The call premium for a non-dividend-paying stock exceeds the put premium by $19

Recall the call put parity equation:

C0 - P0 = S0 - PV(K)

where symbols have usual meanings in the world of derivatives.

The call premium for a non-dividend-paying stock exceeds the put premium by $19.608 , where both options have a strike price of K.

Hence, we get the following equation:

S0 - PV(K) = 19.608

r = effective rate of interest for the period from time 0 to the expiration date of the options = 2%.

Hence, we can write PV(K) = K / (1 + r) = K / (1 + 2%) = K/1.02

Hence, S0 - K/1.02 = 19.608 ----------------(1)

The put premium on the same stock exceeds the call premium by $29.412 , where both options have a strike price that is 5% greater thanK .

S0 - PV[(1 + 5%) x K] = Call price - put price = - 29.412

Hence, S0 - 1.05K / 1.02 = -29.412 ---------------(2)

Eqn (1) - Eqn (2) results into: 0.05K/1.02 = 49.020

hence, K = 49.020 x 1.02 / 0.05 = 1,000.008

From (1), we get the current stock price, S0 = 19.608 + K/1.02 = 19.608 + 1,000.0008 / 1.02 = 1000.008