Mathematical Python — DU B.A. (Prog) Mathematics as Major Previous Year Question Papers

(c) Find the payoff from a bear spread created using put options. Also draw the profit diagram corresponding to this trading strategy. 1. (a) A bank quotes an interestrate of l4% per annum with quarterly compounding. What is the equivalent rate with (i) continuous compounding and (ii) annual compounding? (b) Explain the following type of interest rates : (i) Treasury Rates (c) Portfolio A consists of 1-year zero coupon with a face value of €2000 and a 10-year zero coupon bond with face value of €6000. Portfolio 8 consists of a 5.95-year zero coupon bond with face value of €5000. The current yield on all bonds is 10% per annum. 6. (a) Discuss the delta of a European call option and calculate the delta of an at-the-money 6-month European call option on a non-dividend-paying stock when the risk-free interest rate is 8% per annum and the stock price volatility is 30% per annum. (b) Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment : Fix Rate Floating Rate Company X 8.0% LIBOR Company Y 8.8% LIBOR Company X requires a fixed-rate investment; company Y requires a floating-rate investment. Design a swap that will net a bank, acting as intermediary, 0.2% per annum and will appear equally attractive to X and Y. 5. (a) Given that in a risk-neutral world, 1nsT~¢[hso+(r-£)T,o2T],wheresTisthe stock price at a future time T, So is the current stock price, r is the risk-free rate, a is the volatility and dy(in, v) denotes a normal distribution with mean in and variance v. For the given strike price K, find P(K > ST), the probability that a European put option be exercised in a risk-neutral world. (b) Calculate the price of a five-month European call option on a non-dividend-paying stock with a strike price of €60 when the current stock price is €62, the risk-free. interest rate is 10% per annum, and the volatility is 20% per annum. (c) Show that the Black-Scholes-Merton formulas .for call and put options satisfy the put- call parity. (ii) What are the percentage changes in the values of the two portfolios for a 50/o per annum increase in yields? (You can use the exponential values: ex = 0.905, 0.368, 0.552, 0.861, 0.223 and 0.409 for x i -0.1, -1.0, -0.595, -0.15, -1.5 and -0.893 respectively) 2. (a) Explain Hedging. How is the risk managed when Hedging is done using? (i) Forward Contracts (b) (i) What is the difference between the over-the counter market and the exchange-traded market? (ii) An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.9000 US dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.8900 and (b) (c) Write a short note on European call options. Explain the payoffs in different types of call option positions with the help of diagrams. 3. (a) Name the six factors that affect stock option prices. Explain any three of them.