Put-Call Parity
Put-call parity links the prices of European calls, puts and the underlying: call − put = stock price − present value of the strike. If prices break this relationship, arbitrage is possible, so in efficient markets they stay closely aligned.
Calls and puts on the same stock, strike and expiry aren't priced independently. Owning a call and selling a put gives exactly the same payoff as owning the stock with borrowed money. Put-call parity turns that into an equation that ties all three prices together. This entry explains the formula, why it holds and how traders use it to build synthetic positions.
- Category
- Derivatives
- Reading time
- 4 min
- Also called
- Put call parity, Put-call parity equation, Options parity
- Updated
Put-call parity in plain words
Put-call parity shows how the prices of puts, calls and the underlying asset must stay consistent with one another.1
A long call plus a short put on the same underlying, strike and expiry should equal a forward contract on that asset.1
A call gives the right to buy and a put the right to sell at the strike, while the seller of each takes the matching obligation.2
How to apply put-call parity, step by step
Same terms
Call and put share underlying, strike and expiry.
European style
The classic formula assumes exercise only at expiry. See American and European Options.
Discount the strike
Present value using the risk-free rate. See Risk-Free Rate.
Apply the equation
C − P = S − PV(K).
Compare with market prices
Gaps point to mispricing or costs.
Build synthetics
Combine options to mimic stock. See Options.
Worked examples
Example 1 — Checking parity
Call ≈ $6Stock $100, strike $100, present value of strike $98, put $4.
| S − PV(K) | $100 − $98 = $2 |
| Call = put + 2 | $4 + $2 = $6 |
Parity ties the call price to the put, the stock and the discounted strike.1
Example 2 — Spotting a mispricing
≈ $1 a shareSame inputs, but the call trades at $7.
| Fair call | $6 |
| Market call | $7 (overpriced by $1) |
| Arbitrage idea | Sell call, buy put, buy stock, borrow PV(K) |
When the relationship breaks, a combination of positions can lock in the difference, before costs. See Arbitrage.
Example 3 — A synthetic long stock
Synthetic stockBuy the $50 call for $3 and sell the $50 put for $3.
| Net cost | $0 |
| At expiry | Gains and losses like 100 shares from $50 |
A long call plus a short put behaves like a forward on the stock at the strike price.1
Positions linked by parity
| Aspect | Equivalent to | Use |
|---|---|---|
| Long call + short put | Long stock (forward) | Synthetic long |
| Long put + long stock | Long call + cash | Protective put |
| Short call + long stock | Short put + cash | Covered call. See Covered Call |
| Long put + short call | Short stock (forward) | Synthetic short |
How traders use put-call parity
Spotting mispricings
Comparing calls and puts. See Arbitrage.
Synthetic positions
Replicating stock with options.
Hard-to-borrow stocks
Synthetic shorts when shares are scarce. See Short Locate and Borrow Availability.
Checking implied volatility
Calls and puts should imply similar volatility. See Implied Volatility.
Advantages and disadvantages
Advantages
- Explains how option prices fit together.
- Enables synthetic positions.
- Highlights arbitrage opportunities.
Disadvantages
- Assumes European options and no dividends in the basic form.
- Transaction costs erase small gaps.
- Borrowing costs and dividends complicate it.
Going deeper
Read as far as you need. Each level builds on the one before it.
Rearranging the equation
Beginner
The same relationship can be rearranged in several ways — for example, put = call − stock + present value of strike.1
Dividends
Intermediate
If the stock pays dividends before expiry, their present value is subtracted from the stock price in the equation. See Dividend.
American options
Advanced
Because American options can be exercised early, parity becomes a range rather than an exact equality. See Exercise and Assignment.
Common mistakes
Mismatched strikes or expiries
Parity needs identical terms.
Forgetting to discount
The strike must be in present value.
Ignoring dividends
They shift the balance.
Chasing tiny gaps
Costs usually exceed them.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Put-call parity: C − P = S − PV(K).
- It links calls, puts and the underlying.
- It holds exactly for European options.
- Breaks create arbitrage opportunities.
- It underpins synthetic positions.
Frequently asked questions
Does put-call parity always hold?
Why is it important?
What is a synthetic stock?
Further learning
- Options
Calls and puts basics.
- Option Pricing Models
How options are valued.
- Arbitrage
Exploiting price gaps.
- Forward Contract
What call minus put replicates.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- Corporate Finance Institute. Put-Call Parity (opens in a new tab) Checked .
- FINRA. Options (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.