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SOA真题November2004CourseV（最后一部分）——北美精算师考试SOA

来源：高顿网校 2014-07-28

　　下边是SOA真题November2004CourseV（最后一部分）——北美精算师考试SOA，好好看官方大纲哦，看累了时间长了，就去玩耍吧。
　　19. (6 points) BB No-Show Inc, a US company, is negotiating to buy a Japanese company.

　　The deal is expected to be closed in 3 months, with cash payment in Japanese Yen.

　　The chief financial officer of BB No-Show Inc has decided to buy an at-the- money call

　　option on Japanese Yen to hedge against a sudden increase in Yen relative to the US

　　dollar.

　　You are given the following information:

　　? Option type: at-the-money European call option.

　　? Maturity date of the option: 3 months (65 trading days)

　　? The option-holder has the right to buy 220 billion of Japanese Yen.

　　? US Treasury bond rates are 1% compounded continuously

　　? Japanese government bond rates are 0.05% compounded continuously

　　? Current exchange rate: 1 USD = 110 Japanese Yen

　　? Japanese Yen / USD exchange rate has daily volatility of 0.62%

　　An asset price S follows the stochastic process dS =mSdt+sSdz

　　(a) Apply Ito’s lemma to derive the process followed by G = S exp (r(T-t))

　　where r is the risk- free rate and (T-t) is the time to maturity.

　　(b) Interpret the derived stochastic process if G is a stock paying dividends at a

　　continuous rate.

　　(c) Define the stochastic process of G in the risk neutral world, assuming G is the

　　spot foreign exchange rate.

　　(d) Calculate the value of the call option using the applicable Black-Scholes formula

　　for this call option on Japanese Yen.

　　COURSE 8: Fall 2004 -20- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　20. (3 points) You are given the following information at time t = 0:

　　? Total assets supporting participating life = $74,081,822世纪考试网版权所有

　　? Total participating life liabilities = $66,673,640

　　? Maturity of policy = 10 years

　　? Guaranteed interest rate of the policy = 3% continuously compounded

　　? 10-year European call option values for an asset with current price

　　$74,081,822:

　　Strike price Call Value

　　$85,000,000 $8,520,220

　　$90,000,000 $7,625,000

　　$95,000,000 $4,502,535

　　$100,000,000 $1,204,330

　　$105,000,000 $820,300

　　Calculate the equilibrium participation level for policyholders.

　　**END OF EXAMINATION**

　　AFTERNOON SESSION
　　高顿网校之名人语录：无论我现在怎么样，还是希望以后会怎么样，都应当归功于我天使一般的母亲。我记得母亲的那些祷告，它们一直伴随着我，而且已经陪伴了我一生。

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