Parity & Profit

Put-Call Parity

A long call and a short put are equivalent to a forward at expiry.

highlighted = computed this step

Payoff identity at expiry

Holding a long call together with a short put gives a straight-line payoff, the forward. At $80.00 the curve is $-20.00; at $100.00 it is $0.00; at $120.00 it is $20.00.

C−P=S−K\text{C}-\text{P}=S-K
C - P = S - KPayoff at expiry.C - P = S - KC - P = S - Klong call + short put = forward (S - K)Underlying price at expiryPayoff$80$100$120$-24.00$+0.00$+24.00K=$100

Pricing identity note

This lesson states the payoff identity C-P = S-K at expiry. The next page adds the financing term PV(K) and turns the payoff identity into a cost-today identity.

payoff identity: C−P=S−K\text{payoff identity: } \text{C}-\text{P} = S-K
C - P = S - KPayoff at expiry.C - P = S - KC - P = S - Klong call + short put = forward (S - K)Underlying price at expiryPayoff$80$100$120$-24.00$+0.00$+24.00K=$100