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.
Long call + short put = synthetic long stock. See it visually:
Slope is +1 (one-for-one with underlying) across all prices — identical to owning the stock, except cost is only the small net premium difference (10 × 65 = ₹650).
Because delta ≈ 1 across all prices, the P&L per point moved should mirror an equivalent long-stock position — that’s put-call parity playing out in the simulation.
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 a long-dated deep-ITM call:
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.”
Long-dated (6+ month) single-stock options exist on NSE with limited liquidity. Only large-caps (Reliance, HDFC Bank, TCS, Infosys, ICICI) have tradeable quarterly-and-further contracts. For most stocks, monthlies are the longest liquid tenor — the poor man’s covered call has limited practical use in India outside a handful of names.
Synthetic ≠ identical. Dividends, margin, taxes, and time-value decay all differ. Understand the differences before assuming interchangeability.
For a European option on a non-dividend-paying stock, put-call parity is exactly:
C + K × e^(−rT) = P + S
Where:
Why it must hold:
Consider Portfolio A: long call + short put + K × e^(−rT) rupees in a bond. Consider Portfolio B: long stock.
At expiry, both portfolios pay the same:
Same payoff at expiry with certainty → same price today. Any deviation is arbitrage.
For Indian stocks paying discrete dividends before expiry, replace S with (S − PV of dividends):
C + K × e^(−rT) = P + S − D × e^(−rt_div)
Pre-dividend, puts trade at a premium reflecting the drop that will happen ex-date. This is measurable — the call price falls, put price rises, in the days before the ex-dividend date.
Small for short-dated (weekly, monthly) — the K × (1 − e^(−rT)) term is ₹5-15 on ATM options. Grows on quarterlies. This is why quarterly boxes trade at ~risk-free rate + tiny arb.
Put-call parity is strike-by-strike, expiry-by-expiry. Skew doesn’t violate parity — it means IV differs across strikes. Parity holds for each strike given each strike’s own IV.
You believe Nifty rallies from 25,000 to 26,500 over 2 months. Instead of buying ETF:
Net cost: ₹30/share. Delta = +75 (1 full lot exposure). Below 25,000, you take assignment on the put (equivalent to long stock). Above, you own the call intrinsic.
Advantage: capital tied up ~₹1L margin (short put) vs ₹18.75L for actual Nifty shares. Same delta.
Risk: downside is same as owning stock (unlimited to zero).
You expect Reliance to drop 10% before earnings. Physical short-selling has borrow costs and squeeze risk.
Net cost: ₹10/share. Delta = −250. Same as short stock. No borrow risk; margin for short call similar to short stock.
Long stock + long put = synthetic long call. Payoff identical.
When to use physical (stock + put):
When to use synthetic (just long call):
Both lock in the interest-rate embedded in the option prices. Pure hedge — no directional risk. Retail can rarely execute due to fees; institutions do this constantly.
Institutions buy boxes to park cash. If a Nifty 25,000 / 25,500 box has 6% annualized implicit yield (higher than bank FD), that’s a way to lock in that rate.
Retail feasibility: fees eat the spread. Only worthwhile for institutions or large accounts (>₹50L).
Real markets have small persistent deviations from parity. Reading them tells you what’s happening:
Sign of expected dividend. Around ex-date on stocks, calls trade rich (or puts cheap). Market is pricing the price-drop that will occur.
If short-selling is hard (SLB restrictions, hot short interest), synthetic short (long put + short call) trades rich because it’s an easy way to short.
Example: A stock with high delivery volume and low SLB availability — put IV runs 3-5% higher than call IV at the same strike, well beyond skew.
Nifty futures trade at a premium to spot (cost of carry). Long futures vs spot ≈ interest cost. If synthetic long (call − put + K PV) doesn’t match futures, arbitrage opportunity exists (institutional only).
These are TICK-BY-TICK readings your data feed can show. Advanced traders monitor them for setup signals.
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.