Kevin examines both American- and European-style options that have the same stoc

Question

Kevin examines both American- and European-style options that have the same stock, expiration date, and strike price. Kevin argues that the European-style option will be sold at a higher price than the American-style option.

A. Examine Kevin’s belief given that the stock closed at $40, has an exercise price of $42 on the put and call options, the one-year put option is $3, the Treasury bill is 4.5%, and it expires in one year.

B. Calculate the value of a European-style option given put-call parity.

C. Determine the impact on the call option if (i) there is a rise in volatility; (ii) there is an increase in interest rate; and (iii) the time of option expiration declines.

Please be more specific. Thank you in advance!

Explanation / Answer

Stock Price now (P) 40 Exercise Price of Option (EX) 42 Number of periods to Exercise in years (t)              1.00 Compounded Risk-Free Interest Rate (rf) 4.50% Standard Deviation (annualized s) 20.00% Present Value of Exercise Price (PV(EX)) 40.1519 s*t^.5 0.2000 d1 0.0810 d2 -0.1190 Delta N(d1) Normal Cumulative Density Function 0.5323 Bank Loan N(d2)*PV(EX) 18.1750 Maximum Value of Call Option 3.1169 Value of Put Option 3.2688 increse in volatility, interest rate, time of option declines Input Data Stock Price now (P) 40 Exercise Price of Option (EX) 42 Number of periods to Exercise in years (t)              0.50 Compounded Risk-Free Interest Rate (rf) 6.00% Standard Deviation (annualized s) 30.00% Present Value of Exercise Price (PV(EX)) 40.7587 s*t^.5 0.2121 d1 0.0175 d2 -0.1946 Delta N(d1) Normal Cumulative Density Function 0.5070 Bank Loan N(d2)*PV(EX) 17.2342 Maximum Value of Call Option 3.0448 Value of Put Option 3.8035

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