Lesson 4 of 5 · 12 min

Put–call forward parity

Replace the share with a long forward plus a bond paying the forward price and parity becomes $F_0(T)(1+r)^{-T} + p_0 = c_0 + X(1+r)^{-T}$ .

In short

A long share can be replicated by a long forward plus a risk-free bond paying $F_0(T)$ at T. The bond costs $F_0(T)(1+r)^{-T}$ , which equals $S_0$ for an underlying without income or costs.
A synthetic protective put is that synthetic share plus a long put. It pays $\max(S_T, X)$ , like the protective put and the fiduciary call.
Put–call forward parity: $F_0(T)(1+r)^{-T} + p_0 = c_0 + X(1+r)^{-T}$ .
Rearranged: $p_0 - c_0 = [X - F_0(T)](1+r)^{-T}$ . A long put plus short call equals a long bond paying X plus a short forward.
If $X = F_0(T)$ , the put and the call have the same price.

Create a free account to get 7 days of full access — every lesson, video, flashcard, mock and the question bank. No card needed.