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。