Once you internalise put-call parity, options stop feeling like separate instruments and start feeling like Lego. Any one can be rebuilt from the others.
Put-call parity
For the same strike and expiry:
Call − Put = Stock − Strike (discounted)
Rearranged, this means a call, a put, the stock, and cash are all related. Move any term to the other side and you’ve created a synthetic version of something else.
The synthetic toolkit
- Synthetic long stock = long call + short put (same strike). Behaves just like owning shares — same delta of 1.
- Synthetic short stock = short call + long put.
- Synthetic long call = long stock + long put (a.k.a. a protective put).
- Synthetic long put = short stock + long call.
Each pairing reproduces the payoff of the named instrument, often with different margin or capital requirements.
Why it matters
- Flexibility — if a put is mispriced or illiquid, build it synthetically from the call and stock.
- Capital efficiency — a synthetic can sometimes tie up less capital than the real thing.
- Understanding — every complex strategy decomposes into synthetics. A covered call is just a synthetic short put. A collar is a synthetic position with a cap and floor.
Conversions and reversals
When parity is violated — the synthetic and the real instrument trade at different prices — arbitrageurs step in with a conversion (long stock + synthetic short stock) or reversal (the opposite) to lock in the discrepancy risk-free. In practice these keep prices honest, which is why parity holds.
Worked example: a conversion that locks in risk-free profit
A conversion combines a long stock with a synthetic short stock (short call + long put, same strike). At expiry it’s worth exactly the strike no matter where the stock lands — if the stock is above, it’s called away at the strike; if below, you exercise the put and sell at the strike. So it’s a fixed payout, and any discount to that payout is free money.
Take a stock at $100, the $100-strike options, three months out, and assume interest is ~0% for simplicity:
- Buy the stock for $100.
- Sell the $100 call for $5.00 (you receive $5).
- Buy the $100 put for $4.50 (you pay $4.50).
Net cost today = 100 − 5 + 4.50 = $99.50
At expiry, whatever the price:
- If the stock is above $100, the short call is exercised — your shares are called away at $100.
- If it’s below $100, you exercise your put — you sell the shares at $100.
Either way you collect $100. You paid $99.50 and are guaranteed $100 back:
Risk-free profit = 100 − 99.50 = $0.50 per share, regardless of where the stock goes.
That’s an arbitrage — and traders pouncing on it is exactly what forces Call − Put back in line with Stock − Strike. (In the real world, the discounting by interest rates and any dividends is what the parity equation accounts for; ignore them and you’ll think you see free money that isn’t there.)
The mental model
Stop memorising strategies as separate recipes. See them as combinations of synthetics, and a huge amount of options trading collapses into a single, elegant idea.