SOA Fundamentals Of Actuarial Mathematics (FAM) Practice Test

Put-call parity equation: Which expression holds?

c(t) - p(t) = S_t - Ke^{-rt} c(t) + p(t) = S_t + Ke^{-rt} p(t) - c(t) = S_t - Ke^{-rt} c(t) - p(t) = S_t + Ke^{-rt}

Correct Answer:

c(t) - p(t) = S_t - Ke^{-rt}

Explanation:

Put-call parity shows a fixed relationship between European call and put prices with the same strike and maturity on a non-dividend-paying asset. At expiration, the difference in payoffs between a call and a put with the same strike is (S_T − K). This is because (S_T − K)^+ − (K − S_T)^+ simplifies to S_T − K. If you value that payoff today, its value must equal the difference in option prices: c(t) − p(t) = S_t − K e^{−r(T−t)}. In the notation where the time to maturity is t, this becomes c(t) − p(t) = S_t − K e^{−r t}. So the expression c(t) − p(t) = S_t − K e^{−r t} is the correct relation. The other forms would imply the wrong payoff structure (adding the PV of K or reversing the order), which would not match no-arbitrage pricing.

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