Q4. (structured product with embedded options) The textbook introduces equity-linked CDs in Section 2.6. The payoff of equity-linked CD resembles the payoff of a portfolio of a long call option and a zero-coupon bond. We will say more about equity-linked CD in Lecture 12 if time permits. In real life, there are many other structured products with embedded options. For example, a currency-linked deposit product called the "deposit plus" is provided by some banks. The pictures below show information of a "deposit plus" product: HKD (the deposit currency) - EUR (the linked currency). Suppose you would like to deposit HKD5,000 into this "deposit plus" product for one week (7/365). You choose the conversion rate to be 8.2271 HKD per euro, and the corresponding interest rate is 5% p.a. (this is a quoted annualized rate, so the effective rate for one week is 5%7/365 ). If the actual exchange rate of euro (the number of HKD per euro) one week later is higher than the conversion rate, the product acts just like a regular deposit product, and you will be able to receive the principal and interest ( 5% p.a.) in HKD. However, if the actual exchange rate one week later is below the conversion rate, your HKD5,000 deposit will be first converted to euro at the conversion rate, and you receive the principal and interest ( 5% p.a.) in euro. The spot exchange rate today is 8.2899HKD per euro. (a) If one week later, the spot exchange rate is 8.3HKD per euro, how much in HKD will you be able to get back? (b) If one week later, the spot exchange rate is 8.2HKD per euro, how much in HKD will you be able to get back? (c) Standing from the perspective of a HK based investor, the composition of the "deposit plus" is a long zero-coupon bond that matures in one week + an option on euro with the strike being the conversion rate. What is the face value of the zero-coupon bond? (d) Suppose the 1-week interest rate in HKD is 2% p.a. (so the effective rate for one week is 2%7/365 ), what is the total premium of the option embedded in the product implied by the product's information? (Hint: the option premium is positive)