The one equation that ties everything together

Put-call parity

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.

The six synthetic positions

Every position has an equivalent. Memorize this table:

Actual positionSynthetic equivalent
Long stockLong call + Short put (same strike)
Short stockShort call + Long put (same strike)
Long callLong stock + Long put
Short callShort stock + Short put
Long putShort stock + Long call
Short putLong stock + Short call (this is a covered call!)
💡 The covered call insight

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.

Why this matters

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.

A worked example: converting a losing long put

Example

Turning a bad long put into something better

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:

  1. Cut the loss — sell for ₹80, take ₹3,000 loss
  2. Convert to a bull spread — sell a 24,800 put for ₹40; net position now is a bear put spread with different risk profile
  3. Convert to a synthetic short call — sell a matching call at the same strike; you now have a synthetic short position
  4. Add stock — buy Nifty ETF; put + stock = married put = long call synthetic

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.

Conversion & Reverse Conversion (arbitrage)

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.

Box spread — the classic arbitrage

A box = bull call spread + bear put spread at the same strikes. Payoff at expiry is always the spread width, regardless of underlying.

Example

Nifty 25,000 / 25,200 box

  • Buy Nifty 25,000 call @ ₹200
  • Sell Nifty 25,200 call @ ₹110
  • Buy Nifty 25,200 put @ ₹250
  • Sell Nifty 25,000 put @ ₹160

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.

Practical use: LEAPS + short call = stock replacement

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.”

⚠️ Not exactly the same

Synthetic ≠ identical. Dividends, margin, taxes, and time-value decay all differ. Understand the differences before assuming interchangeability.

When to reach for synthetics

Try it

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.