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经典历年真题November2004CourseV（5）——SOA精算师考试

来源：高顿网校 2014-07-22

　　以下则是高顿网校小编为您汇编了经典历年真题November2004CourseV（5）——SOA精算师考试，请尽快吸收，一周内应该差不多哦。
　　15. (8 points) BMC Olympiad Inc. is looking for a potential acquirer within the next 12

　　months. You have been asked to assess the company’s near-term credit risk exposure

　　before proceeding with an appraisal analysis of BMC Olympiad’s operating businesses.

　　You are given the following information:

　　? Company’s credit rating: BBB

　　? Risk-free rate: 5% per annum compounded continuously

　　? Market value of company’s assets today: $21 billion

　　? Market value of company’s equity today: $5 billion

　　? Company’s debt due to be repaid including interest one year from now:

　　$17 billion

　　? Volatility of equity returns: 80%

　　? Volatility of asset returns: 20%

　　? A company with similar credit risk has five-year corporate zero-coupon

　　bonds trading at 350 basis points above risk-free rate

　　? Assumed recovery rate in the event of a default: 40% (as percent of bond’s

　　no-default value)

　　(a) Estimate the risk-neutral probability that the company will default on its debt

　　using Merton’s model.

　　(b) Determine the expected loss on the debt and the expected recovery in the event of

　　a default.

　　(c) Compare the default probability produced by Merton’s model versus the

　　annualized risk- neutral default probability inherent in the company’s current

　　corporate bond pricing. Explain possible reasons for discrepancy between these

　　two estimates of default probabilities.

　　COURSE 8: Fall 2004 -16- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　16. (8 points) BH Life is a small insurance company that has sold a product with a minimum

　　return guarantee. The investment guarantee is equivalent to a European put option on

　　the S&P 500 index with a notional amount equal to 5,000 times the index.

　　You are given the following information:

　　? Risk free rate is 2.5%

　　? Current index value is 1200

　　? Strike price is 1100

　　? Time to maturity is 1 year

　　? Black Scholes value of the put option with implied volatility of 22% is

　　$242,900

　　? No dividends

　　? Trading costs equal 0.10%

　　? Proceeds are invested at the risk-free rate

　　? Risk- free rate and volatility do not change during the year

　　The firm wishes to delta hedge the risk on the put with quarterly rebalancing by using

　　shares of a fund tha t track the S&P 500.

　　(a) (2 points) Calculate the expected profit at the time the product is sold assuming that

　　expected volatility is 22% and the put option was priced using a volatility of 25% per

　　year.

　　(b) (1 point) Calculate the initial hedge position the firm should hold for delta neutrality if

　　the volatility assumed in their hedge is 22%.

　　(c) (3 points) Calculate the firm’s net gain or loss on the transaction, assuming that over the

　　course of the year the S&P 500 takes the following path given below, and that the

　　volatility assumed in their hedge is 22%. N(d1) factors are provided for European

　　options with the same maturity date and strike price and a volatility of 22%.

　　Time Index Level ( ) 1 N d

　　Point of sale 1200

　　End of Quarter 1 1250 0.8051

　　End of Quarter 2 1150 0.6700

　　End of Quarter 3 1050 0.3783

　　End of Quarter 4 1000

　　(d) (2 points) Describe other risk management strategies the firm can use.

　　COURSE 8: Fall 2004 -17- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　17. (4 points) You are considering investing in government issued fixed income securities in the

　　three countries listed below.

　　You are given the following information:

　　Country A B C

　　Continent Europe Asia Asia

　　Population 3M 400M 50M

　　Oil Exports 1B 150B 5B

　　Agriculture Exports 1B 150B 15B

　　Agriculture Domestic 3B 450B 40B

　　Manufacturing Exports 8B 150B 300B

　　Manufacturing Domestic 13B 600B 240B

　　Total GDP 26B 1500B 600B

　　Government type Stable Democracy Stable Democracy Emerging Democracy

　　Inflation Range 2%-20% 0%-30% 8%-16%

　　Infant deaths per 1000 1 3 5

　　Life expectancy 75 70 65

　　(a) Describe the risks of the potential investments and propose how to mitigate them.

　　(b) Rank the countries by their political stability and justify your ranking.

　　COURSE 8: Fall 2004 -18- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session
　　高顿网校之名言警句：慈母的胳膊是由爱构成的，孩子睡在里面怎能不香甜？——雨果

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