Question 5. (14 marks) (a) Consider 6-month European call and put options with strike price of $20 on a dividend paying stock. The current stock price is $20 and the stock will pay a $0.60 dividend in 2 months time. The call option is priced at $0.20, the put option at 80.25. The 2-month risk free rate is 4.2% and the 6-month risk free rate is 4.5%, where the interest rates are continuously compounded. Is there an arbitrage opportunity in this market? If so, how would you exploit such an opportunity? (6] (b) Zhihao Trading (ZHI) sells variable annuity contracts embedded with guaranteed minimum maturity benefit (GMMB) riders to policyholders approaching retirement. A variable an- nuity contract is structured as a contract between the policyholder and ZHI under which the policyholder makes a single premium payment at the start of the contract. In return, ZHI guarantees minimum guaranteed return of 3.5% per annum as long as the contract is still in force. At initial time, f = 0, the policyholder makes a premium payment of P of which P x 1% is deducted by ZHI as insurance charges associated with providing the guarantees embedded in the variable annuity contract. The net premium after deducting insurance charges is invested in a fund whose return is indexed to the performance of the main benchmark index whose level at initial time is So- Upon maturity of the variable annuity contract at time, T, ZHI will pay the policyholder P(1 - 1%) X max [S(7) 1.035 You are also given the following information: (i) The contract matures in 5 years. (il) Dividends are not incorporated In the benchmark index. That is, the index is con- structed so that stock dividends are not reinvested. (iii) The continuously compounded dividend yield of the index is 5% per annum. (lv) The initial index level is S(0) = 100. (v) The price of a 5-year European put option on the benchmark index with strike price of $135 is $27.50. (vi) The continuously compounded risk-free rate of interest is 3% per annum