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Homework3

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Submitted By personalfang
Words 257
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Homework #: 3: Due: November 20, 2015

You are given the following information. S=50, X=50, simple annual risk-free interest rate is 5%, standard deviation of monthly stock returns is 10%. [Caution: must covert to annualized continuous compounding values]

1. What is the value of a one-year European call option using the Black-Scholes option pricing model? Show values of N(d1) and N(d2) using Excel and using the formula provided in the lecture note.

rc = ln (1+rs) = 0.04879 = 4.879%

d1 = [ln 50/50 + 4.879%*1 + (10%2*1)/2] / (10%*√1) = [0 + 4.879% + 0.005] / 0.1 = 0.05379/0.1 = 0.5379
N(d1) = 0.70467695

d2 = 0.5379 – 10%*√1 = 0.5379 – 0.1 = 0.4379
N(d2) = 0.66927061

e-rcT = e-0.04879*1 = 0.952381

C0 = 50*0.70467695 – 50*0.952381*0.66927061 = 35.2338475 – 31.8700306 = 3.3638

2. Solve the value of the above one-year American call using CBOE Options Toolbox

[pic]

3. Noting the Greek values: How will the call value change for

a. 1% change in interest rate
[pic]
b. $1 increases in the stock price
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c. Reduction of one-day in maturity
[pic]

4. All options are European and the stock does not pay a dividend. Which option is relatively more expensive? Explain. (Hint: Compute implied volatility).

a. S = $50, C (X=$60) =$14
[pic]
b. S = $50, C (X=$65) =$10
[pic]
Option (a) is relatively more expensive because the higher Implied Volatility.

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