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北美精算师真题考纲曝光：November2003Course8V（最后一堂课内容）

来源：高顿网校 2014-08-29

　　以下是北美精算师真题考纲曝光：November2003Course8V（最后一堂课内容），北美精算师考生们用心记在脑子里呀，内容很多，可分批记忆。
　　20. (6 points) A financial institution has sold short three European call options on a stock

　　with the following characteristics:

　　Stock price: 100

　　Strike price: 110

　　Volatility: 20%

　　Expiry: 2 years

　　Contract size: 1,000 shares

　　Dividends: none

　　Risk-free rate: 5%

　　(a) (4 Points) Describe and evaluate strategies the financial institution can use to

　　manage the risk of this portfolio.

　　(b) (1 Point) Calculate delta, theta and gamma for the portfolio.

　　results for the portfolio satisfy the Black-Scholes-Merton differential equation.

　　COURSE 8: Fall 2003 - 17 - GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　21. (6 points) A model of the type GARCH(1,1) is being used to set volatility for integer

　　values of strike price for an option pricing model that is based on a lognormal

　　distribution. You have the following information on the model for a specific underlying

　　asset:

　　? A weight of 10% is given to a variance of 4% that is reached

　　asymptotically as the strike price increases toward infinity.

　　? The model assumes returns are a constant 20%.

　　? A weight of 80% is given to the variance determined for the prior strike

　　price.

　　? The variance is 9% for a strike price of 0.

　　(a) Calculate the change in volatility for each of strike prices of 1 and 2 assuming the

　　variance for a strike price of 0 decreases from 9% to 8%.

　　(b) Assess whether the model with the given parameters is more appropriate for an

　　equity option or a currency option. Support your answer by interpreting the

　　resulting implications for the volatility smile.

　　assuming the distribution of returns conditioned on the variance is normal.

　　COURSE 8: Fall 2003 - 18 - GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　22. (7 points) You would like to calibrate a new Monte Carlo pricing model by comparing

　　the model price to the Black-Scholes price of a European call option on a non-dividend

　　paying stock. The European call option and the underlying stock have the following

　　characteristics:

　　Current stock value = 100

　　Expected growth rate of the stock price = 10%

　　Volatility = 25%

　　Exercise price = 95

　　Time to maturity = 6 months

　　Risk-free interest rate = 6%

　　Black-Scholes price of the option = 11.37

　　Assume that the percentage change in the stock price is normally distributed.

　　(a) Calculate the control variate technique adjustment using stratified sampling on 3

　　intervals.

　　(b) Describe additional techniques that can be used to improve the efficiency of the

　　Monte Carlo method.

　　American options.

　　COURSE 8: Fall 2003 - 19 - GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　23. (6 points) You are given the following information about an interest rate collar with

　　quarterly resets. Assume quarterly compounding unless otherwise indicated.

　　Notional amount = 100,000,000

　　Strike interest rate for cap = 7.0%

　　Strike interest rate for floor = 4.5%

　　Time to expiration = 2 years

　　Time t Forward 3-month interest

　　rate starting at time t

　　Zero-coupon interest rate

　　to time t (continuous

　　compounding)

　　9 months 5.0% 4.49%

　　12 months 5.2% 4.64%

　　15 months 5.3% 4.77%

　　(a) Compare the collar to a portfolio of bond options with equivalent payoffs.

　　(b) Calculate, using Black’s model, the price of the floorlet that prevents the interest

　　rate from being lower than the strike price for 3 months starting in one year.

　　Assume that the volatility of the underlying three-month rate is 20%.

　　mortgage backed security.

　　COURSE 8: Fall 2003 -20- STOP

　　Investment

　　Morning Session

　　24. (3 points) You have been asked to review the trading costs of the following stock:

　　Time Price Number of

　　shares traded

　　(Previous close is 44 1/8)

　　1:40 pm 44 1/8 1000

　　1:42 44 1/4 2000

　　1:45 44 500

　　1:46 43 7/8 5000

　　1:50 43 3/4 2000

　　1:51 43 7/8 400

　　1:54 44 1/4 6000

　　(a) Explain why the measurement of trading costs is important.

　　(b) Calculate the price impact of trading for the above stock using the “money flow”

　　system as adapted by Birinyi.
　　那隐藏着的宇宙本质自身并没有力量足以抗拒求知的勇气。对于勇毅的求知者，它只能揭开它的秘密，将它的财富和奥妙公开给他，让他享受。——高顿网校做人道理

扫一扫微信，关注精算师*7考试动态

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