STATISTICS IN FINANCE — DU B.Sc (hons) Statistics Previous Year Question Papers

Statistics in Finance (NEP) Attempt a total of six questions in all. i. ii. iii. Deflne nominal and effective rates of interest. Explain the relationship between them and explain the impact of compounding frequency. Find the corresponding effective rates for nominal rates: 6% compounded monthly and 12% compounded quarterly. If you receive 6% interest compounded yearly, approximately how many years will it take for your money to quadruple? What is it if this interest was only 3% ? $1000 is kept in a savings account at 3% compounded continuously for 3 years. It is then withdrawn and placed in another bank account at a rate of 4% compounded continuously for 5 years. What will be the balance in. the second account after 5 years? iv. An investor sold 2000 calls and 1500 puts with the sane exercise price and same maturity on the same underlying stock. Delta for the call is 0.42, and delta for the put is -0.38. How many stocks should the investor sell or buy in order to have a delta-neutral position? (5X3= 15marks) Q2 (a) An investor has a capital of € 8,400 at his disposal to buy stocks whose current price is €100. Further put options on the same stock with a delivery price of K= €100 and a time to maturity of 1 year are quoted at a market price of €5 per contract. Consider two alternative investment plans: PortfolioA: Buying 84 stocks Portfolio B: Buying 80 stocks for 8,000 and buying 80 put.options for400. Discuss the effect of portfolio insurance on portfolio value and return. (b) Explain `The Comparison Principle' with an example in the context of financial markets. Consider the 5-year coilpon bonds: one has a coupon of 9% and sells for Rs. 101.00, and the other has a coupon of 7% and sells for Rs. 93.20. Find the price of a 5-year zero-coupon bond. (8,7) Q-3 (a) What do you mean by Derivatives? Explain the types of derivatives with examples. (b) Draw the payoff matrix for the following strategies: (i) Consider the following strategy where K=100 The purchase of one stock The purchase of one European call with exercise price K The sale of one European call with exercise price K (ii) Consider the following option combination strategy, Q4 (a) Explain a yield curve. What do you mean by discount factors, and how do you calculate the present value by using the discount factor? Also, give the formula for the spot price for a 2-year bond. (b) Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, with continuous compounding. Estimate the cash 'price of a bond with a face value of loo that will mature in 30 months and pay a coupon of 4% per annum semiannually under continuous compounding. (8, 7) Q5 (a) The price of a stock i§ $50 at time t=0. It is estimated that the price will be either $25 or $100 at t=l. It is assumed that no dividends are paid. A European call with an exercise price of $50 is available at t=0. This call will expire at t=1. The market rate of interest is