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AEM4210_assignment4_Sol

# AEM4210_assignment4_Sol - AEM 4210 Derivatives and Risk...

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AEM 4210 Derivatives and Risk Management Spring Semester 2010 Homework Assignment 4 Suggested Solutions This assignment is due in class on Friday, April 9, 2010. Total 110 points. Question 1: In the Black's Option Worksheet I want you to gain an understanding of the basic calculus and boundary conditions of Options pricing by changing values in rows 10-14. Whenever you change the value in the rows make sure that you reinitialize any previously changed so that the time to maturity is 0.5 (half a year), volatility is 0.25, risk free interest rate is 3%, Current futures price is 100, and strike price is 100. In all cases provide a properly labeled graph of the put and call prices and briefly describe what you observe. (10 points each) a) Change time to maturity starting with 1.0 (1 year=12 months) to 1 months (1/12) Put and Call option premiums are identical. As the time to maturity increases, the call and put option premiums increase at a decreasing rate. The longer time to maturity gives higher flexibility and greater probability of the option moving in or out of the money. 1

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b) Change the volatility starting with 0.05 and incrementing each column by 0.05 to a max of 0.60. Put and Call option premiums are identical. The price of option increases as volatility increases. The more volatility creates the larger price swings and higher probability of the option moving in the money. c) Change the risk free interest rate from 0 to 5.5% by incrementing each column by 0.005. Put and Call option premiums are identical. The value of the call and put option is decreasing with the risk free interest rate. The higher the risk free interest rate, the lower 2
the present value of the underlying futures, and the value of the option. As the risk free rate increases, investing in the risk free asset becomes more valuable, so investors shift their money to invest in the risk free asset. Demand of risky asset is lower, therefore; the option price decreases.

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AEM4210_assignment4_Sol - AEM 4210 Derivatives and Risk...

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