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2014年份北美精算师——SOA真题放送November2001Course8V（2）

来源：高顿网校 2014-07-28

　　依然奋斗在一线的高顿网校的北美精算师的青年人们，请时刻监督我们每日更新考试辅导的讲义哦。2014年份北美精算师——SOA真题放送November2001Course8V（2），请收下。
　　3. (22 points) LifeCo wants to establish a delta/gamma/vega/rho hedge on the equity

　　exposure of their variable annuity business, using positions in some or all of the

　　following assets.

　　Asset Price Delta Gamma Vega Rho

　　S&P 500 Future 0 100 0 0 0

　　30-year Treasury

　　bond future

　　0 0 0 0 -12,598

　　1-year Put 51.98 -0.34608 0.00184 3.688 -3.98

　　1-year Call 109.45 0.65392 0.00184 3.688 5.45

　　10-year Put 42.88 -0.10529 0.00029 5.761 -14.82

　　10-year Call 489.57 0.89472 0.00029 5.761 40.51

　　LifeCo’s liabilities have the following sensitivities:

　　Delta – 2,659.90

　　Gamma 1.036

　　Vega 1952

　　Rho – 101,910,000

　　All deltas and gammas are per unit change in the S&P 500 index.

　　Vegas are per 1% change in volatility

　　Rhos are per 1% change in interest rates

　　Current value of the S&P 500 is 1300

　　(a) (6 points) Construct a hedge position using the above assets that minimizes the

　　cost of the hedge without regard to the operational guidelines.

　　(b) (1 point)

　　(i) Assess whether the hedge determined in part (a) would be in violation of the

　　operational guidelines for use of derivatives.

　　(ii) Recommend any necessary changes to the guidelines.

　　COURSE 8: Investment - 5 - GO ON TO NEXT PAGE

　　N

　　ovember 2000

　　Morning Session

　　3. (Continued)

　　(c) (6 points)

　　(i) Calculate the 1-day, 99%VAR on the portfolio, before and after the hedge is

　　applied using delta and gamma to approximate it.

　　(ii) Assess the validity of these numbers.

　　(d) (4 points) LifeCo is worried about the liquidity of the 30-year Treasury bond

　　future.

　　(i) Analyse the effectiveness of the proposed hedges with respect to rho.

　　(ii) Propose alternative methods and alternative assets to improve rho exposure

　　coverage.

　　(e) (5 points) The newly appointed Chief Risk Officer is concerned about the use of

　　derivatives in the hedging strategy. Verify that the operational and credit risks of

　　managing derivatives have been adequately covered by LifeCo’s operational

　　guidelines for use of derivatives.

　　COURSE 8: Investment - 6 - GO ON TO NEXT PAGE

　　November 2000

　　Morning Session

　　4. (6 points) You have the following market information:

　　? Price of a 2-year zero coupon bond: 89

　　? 1-year short rate i0 b g: 7%

　　A new actuarial student in your company has implemented an interest rate model to price

　　interest rate derivatives. His model gives the following results:

　　Sample space i1

　　w1 6.0%

　　w 2 8.0%

　　(a) Describe the different types of model risk that must be considered when building

　　or using a model.

　　(b) Explain the concept of arbitrage-free in the context of an interest rate model for

　　pricing derivatives.

　　(c) Assess the validity of the proposed model given the information above.

　　5. (4 points)

　　(a) Describe how the following factors will generally impact the Option-Adjusted

　　Spread (OAS) of a Planned Amortization Class (PAC) for a typical PAC bond.

　　(i) Average life of the PAC

　　(ii) Premium versus discount collateral

　　(iii) Lockout versus no lockout

　　(iv) Window length

　　(v) Whether or not a Z-bond funds the PAC

　　(b) Describe the shortcomings associated with OAS in evaluating mortgage-backed

　　securities.

　　(c) Describe how you would use OAS, considering the shortcomings.

　　COURSE 8: Investment - 7 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　6. (5 points) You are given the following information on a European put option on a bond:

　　? Put option

　　? Maturity of option 1 year

　　? Strike price level 1000

　　? Underlying bond

　　? Cash price 1000

　　? Present value of bond coupon payments 100

　　? 1 year forward yield volatility 10%

　　? Modified duration 10 years

　　? Forward yield 7%

　　? Risk-free rates are flat at 5.13%

　　(a) Calculate the price of this option using Black’s model. Show your work.

　　(b) Contrast alternatives for calculating delta and gamma for this option with a stock

　　option.
　　高顿网校之名人名言：母爱，你如春天里温暖的阳光，也像婆裟的大树，让我淋浴在明媚的春光之中，借着大树的绿荫庇护，如小草一样茁壮成长。

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