Question

Consider an option on a non-dividend paying stock when the stock price is $67, the exercise price is $61, the risk-free rate is 0.5%, the market volatility is 30% and the time to maturity is 6 months. Using the Black-Scholes Model

(i) Compute the price of the option if it is a European Call.

(ii) Compute the price of the option if it is an American Call.

(iii) Compute the price of the option if it is a European Put.

(iv) Assuming two dividend payments $1.75 and $2.75, two months and five months from now, compute the price of the option if it is a European Call.

(v) Refer to the dividend information provided in (iv) above. Compute the price of the option if it is an American Call. Provide a graphical illustration to demonstrate how the price of this American Call and the payoff from the same change with respect to changes in the stock price.

Answer 1

Solution:

i)

ii) In case of Call Option of a non dividend paying stock, the Price of the American Call option is the same as that of the European Call option, i.e., in this case it would be $8.42.

iii) To compute the price of the European put option we would use Put Call Parity, i.e.,

• Price of Put (P) + Stock Price (S) = Price of Call (C) + Present value of Strike Price (K)

therefore,

P = C + PV of K - S

P = 8.42 + 61/e .0025 - 67

P = 8.42 + 61/1.025 - 67

P = $ 0.9139

iv) In case where the stock is a dividend paying stock, the price of the stock needs to be adjusted with the present value of the expected dividend. We shall denote the value by (S*).

Note: t* used in the answer above denotes the period within which the dividend is expected.