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

2373010015 (NEP-UGCF) Financial Statistics (DSE) BSc. (Hons.) 2. There are TWo sections in this paper. What is intemal rate ofretum? Explain with the help of example. An 8% bond with 1 8 years to maturity has a yield of9%. What is the price of this bond if the coupon payments are made (i) annually (ii) half yearly and face value is $1,000? Define `intrinsic value' of a.call and put option at time i. Under what conditions is an option said to be `in-the-money', `at-the-money'; and `out-of-money'? One of the most popular types of spread is a bull spread. A bull call-price spread can be made by buying a call option with a certain strike price and selling a call option on the same stock with higher exercise price. Both call options have same maturity date. Consider a European call with a delively price of Ki and second European call with delivery price of K2. Draw the payoff for this strategy. Consider a butterfly strategy: a long call option with an exercise price of 100 USD, a second long call option with an exercise price of 120 USD and two short calls with an exercise price of 110 USD. Give the payoff table for different stock values. When will this strategy be preferred? ®. (8). 2. (a) (b) Consider a long forward contract on a 5-year bond currently trading at a price of € 900. The delivery price is €910, the time to maturity of the forward contract is 1 year. The coupon payment of the bond of € 60 occurs after 6 and 12 months. The continuously compounded armual interest rate for 6 and 12 months are 9% and 10% respectively. Obtain the value of forward contract. Derive /ot ws2dws, where wc is a Brownian motion. The projected cashflows in (€) for a multinational company from a 4-year project are as follows: Initial cost 4,68,_000 Year Cashflow Ist Year 1,35,000 IInd Year 2,40,000 IIIrd Year 1,85,000 Ivth Year 1,35,000 Consider a long forward contract to buy a stock which has a price ofst at time t. Let K be the delivery price and I be the maturity date. Further let V¢, St) denote the value of the long forward contract at time t as a function of the current price St = s . The time to maturity is 7 = T - t. Assume that the interest rate is constant during the time to maturity. The stock does not pay any dividend and does not involve any costs during the time to maturity I. Then show that Hence obtain the forward price. 3. (a) The correlation (p) betweentwo assets `A' and `B' is o.1. The expectedretuns and standard deviations of returns are given in the following table: Asset Return (%) Standard Find the proportions er and (1-Ch) of `A' and `8' respectively that defines a portfolio consisting of them such that it has minimum variance. (ii) Find the expected retun and the standard deviation of this portfolio. a) Construct the payoff table along with the payoff graph for the following two alternative strategies: Strategy 1 : consists of buying a European call option with a strike price $110