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 - KK=$100$80$100$120$-24.00$+0.00$+24.00Underlying price at expiryPayofflong call + short put = forward (S - K)

Pricing identity note

This lesson states the payoff identity C-P = S-K at expiry. The pricing identity C-P = S-PV(K) depends on discounting and is covered in fixed-income material.

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