Every options position has a twin — an equivalent constructed from different instruments. Understanding synthetics is the difference between an amateur and a professional. It's also the arbitrage relationship that prevents crazy mispricings.
Long Stock = Long Call + Short Put (same strike, same expiry)
or rearranged: Call − Put = Stock − Strike × e^(−rT)
For short-dated equity options, roughly: Call price − Put price ≈ Spot − Strike
This isn’t theoretical. It’s an actual arbitrage relationship. If the equation breaks, market makers immediately profit by trading the mispriced side. That’s why option prices always respect parity.
Every position has an equivalent. Memorize this table:
| Actual position | Synthetic equivalent |
|---|---|
| Long stock | Long call + Short put (same strike) |
| Short stock | Short call + Long put (same strike) |
| Long call | Long stock + Long put |
| Short call | Short stock + Short put |
| Long put | Short stock + Long call |
| Short put | Long stock + Short call (this is a covered call!) |
A covered call (long stock + short call) has the exact same payoff shape as a short put at the same strike. Same risk, same reward. Which is easier for you? Depends on your capital: short put ties up less; covered call may have better tax treatment on stock dividends. But they’re equivalent trades.
1. You can build any position multiple ways. If liquidity is bad on one side, use the synthetic.
2. Arbitrage awareness. If put-call parity breaks, you know something is wrong (dividend expected, hard-to-borrow stock, order imbalance).
3. Risk transformation. A losing position can be adjusted into a completely different one by adding legs.
You bought a Nifty 25,000 put for ₹200. Nifty rallies to 25,300. Your put is now worth ₹80 — you’re down ₹3,000.
Options:
Each transforms a losing trade into a different position with different characteristics. Whether it’s smart depends on your view, but the flexibility is powerful.
If put-call parity is violated, market makers do these:
Conversion: buy stock + buy put + sell call (same strike). Lock in a small profit if the call is overpriced or put is underpriced.
Reverse conversion: short stock + sell put + buy call. Opposite; locks in profit if the call is underpriced.
For retail traders, these are almost never profitable because:
But — knowing they exist tells you why parity is enforced.
A box = bull call spread + bear put spread at the same strikes. Payoff at expiry is always the spread width, regardless of underlying.
Net cost: 200 − 110 + 250 − 160 = ₹180
At expiry, payoff is guaranteed 200 (the width): ₹200.
Profit = 200 − 180 = ₹20 per share = ₹500 per lot.
Effectively a fixed-return trade. The 20 profit represents the risk-free rate embedded in the options. Institutions use boxes to park cash at this “implied” rate. Retail: not worth the fees.
Combine synthetic thinking with LEAPS (Chapter 19):
You’ve built a synthetic covered call at 40% of the capital of a real one. This is called a “diagonal covered call” or “poor man’s covered call.”
Synthetic ≠ identical. Dividends, margin, taxes, and time-value decay all differ. Understand the differences before assuming interchangeability.
Payoff calculator → build a “Covered call” preset. Then build “Cash-secured put” preset. Notice the payoff shapes look different only because of scale — the risk profile is the same.