Problems You are considering whether to invest in the following option-embedded tailored bond (so called "structured bond"). Hedge Fund-linked Bond Name: Hedge Fund Index-linked Note Issuer: Bank Y its credit rating is very high, so in this problem we ignore its credit risk) Face Value: 100 Japanese Yen Redemption Price: 100 Japanese Yen Issue Price: 100 Japanese Yen Term to Maturity: 1 Year Coupon Frequency: Quarterly Payment Another example is a lookback option which is covered in Assignment1. 3 Coupon at time t: (i) if hedge fund index at timet > target point at timet: [exceedance amount of the index over the target point at time t] [multiplier at time t] (Japanese Yen), (ii) else: 0, where the hedge fund index is calculated based on the performance of Hedge Fund Z. The index starts at 100 on the issue date of this bond. The target point and multiplier for each coupon payment date is given as follows. Coupon Payment 1st 2nd 3rd 4th Target Point 102 104 106 108 Multiplier 0.25 0.50 0.75 1.00 (a) This bond can be expressed as the combination of the bond part and the option part. Describe this combination in detail. (b) Suppose that the hedge fund index follows a geometric Brownian motion process. The volatility of the index is o = 7% per annum and the risk-free interest rate is r = 10% per annum (continuously compounded). Then, based on the observation obtained in (a), compute the present value of this bond. Problems You are considering whether to invest in the following option-embedded tailored bond (so called "structured bond"). Hedge Fund-linked Bond Name: Hedge Fund Index-linked Note Issuer: Bank Y its credit rating is very high, so in this problem we ignore its credit risk) Face Value: 100 Japanese Yen Redemption Price: 100 Japanese Yen Issue Price: 100 Japanese Yen Term to Maturity: 1 Year Coupon Frequency: Quarterly Payment Another example is a lookback option which is covered in Assignment1. 3 Coupon at time t: (i) if hedge fund index at timet > target point at timet: [exceedance amount of the index over the target point at time t] [multiplier at time t] (Japanese Yen), (ii) else: 0, where the hedge fund index is calculated based on the performance of Hedge Fund Z. The index starts at 100 on the issue date of this bond. The target point and multiplier for each coupon payment date is given as follows. Coupon Payment 1st 2nd 3rd 4th Target Point 102 104 106 108 Multiplier 0.25 0.50 0.75 1.00 (a) This bond can be expressed as the combination of the bond part and the option part. Describe this combination in detail. (b) Suppose that the hedge fund index follows a geometric Brownian motion process. The volatility of the index is o = 7% per annum and the risk-free interest rate is r = 10% per annum (continuously compounded). Then, based on the observation obtained in (a), compute the present value of this bond