Synthetic long and put-call parity

Two options that act like one future

Buy the 22400 call and sell the 22400 put, same expiry:

Drag: where does NIFTY close on expiry day?22,400

If NIFTY ends at 22,400, you lose ₹3,624.

No kink, no floor, no ceiling — a straight line. Above 22,400 the call gains point-for-point; below 22,400 the sold put loses point-for-point. Every point NIFTY moves is ₹65 to you, up or down. That's exactly how a futures contract behaves.

Where does the line cross zero? At 22,400 + 55.75 = 22,455.75. So this pair of options behaves like buying NIFTY futures at 22,455.75.

Why not just buy the futures?

Usually you would! But the synthetic is useful to understand because of what it reveals…

Put-call parity: the rule that links everything

The fair price of NIFTY futures 14 days out (interest rate 6.5%) is about:

22,400 × e^(0.065 × 14/365) ≈ 22,455.92

Now compare:

That's put-call parity:

Call − Put ≈ Future − Strike (same strike, same expiry)

It must hold, because otherwise there'd be free money. That also answers the puzzle from Module 1 — why the ATM call cost more than the ATM put: the futures price sits above spot (because of interest), so calls at the spot strike are a bit "in the money" relative to the future.

The arbitrage idea

Suppose the market somehow priced the synthetic at 22,420 while futures traded at 22,456. You could:

1. 1

   Buy the cheap thing

   Buy the call and sell the put (synthetic long at 22,420).

2. 2

   Sell the expensive thing

   Sell NIFTY futures at 22,456.

3. 3

   Wait for expiry

   Both positions converge to the same settlement price, so the 36-point gap is locked in no matter where NIFTY ends.

In real markets, professional traders and algorithms close such gaps within moments, and after brokerage, taxes and slippage there's rarely anything left for retail traders. But knowing the rule helps you spot mispriced options — and sanity-check what you see on the chain.

Synthetic short

Flip it — sell the call, buy the put — and you get a straight line sloping down: a synthetic short future.