所有滴高顿网校赴考者们，无论你来自何方，大家请再接再厉，拿下10月秋季精算师资格证哦！2002.11北美精算师真题Course8V课程（第二节）历年的最重要了。
　　5. (5 points) You are a research analyst supporting the corporate bond desk at LifeCo and
　　have been asked to consider investing in synthetic convertible notes (SCN) as a new asset
　　class for the Equity Linked GIC portfolio.
　　You are given the following information for an SCN:
　　Face amount: $100 million
　　Maturity: 7 years
　　Coupon: 4% paid annually
　　Strike: 1.3 ? purchase price
　　Purchase price: par
　　Index: S&P 500
　　At-the-market swap rate on LIBOR: 7.5%
　　(a) List and briefly describe the 3 factors that impact price volatility and performance
　　sensitivity of structured notes.
　　(b) Calculate the up- front payment the swap dealer receives on the hedge.
　　(c) Calculate the annual internal rate of return (IRR) over the term of the SCN for the
　　following 2 scenarios of annual returns of the S&P 500 index:
　　Scenario Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
　　1 -5% -7% 12% 0% 16% 8% -1%
　　2 8% 15% 3% 9% -6% 20% -10%
　　(d) Analyze the suitability of this SCN for the asset portfolio backing LifeCo’s Equity
　　Linked GICs.
　　COURSE 8: Fall 2002 - 6 - GO ON TO NEXT PAGE
　　Investment
　　Morning Session
 
　　6. (7 points) A risk- free investment, R, and investments S and T have the following Ito
　　processes:
　　dR = 0.05Rdt + 0.10Rdz1
　　dS = 0.10Sdt + 0.20Sdz2
　　dT = 0.03Tdt + 0.20Tdz3
　　The correlation matrix for R, S and T is known.
　　The payoff of a European derivative, F, is determined from the values of R, S and T on
　　F’s exercise date.
　　(a) Formulate an * for the process followed by F using constants where
　　possible.
　　(b) Describe the steps required to value F using a Monte Carlo simulation.
　　COURSE 8: Fall 2002 - 7 - GO ON TO NEXT PAGE
　　Investment
　　Morning Session
 
　　7. (11 points) A regulatory proposal would require companies to disclose the value of
　　options granted to their employees. Your CFO is concerned that under this proposed
　　regulation, changes in your firm’s stock price will create earnings volatility, and has
　　identified two options programs which would impact earnings under this proposal.
　　Price at purchase Purchasing rights
　　Stock Option
　　Plan (SOP)
　　market price that
　　prevailed when the
　　option was granted
　　employees are given the right to purchase
　　shares of the firm’s stock at the end of two
　　years
　　Employee Stock
　　Purchase Plan
　　(ESPP)
　　80% of the market
　　price at the beginning
　　of the year
　　stock is delivered to employees at the end of
　　the year if the stock price is above the
　　discounted level at that time, however, if the
　　price is below this level, the employee’s
　　money is returned and no stock is delivered
　　?  The options granted under the SOP from year-end 1999 have expired.
　　?  At year-end 2000, options on 10,000 shares were granted under the SOP when the
　　stock price was $24.
　　?  At year-end 2001, options on 15,000 shares were granted under the SOP when the
　　stock price was $30.
　　?  Under the ESPP, employees have subscribed to purchase $360,000 worth of stock in
　　2002.
　　It is January 1, 2002. The firm pays a continuous annual dividend of 3.0%, the stock’s
　　annual volatility is 40%, and the risk free rate is 5.0%. There are no exchange-traded
　　options available on this stock.
　　(a) List the options embedded in these two programs.
　　(b) Propose alternatives to hedge against changes in the stock price.
　　(c) Determine the probability that the options granted under the ESPP will finish inthe-
　　money.
　　(d) Calculate the delta of the portfolio of options under the SOP and ESPP programs
　　and interpret the sign of the delta.
　　(e) Determine the total value of the options granted under these two programs.
　　(f) Select a second order measure that can be used to hedge variations in value and
　　describe how it would be applied.
　　COURSE 8: Fall 2002 - 8 - STOP
　　Investment
　　Morning Session
　　乐观者在灾祸中看到机会；悲观者在机会中看到灾祸。——高顿网校谚语相赠

 

 
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