Mathematical Finance — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

(1) What is the bond's price? (a)Define Derivative and present a comparative study for Future and Forward Derivative. Investor shorts 50,000 pounds forward contract for U.S dollars at an exchange rate of 1.4000 USD per pound. Find gain or loss if exchange rate at the end of the contract is (i)1.3800 (ii) 1.4200. (b) (i)Present a comparative study for different types of traders in the financial markets? (ii) A portfolio contains 10,000 shares worth $50 each. How can put options be used to provide insurance against a decline in the value of the holding over the next 4 month. (c) A one-year forward contract on a non-dividend paying stock is entered into when the stock price is 50, and the risk-free rate of interest is 8% per annum with continuous compounding. What is the forward price? Justify using no arbitrage arguments. (a) List the four types of option positions. Illustrate each with their respective payoff functions and payoff diagrams from positions in European options. (b) Define the upper bound and lower bound for European options on a non-dividend- paying stock. Also, what is a lower bound for the price of a 2-month European put option on a non-dividend-paying stock when the stock price is boo, the strike price is $65, and the risk-free interest rate is 5% per annum? (You can use the exponential value e 0.0083 = 0.9916). (c)Derive the relationship between the prices of European put and call options that have the same strike price and time to maturity, assuming the underlying stock pays no dividends. Using this relationship, determine the price of a 3-month European call option when the price of a non-dividend-paying stock is $31, the price of a 3-month European put option on the stock with a strike price of $30 is $1.259 and the risk-free rate is 10% per annum. (You can use the exponential value e 0.025 = 0.9753). (a)Explain how a bear spread can be created using European put options on a stock. Also, present the payoff table and draw the corresponding profit diagram for this strategy. Call options on a stock are available with strike prices of $15, $17-, and $20, and expiration dates in 3 months. Their prices are $4, $2, and s, respectively. Explain how the options can be used to create a butterfly spread. Create a table showing how profit varies with stock price for the butterfly spread. (b) A stock price is currently $80. It is known that at the end of 4 months it will be either $75 or $85. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 4-month European put option with a strike price of $80? Use no- arbitrage arguments. (You can use the exponential value e0.0167 = 1.0168).