Question

Suppose the premium on a 6-month S&R call is $109.20 and the premium on a put with the same strike price is $60.18. Given that the effective 6-month interest rate is 2%, the S&R 6-month forward price is $1020, what is the strike price?

Answer 1

The Put-Call Parity describes the relationship between put and call premiums of the same strike price and time period with the forward price of the contract and this strike price:

\( \begin{align*} Call(K,T) - Put(K,T) &= PV(F_{0,T} - K) \end{align*} \)

If the forward price is 1020 and the interest rate is 2%, then the present value of 1020 is \( 1020(1.02)^{-1} = 1000 \). Then to find the strike price so:

\( \begin{align*} Call(K,T) - Put(K,T) &= PV(F_{0,T} - K) \\ PV(K) &= PV(F_{0,T} ) - Call(K,T) + Put(K,T) \\ &= 1000 - 109.20 +60.18 \\ &= 950.98 \\ FV(PV(K))&=FV(950.98)\\ K&=(950.98)(1.02)\\ &=969.9996\\ &\approx 970 \end{align*} \)

So therefore the strike price is approximately $970.

The strike price is 970 and this can be found using the put-call parity.