MASTER OF ARTS (ECONOMICS) Term-End Examination June, 2016 MECE-003 : ACTUARIAL ECONOMICS : THEORY AND PRACTICE SECTION - A

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1 No. of Printed Pages : 6 I MECE-0031 MASTER OF ARTS (ECONOMICS) Term-End Examination June, MECE-003 : ACTUARIAL ECONOMICS : THEORY AND PRACTICE Time : 3 hours Maximum Marks : 100 Note : Attempt questions from each section as per instructions given under each section. SECTION - A Attempt any two questions from this section. 2x20=40 1. What do you mean by survival distribution function? Discuss how you would derive future lifetime from survival distribution function. 2. The annual continuously compounded interest rate is given as The stock of a company Colra trader trades for 23 per share, and the annual continuously compounded dividend yield on stock is 0.05, in two months, its stock will trade for either 18 per share or 29 per share. The strike price of a European Call option on Colra's stock is Z 25. Using the one period binomial option pricing model, find the price to-day for one such call option of Colra's stock. 3. Name the three distributions to which extreme of a series converges to. Which of these can be used to analyse financial data? Give reasons in support of your answer and discuss the method of estimation of the relevant distributions. MECE P.T.O.

2 4. (a) (b) Discuss the features of classical Credibility. If the number of claims has a Poisson distribution, compute the probability of being within 5% of a mean of 100 claims using the Normal Approximation to the Poisson distribution. SECTION - B Answer any five questions from this section. 5x12=60 5. You bought a house For 100,000. A year later you sold it for 80,000. What is the effective rate of return on your investment? 6. The survival distribution function for an individual is determined to be s(x) \ 75 x ,0 (a) Find the probability that the person dies before reaching the age of 18. (b) Find the probability that the person lives more than 55 years. (c) Find the probability that the person dies between the ages of 25 and You are given l x = 10000(100 x) 2, 0 < x 100. Calculate the probability that a person now aged 20 will reach retirement age of A call option on Reliance Inc. stock currently trades for 45. The stock itself worth Z 900 per share. Using one-period binomial option pricing model a replicating portfolio for the call option is equal to buying (1/5) shares of stock and borrowing X. Calculate X. MECE-003 2

3 9. The stock of Black Berry currently sells for 1500 per share. The annual stock price volatility is 0.2 and the annual continuously compounded risk-free interest rate is The stock's annual continuously compounded dividend yield is Find the value of d 2 in the Black-Scholes formula for the price of a call option on Black Berry stock with strike price Z 1600 are time to expiration of 3 years. 10. A life insurance company has insured 5 individuals with the following characteristics : Individual Probability of death in the next year Benefit receivable upon death Find the variance of aggregate losses next year for this group of five life insurance policies. 11. (a) Ellen bought a share of stock for 10, and it is believed that the stock price moves (day by day) as a simple random walk with p = What is the probability that Ellen's stock reaches the high value of 15 before the low value of 5? (b) What is the probability that Ellen will become infinitely rich? 12. List the operational functions of LIC which have been included for exercising control by the government. Support such steps by giving the rationale. MECE-003 3

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