Put-Call Parity: Meaning, Formula and Example

Options traders often spend a lot of time studying premiums, volatility and expiry, but one idea quietly holds the entire pricing framework together. Put call parity explains how the price of a call option, a put option and the underlying asset stay connected. When this relationship holds, the market is considered balanced. When it does not, traders may find risk free opportunities. Understanding this concept helps investors judge whether an option is priced sensibly and whether something in the market is temporarily out of line.

This guide breaks down the put call parity meaning, shows how the put call parity formula works and shares an example that keeps the idea grounded.

What is Put-Call Parity?

Put call parity describes the mathematical relationship between European call options, European put options and the underlying asset when all three share the same strike price, expiry and underlying.

At its core, the put call parity equation says that owning a call option and selling a put option should create a position similar to holding the underlying asset financed at the risk free rate. When the prices drift away from this balance, it signals mispricing.

Since European options can be exercised only at expiry, the parity relationship fits them neatly. American options may behave differently because of early exercise features.

Why is the Put-Call Parity Important

The idea may appear theoretical at first, but it influences real market behaviour in several ways.

• Indicates fair value

Traders can check whether call and put premiums make sense relative to each other.

• Reduces arbitrage

When the parity holds, there are no risk free profits left on the table.

• Helps create synthetic positions

Using a mix of options and the underlying, traders can replicate long or short positions even if they cannot access the underlying directly.

• Supports hedging decisions

Understanding parity helps traders build exposure that behaves like the underlying while managing risk differently.

• Provides pricing structure

Several option pricing models rely on the logic behind put call parity.

Once this relationship is clear, traders can judge market behaviour with much more confidence.

The Put-Call Parity Formula and Calculation

The standard put call parity formula for European options is:

Where:

C = Price of the call option

P = Price of the put option

S = Spot price of the underlying

PV(K) = Present value of the strike price discounted at the risk free rate

This shows that one combination of positions must match the value of another combination if the market is fairly priced.

To calculate fair values, the formula can be rearranged:

Fair value of a call:

C = P + S − PV(K)

Fair value of a put:

P = C + PV(K) − S

These versions help traders identify when an option appears cheap or expensive.

Put-Call Parity Arbitrage: How It Works

If the prices do not match the put call parity equation, arbitrage traders may step in. Arbitrage works because different combinations of options and the underlying produce the same payoff at expiry. If one combination is cheaper or more expensive than the other, traders can lock in a profit.

Common Mispricing Cases

1. Call option is overpriced

A trader may:

• Sell the call

• Buy the put

• Buy the underlying

• Borrow the present value of the strike price

2. Put option is overpriced

A trader may:

• Sell the put

• Buy the call

• Short the underlying

• Invest the present value of the strike price

These trades eventually converge at expiry, leaving the trader with a risk free profit.

Example of Put-Call Parity

Consider a European option with a three month expiry and the following details:

• Call premium (C): ₹12

• Put premium (P): ₹8

• Spot price (S): ₹100

• Strike price (K): ₹100

• Risk free rate: 6% per year

Step 1: Present value of the strike price

PV(K) = 100 / (1 + 0.06 × 3/12)

PV(K) = 100 / 1.015

PV(K) ≈ ₹98.52

Step 2: Compare both sides

Left side:

C + PV(K) = 12 + 98.52 = ₹110.52

Right side:

P + S = 8 + 100 = ₹108

These numbers do not match, so put call parity does not hold.

Step 3: Arbitrage strategy

Since the call side is overpriced:

• Sell the call

• Buy the put

• Buy the underlying asset

• Borrow ₹98.52 at the risk free rate

The positions will settle to the same payoff at expiry, and the trader keeps the difference as risk free profit. Small pricing gaps like this often close quickly because arbitrage traders respond to them.

Conclusion

Put call parity explained simply is a pricing balance between calls, puts and the underlying. When this balance works, the market behaves efficiently. When it does not, traders can spot potential arbitrage. Knowing how to calculate put call parity helps investors examine option prices with a clearer view and build synthetic or hedged positions more deliberately. With a little practice, the idea becomes a practical tool rather than a formula on a page.