(a) A company has decided to use bonds to make a payment of $12,000 that is due in six years. There are currently two bonds in the market that are suitable for this purpose, Bond 1 which is a three-year 10% coupon bond with a face value of $1000 and a current price of $1192 and Bond 2 which is a ten-year pure discount bond issued two years ago, with a present value of $1200. Given that the yield to maturity in the bond market is 3%, determine: 1. (i) a portfolio strategy that will allow the company to immunize the liability. [5 marks] (ii) the number of units the company should buy in each bond. [3 marks] 2. (b) The strike price of a European put option is $25, the current price of the underlying stock is $20, the risk-free rate of return is 4% and each year the stock can either increase by a factor of 1.2 or decrease by a factor of 0.7. If the probability of the stock decreasing each year( Tid) is 0.7, calculate the price of the put option if it is priced under the Binomial Method and expires in two years. [5 marks] 3. (c) The strike price of a European put option is $50, the current price of the underlying stock is $45 and the risk-free rate of return is 4%. If N(-d1) and N(-d2) (as defined under the Black-Scholes model) have values of 0.1 and 0.7 respectively, calculate the price of the equivalent call option if both contracts are priced under the Black-Scholes model and expire in 6 months. [3 marks] 4. (d) Using the information from Part (c) above and given that the actual price of the European put option was $60 as well as when the contract expired the price of the underlying stock was $55, outline a possible arbitrage strategy and hence compute the profit from this strategy. [3 marks] (a) A company has decided to use bonds to make a payment of $12,000 that is due in six years. There are currently two bonds in the market that are suitable for this purpose, Bond 1 which is a three-year 10% coupon bond with a face value of $1000 and a current price of $1192 and Bond 2 which is a ten-year pure discount bond issued two years ago, with a present value of $1200. Given that the yield to maturity in the bond market is 3%, determine: 1. (i) a portfolio strategy that will allow the company to immunize the liability. [5 marks] (ii) the number of units the company should buy in each bond. [3 marks] 2. (b) The strike price of a European put option is $25, the current price of the underlying stock is $20, the risk-free rate of return is 4% and each year the stock can either increase by a factor of 1.2 or decrease by a factor of 0.7. If the probability of the stock decreasing each year( Tid) is 0.7, calculate the price of the put option if it is priced under the Binomial Method and expires in two years. [5 marks] 3. (c) The strike price of a European put option is $50, the current price of the underlying stock is $45 and the risk-free rate of return is 4%. If N(-d1) and N(-d2) (as defined under the Black-Scholes model) have values of 0.1 and 0.7 respectively, calculate the price of the equivalent call option if both contracts are priced under the Black-Scholes model and expire in 6 months. [3 marks] 4. (d) Using the information from Part (c) above and given that the actual price of the European put option was $60 as well as when the contract expired the price of the underlying stock was $55, outline a possible arbitrage strategy and hence compute the profit from this strategy. [3 marks]
