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SOA真题Course8V（第四课）：November2002北美精算师考试

来源：高顿网校 2014-08-26

　　以下为高顿网校美女小编们8月26日下午1点14分辛勤到现在的劳动成果：SOA真题Course8V（第四课）：November2002北美精算师考试。
　　13. (8 points) You are buying an over-the-counter one year American call option on a zerocoupon,

　　default risk-free, bond with a one year maturity.

　　You are given:

　　? the risk free interest rate is 0% at every duration

　　? the default risk premium on a one year zero-coupon bond issued by the option

　　writer that ranks equal to the option in the event of default is 1.5%

　　? the strike price and the forward value are $1000

　　? the volatility is 20%

　　(a) (2 points) Calculate the price of this option in the no-default world using Black’s

　　model.

　　(b) (4 points) Demonstrate how the answer in (a), appropriately adjusted for the

　　presence of risk of default by the option writer, can be used as the lower bound

　　for the price of this option. Calculate this lower bound.

　　(c) (2 points) Explain how the over-the-counter dealer can create a replicating

　　portfolio to delta-hedge a similar European call option on this bond against

　　movements in interest rates and credit rating.

　　COURSE 8:Fall 2002 -13- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　14. (13 points) You are an investment actuary in charge of the derivatives trading and

　　research department for an investment banking firm. A Wall Street venture capitalist has

　　approached you regarding a potent ial acquisition of an industrial company.

　　You have been asked to study the following acquisition project and explain the use of

　　contingent-claims analysis in capital budgeting:

　　? After one year the project is assumed to generate expected values of

　　subseque nt cash flows which follow a multiplicative binomial process.

　　? For each annual period, the value either increases to u = 1.7 or decreases to

　　d = 0.8 of its earlier value.

　　? The gross value of the project’s expected cash flows is currently valued at $50

　　million.

　　? The probability that governs state transitions is equal to 0.5.

　　? The buyer is considering the opportunity to invest a required immediate outlay

　　of $52 million (all equity).

　　Use the following assumptions:

　　? A twin security for this transaction exists in the financial markets, and its

　　payoffs are 10% of the gross project values.

　　? The expected rate of return (or risk-adjusted discount rate) is 25% per annum.

　　? The risk- free rate is 10% per annum.

　　(a) Explain how real options on projects and call options on stocks are analogous and

　　record the major areas where this analogy is deficient.

　　(b) Describe the key strategic questions that the management of the acquiring

　　company must address when evaluating an investment.

　　(c) Review the possible option classifications and the different components of the

　　option value to help management recognize and understand the potential

　　combinations of real options available in an investment opportunity.

　　(d) Compare and contrast the use of the traditional (passive) discounted cash flow /

　　decision-tree analysis (DCF/DTA) approach versus the options-based approach of

　　contingent-claims analysis to valuing real investments when operating and

　　financial flexibility options are present.

　　COURSE 8:Fall 2002 -14- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　14. Continued

　　(e) Assume the firm has a one-year deferral agreement granting it the exclusive right,

　　but not the obligation, to make the investment by next year if the project value

　　next year turns out to exceed the necessary investment at that time.

　　Determine the value of the option to wait provided by the agreement using both

　　the contingent-analysis and traditional DCF/DTA approaches.

　　(f) Select the approach in (e) that produces the correct value for this investment

　　opportunity. Justify your choice by describing how the firm would arrange for the

　　least amount of funds needed to purchase the project.

　　(g) Assume that the firm has the option to finance $25 million out of the required

　　investment outlay of $52 million by borrowing it against the project’s expected

　　future cash flows. The amount is to be repaid with interest in two years at an

　　annual interest rate of 14%. The balance of $27 million is to be supplied today by

　　the firm’s equity holders.

　　Determine the value of the financial flexibility provided in this debt financing

　　arrangement.

　　COURSE 8:Fall 2002 -15- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　15. (4 points) A pension fund has an asset allocation target of 40% bonds and 60% equities.

　　You are given the following assumptions:

　　Expected return Standard deviation

　　Bonds 6% 5%

　　Equities 7% 10%

　　Return correlation = 0.80

　　Risk tolerance = 0.75

　　Tracking-error tolerance = 0.02

　　(a) Explain why the optimal asset allocation based on the mean-variance

　　(MV) optimizer is often different from the real world asset allocation.

　　(b) Calculate the optimal asset allocation using the mean-variance/trackingerror

　　(MVTE) utility function.

　　(c) Predict the results if the tracking-error tolerance goes to:

　　(i) infinity

　　(ii) zero

　　COURSE 8:Fall 2002 -16- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session
　　压力不是有人比你努力，而是那些比你牛B几倍的人依然比你努力。——高顿网校极品语录

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