【北美精算师考试】SOA真题November2004CourseV（最后一部分），这是很重要的精算师考点，请大家时刻拿出来背诵。
　　18. (6 points) You are a Risk Manager for a US-based trading company with international
　　operations. The company has the following risk exposures:
　　?  a contract to deliver 1,000 ounces of gold semi-annually for one year at a maximum
　　price of $400 USD per ounce
　　?  beginning of period 1 year LIBOR (in USD) on a $10,000,000 bank deposit payable
　　at the end of the year
　　?  7,000,000 Euro receivable from financing a customer purchase due in 1 year
　　You are given the following information:
　　?  Available hedging instruments include currency forwards, USD swaps, and gold
　　options.
　　?  Current exchange rate = .75 Euro / $1 USD
　　?  Risk free rates USD Euro
　　6 month 2.5% 4.0%
　　1 year 3.0% 5.0%
　　Swap rates (USD) Floating rate Fixed Rate
　　6 month LIBOR 2.75%
　　1 year LIBOR 3.25%
　　?  Option price per 1 ounce go ld contract with strike of USD 400:
　　Buy
　　Call
　　Sell
　　Call
　　Buy
　　Put
　　Sell
　　Put
　　6 month 4.0 3.6 6.0 5.2
　　1 year 6.0 5.6 8.0 7.2
　　(a) Describe the advantages of managing risk of strategic exposures in general as
　　defined in Chew.
　　(b) Propose a methodology to completely hedge the company against its strategic
　　risks.
　　(c) Calculate the market value of the risks in USD.
　　COURSE 8: Fall 2004 -19- GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
 
　　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
　　?  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
　　高顿网校之精品语录：多读一些书，让自己多有一点自信，加上你因了解人情世故而产生的一种对人对物的爱与宽恕的涵养。那时，你自然就会有一种从容不迫、雍容高雅的风度。——罗兰