Kevin examines both American- and European-style options that have the same stoc
ID: 2758114 • Letter: K
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 in your response. Thank you in advance!
Explanation / Answer
Solution 1
American Option is always worth more than the European Option. In the given data, the exercise price is $42 for both the call and put option. The stock price is currently $40. The one year Put option value is $3. It means, for European style option, investor has to wait for next one year and then he can exercise only the option if the stock price is less than $42. But in the case of American style option, he can exercise the right at any time before the expiration. There may be a case when the stock price may get lower deep during a year say for example, $35, then on exercising the option, he can make pay off of $7 (42 - 35). It may be higher than the payoff made on European style option. Thus American style option has always higher value. In this case, its value would be higher than $3.
Solution 2
According to Put Call Parity theorem,
C + Ke-rt = P + S
Where,
C = Call Option price
K = Exercise Price of Option
P = Put Option price
S = Stock price
Hence,
C + 42*e-0.045*1 = 3 + 40
C + 42*e-0.045 = 43
C + 42*0.956 = 43
C + 40.152 = 43
C = 43 - 40.152
C = 2.848 = 2.85
Solution 3
(a) With the increase in the volatility of underlying stock’s price, the value of option increases. It is due to the fact that with the high fluctuation in stock’s price there will be high chance to get higher payoff through exercising the option.
(b) With the increase in interest rate, the value of call option increases while the value of Put option decreases.
(c) With the date of expiration decreases, the value of option decreases.
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