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2002.11北美精算师真题Course8V课程（第二节）

来源：高顿网校 2014-08-26

　　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 expression 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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