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历年SOA真题November2001Course8V（四）——SOA精算师考试

来源：高顿网校 2014-07-21

　　请认真看历年SOA真题November2001Course8V（四）——SOA精算师考试，请仔细记住其中的纲要。
　　12. (6 points) XYZ Life Insurance Company originates home equity loans to elderly

　　homeowners. The loan is not due for repayment until the borrower dies or moves out of

　　the property. The amount of the initial loan is based on the age of the borrower and the

　　property value. Interest and fees are accumulated until repayment. The only source of

　　repayment is the property.

　　A government institution provides insurance against the risk that the eventual repayment

　　amount is less than the loan balance at that time. The premium, which is added to the

　　loan balance, is an initial fee of 2% of the loan value and 0.5% of the outstanding loan

　　balance annually. The homeowner can repay in full at anytime without penalty.

　　The loan interest rate is reset every six months. The net rate of interest, after insurance

　　premium and expenses, is the rate on 6 month CD's plus 3%. Based on projected cash

　　flow, the company issues GICs of 1, 3 and 5-year maturities.

　　The following three strategies have been proposed:

　　(i) Issue fixed rate instead of variable rate loans.

　　(ii) Swap the variable interest rates for fixed interest rates.

　　(iii) Purchase insurance against the risk of homeowners dying earlier or later

　　than expected.

　　(a) Analyze the risks associated with the current strategy.

　　(b) Describe the risks associated with the three proposed strategies.

　　COURSE 8: Investment - 14 - STOP

　　November 2000

　　Morning Session

　　13. (7 points) You are given the following information about a European put option on a

　　non-dividend paying stock:

　　? Stock price 40

　　? Risk-free interest rate 7% (continuously compounded)

　　? Strike price 35

　　? Time to maturity 8 months

　　You are also given the following volatilities derived from actively-traded European call

　　options on the stock:

　　Strike Price

　　Time to maturity 30 35 40 45

　　3 months 0.290 0.225 0.180 0.150

　　6 months 0.280 0.230 0.230 0.160

　　1 year 0.275 0.236 0.221 0.180

　　(a) Calculate the price of this option using the Black-Scholes formula. Show your

　　work.

　　(b) Contrast the stock price distribution implied by the volatility matrix with the lognormal

　　distribution.

　　(c) Describe models of stock price behavior that are consistent with the implied

　　distribution.

　　14. (5 points) The asset portfolio of a U.S. life insurance company includes real estate

　　properties. The portfolio manager is currently considering adding to the portfolio an

　　equity investment in an office building in Atlanta. The building is fully leased at fixed

　　rates with 10 years remaining on its leases and subject to a mortgage equal to 50% of its

　　current market value. The mortgage is for 10 years, interest-only, and interest is paid

　　monthly at 1 month LIBOR plus a fixed spread.

　　(a) Evaluate the risks of this specific investment.

　　(b) Propose approaches to reduce the risks identified in (a).

　　COURSE 8: Investment - 15 - STOP

　　November 2000

　　Morning Session

　　15. (7 points) The debt of Company X consists of one zero coupon bond with the following

　　payment probabilities at maturity:

　　Default Risk Probabilities

　　Real World Risk-Neutral

　　No default 85% 75%

　　Default with 70% recovery 10% 15%

　　Default with 35% recovery 5% 10%

　　Additional information is as follows:

　　? Debt maturity 5 Years

　　? Payment due at maturity 1000

　　? Risk-free rate 5% (continuously compounded)

　　Company Z has written a European option which will pay 1000 in 5 years in exchange

　　for Company X’s debt.

　　Assume Company X and Z have equal but independent default risk.

　　(a) Calculate the market's expected spread for the bond over the risk-free rate. Show

　　your work.

　　(b) Determine the possible payoffs at maturity of a European option written by

　　Company Z which will pay 1000 in 5 years in exchange for Company X's debt.

　　(c) Calculate the value of this option. Show your work and state your assumptions.

　　COURSE 8: Investment - 16 - STOP

　　November 2000

　　Morning Session

　　16. (6 points) You are given the following information about two estimations of the Market

　　Value (MV) of the total policy liabilities of a life insurance company:

　　Method used Estimation

　　MV (Liability) $2.0 billion

　　MV (Asset) – MV (Equity) $1.8 billion

　　(a) Contrast the two methods.

　　(b) Explain how the uncertainty of cash flows can be reflected in the estimation of the

　　market value under the MV (Liability) method.

　　17. (5 points)

　　(a) Describe the following fixed income risk measures:

　　(i) prepayment uncertainty,

　　(ii) volatility risk (vega),

　　(iii) zero volatility spread (ZVO),

　　(iv) spread duration.

　　(b) Your company’s fixed income portfolio contains MBS, CMBS, CMO, ARM,

　　callable and putable corporate bonds, and ABS. Explain the impact of each of the

　　risk measures above on the different fixed income asset classes.

　　** END OF EXAMINATION **

　　AFTERNOON SESSION
　　高顿网校之极品语录：我们不得不饮食睡眠游惰恋爱，也就是说，我们不得不接触生活中最甜蜜的事情：不过我们必须不屈服于这些事物。 —— 约里奥·居里

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