Stock Market · Options Theory

Put-call parity

Put-call parity is a fundamental relationship between call prices, put prices, and the underlying. It ensures that equivalent positions created through different combinations price consistently, preventing arbitrage.

The relationship

C − P = S − K × e^(−rT)

In simpler terms: Call − Put = Spot − Present value of Strike

Or practically: buying a call and selling a put at the same strike creates a synthetic futures position equivalent to owning the actual underlying.

> If put-call parity is violated, arbitrageurs instantly exploit the gap, bringing prices back into line.

Practical application

If you know the call price, strike, spot price, and interest rate. You can calculate what the put price should be. If the actual put trades differently, there's an arbitrage opportunity (which professional desks exploit instantly).

Synthetic positions

Using put-call parity, you can recreate any position synthetically:

• Synthetic long futures = Buy ATM call + Sell ATM put (same strike, same expiry)
• Synthetic short futures = Buy ATM put + Sell ATM call
• Synthetic call = Long underlying + Long put

These synthetics are sometimes used when one instrument is more liquid or tax-efficient.

Put-call paritythe law of one price for options. Equivalent payoffs must trade at equivalent prices.

Why retail traders care

When you see a call trading significantly cheaper than the equivalent put, it might signal a pending dividend (which reduces futures fair value and shifts parity). Always check dividends before concluding an arb exists.

Takeaway. Put-call parity: equivalent positions must price identically to prevent arbitrage. Buying a call and selling a put at same strike = synthetic futures. Parity violations are exploited instantly by institutions.