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2004年11月北美精算师SOACourseV（最后一块内容真题）

来源：高顿网校 2014-08-13

　　高顿网校小编提醒您，及时登录北美精算师各地的官方网站报名，以免耽误您精算师的考试。2004年11月北美精算师SOACourseV（最后一块内容真题），再多看看吧。
　　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.

　　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.

　　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.
　　路是脚踏出来的，历史是人写出来的，人的每一步都是在书写自己的历史。——高顿网校生活感悟

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