Question

Question 17.

You have the following information for a three-month Call option. S(0): 150 kr

X: Call: rf: T:

140 kr 12 kr

1%
3 months

(S(0) = Stock price at time 0, X = Strike price, Call = price or a Call option, rf = the risk free rate, T = time to maturity)

1. a) How much is a three month Put option worth with the same strike and underlying asset?

2. b) What would rf have to be for the Put to be worth 2 kr?

Answer 1

Part (a)

Recall the call put parity equation:

Put-Call Parity Equation: C + X/(1+r)t = So + P C = Call Premium, r= Annual Interest Rate, P= Put Premium, t= Time in Years, X= Strike Price of Call and Put, S, = Initial Price of Underlying.

Hence, 12 + 140 / (1 + 1%)^3/12 = 150 + P

Hence, P = 12 + 139.65 - 150 = 1.65 kr

Part (b)

If P = 2 kr

then, 12 + 140 / (1 + r)^3/12 = 150 + 2

Hence, 140 / (1 + r)^3/12 = 152 - 12 = 140

Hence, (1 + r)^3/12 = 1 = 1^3/12

Hence, 1 + r = 1

Hence, r = 1 - 1 = 0

Hence, rf has to be 0% to enable the Put to have a price of 2 kr