Question

The price today of a European put option that matures in one year and has a strike price of $70 is $7. The underlying stock price today is $71. A dividend of $1.50 is expected in four months and another dividend of $1.50 is expected in eight months. The continuously compounded risk free rate of interest is 4% per annum for all maturities. Using put-call parity: a) Compute the price today of a European call option which matures in one year and has a strike price of $70. b) Compute the price difference today between a put and a call on the stock, when both options mature in one year, are European, and have a strike price of $75.

Answer 1

a)

Put Call Parity C - P = S – K * e-rt - Dividends PV

   C = P + S – K * e-rt - Dividends PV

Information given in question (all values in $):

P = put option price = 7

S = stock price = 71

K = strike price = 70

r = risk free rate = 4%

T = time to maturity = 1

Dividend = 1.50 in 4 months and 8 months each

C = call option price = ?

Call option price using Put-call parity:

C = P + S – K * e-rt - Dividends PV

C = 3 + 71 - 70 * e-.04*1 - 1.50 * e-.04*0.33- 1.50 * e-.04*0.67

C = 3.80 is the answer

b) The equation in part a can be presented as below :

P - C = -S + K * e-rt + Dividends PV

Changing the value of K as 75 and using all other values from part a in right hand side of the equation, we get (all values in $) :

P - C = -71 + 75 * e-.04*1 + 1.50 * e-.04*0.33 + 1.50 * e-.04*0.67

P - C = 4 is the answer

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