is 9 months. If arithmetic average is used, find the price of this average price Asian call option. [10 marks) Question 4 (a) A financial institution has sold a European call option on 10,000 shares on a non-dividend- paying stock that has 4 weeks to run until expiration. The current stock price is $50, the exercise price is $51, the interest rate is 4% p.a. compounded continuously, and stock's volatility is 15% p.a. Assume the distribution of stock price is lognormal. The stock prices in the next 4 weeks are given in the following table. Weeks Price ($) 0 50 51 2 52 3 53 4 52 Determine the total cost of writing this option by Dynamic Delta Hedging when it is rebalancing weekly. [10 marks] (b) Consider an Asian call option on a stock with a dividend rate of 1% p.a. The current stock price is $50, the exercise price is $51, the risk-free interest rate is 3% p.a. compounded continuously, the volatility is 15% p.a. and the time to expiry is 9 months. If arithmetic average is used, find the price of this average price Asian call option. [10 marks)