Question 1 a. Using the following data for Theta Ltd., calculate the value of a call option and a put option using the Black-Scholes formula: Current share price =$190 Exercise price = $185 Interest rate per annum = 6% Dividend yield per annum = 3% Time to expiration = 3 months Standard deviation = 0.6 per annum 10 marks b. Assume you have purchased 100,000 equity shares of a listed company in Australia and want to sell these shares after 6 months to buy a house in Sydney. A call option and a put option on these shares are currently selling at $3 and $3, respectively. The exercise prices of the call and put options are $120 and $100, respectively. You are considering using one of the following strategies to protect the value of your portfolio till you sell the shares in six months: i. Aa protective put ii. a covered call iii. A zero cost collar Calculate the income from your portfolio after 6 months for the following three market prices: $ 125, $110 and $90. Out of the above three strategies, which one is the best strategy? Justify your answer based on the calculations you have performed. 10 marks c. Using the data and calculations in part a., determine the value of the put option using the put-call parity relationship. If the current market value of the put option is $1 below the price of put you have calculated, explain if there are any arbitrage opportunities. If there are arbitrage opportunities what steps would you undertake to profit from the arbitrage? 5 marks d. If the share price in part a. above increase by $1, estimate the new prices of the call and put options. 2 marks If the share price in part a. above increase by $1, estimate the elasticities of the call and put options and interpret them. 3 marks f. Assume that you have sold 1000 call options of Theta Ltd. In order to eliminate the price risk of call options, how many shares of Theta Ltd do you need to buy? Explain the reason for your answer. 3 marks e