Question

Consider a European option on a stock expiring at time t. Let p(K) be a put option with strike price K, and c(K) be a call option with strike price K. You are given

(1) p(50)-c(55)=-2

(2) p(55)-c(60)=3

(3) p(60)-c(50)=14

Determine c(60)-p(50)

Answer 1

The given above question descibes the put-call parity.

By using the put call parity, we will do the following calculations:

Adding up the given three equations:

p(50) - c(55) + p(55) - c(60) + p(60) - c(50) = (50 + 55 + 60)e^−r t − 3Se^−δt = −2 + 3 + 14 = 15

rearranging the left side of the equation,

p(50)- c(50) + p(55) - c(55) + p(60) - c(60) = (50 + 55 + 60)e^-rt - 3Se^-t = -2+3+14 = 15

Therefore, p(50) - c(50) + p(60) - c(60) = 110e^-rt - 2Se^t = (2/3) * 15 = 10

Since p(60) - c(60) = 14 it follows that, p(50) - c(60) = 10 - 14 = - 4

and c(60) - p(60) = 4.

Hence, the required answer is 4.