Key Takeaways
- Links European call and put prices with same strike.
- Ensures no-arbitrage by equating portfolio payoffs.
- Adjusts for dividends and interest rates.
- Holds strictly for European options only.
What is Put-Call Parity?
Put-call parity is a fundamental no-arbitrage principle that links the prices of European call options and put options with the same strike price and expiration date to the underlying asset's spot price. It ensures that the cost of a portfolio consisting of a call option and the present value of the strike price equals the cost of a portfolio with a put option and the underlying asset.
This relationship prevents risk-free arbitrage opportunities by enforcing price consistency between options and the underlying security, assuming no early exercise and no dividends or adjusted for them accordingly.
Key Characteristics
Put-call parity has several defining features relevant to options traders and investors alike.
- European Options: It applies strictly to European-style options, which can only be exercised at expiration, distinguishing it from scenarios involving early exercise.
- No-Arbitrage Condition: The parity prevents riskless profit by ensuring equivalent portfolios have the same value.
- Strike Price and Expiration: Both the call and put options must share the same strike price and expiration date for parity to hold.
- Adjustment for Dividends and Interest Rates: Expected dividends and the risk-free rate affect the parity formula and must be incorporated for accuracy, especially for dividend-paying stocks.
How It Works
Put-call parity arises from constructing two portfolios with identical payoffs at option expiration. One portfolio holds a call option plus cash equal to the present value of the strike price, while the other holds a put option and the underlying asset.
At expiration, these portfolios yield equal payoffs, so any price discrepancies between them create arbitrage opportunities. Traders exploit these differences by buying the cheaper portfolio and selling the more expensive one, driving prices back into parity. This principle relies on assumptions such as frictionless markets, no dividends (or proper dividend adjustments), and European exercise style.
Examples and Use Cases
Put-call parity is widely used to price options fairly and to create synthetic positions replicating other assets or strategies.
- Index ETFs: The parity principle helps in pricing options on funds like SPY, ensuring fair value across related instruments.
- Bond Markets: Applying put-call parity concepts assists in understanding option-embedded features in bonds such as those traded through BND.
- Dividend Adjustments: For stocks paying dividends, adjusting the parity formula using expected dividend payments is critical to maintain accurate pricing.
Important Considerations
When using put-call parity, be mindful of market conditions like transaction costs, bid-ask spreads, and early exercise possibilities that can cause deviations. American options, which allow early exercise, do not strictly follow parity, although approximations exist.
Understanding related concepts such as the par yield curve can enhance your grasp of interest rate impacts on the parity relationship. Keeping these factors in mind helps you apply put-call parity effectively in real-world investing and options trading.
Final Words
Put-call parity ensures option prices remain consistent with the underlying asset and strike price, preventing arbitrage opportunities. To apply this, compare current call and put prices with the parity formula to identify mispricings or fair value estimates.
Frequently Asked Questions
Put-call parity is a financial principle that links the prices of European call and put options with the same strike price and expiration date to the underlying asset's spot price. It ensures no arbitrage opportunities exist by stating that the price of a call plus the present value of the strike equals the price of a put plus the current stock price.
The basic formula is C + PV(K) = P + S, where C is the call price, P is the put price, S is the spot price of the underlying asset, and PV(K) is the present value of the strike price. This relationship means that holding a call option plus cash equal to the discounted strike price has the same value as holding a put option plus the underlying asset.
Put-call parity strictly applies to European options, which can only be exercised at expiration. For American options, the possibility of early exercise introduces complexities, so exact parity doesn’t hold, although approximate relationships can be used.
When the underlying asset pays dividends, the Put-Call Parity formula adjusts to account for the present value of expected dividends. The modified formula is C + PV(K) = P + (S - D), where D represents the discounted value of dividends during the option's life.
Put-call parity is based on the idea that two different portfolios—one with a call option plus cash, and another with a put option plus the underlying asset—should have identical payoffs at expiration. If their prices diverge, traders can exploit arbitrage opportunities, and market forces will push prices back to parity.
Yes, by comparing observed call and put prices using the parity formula, traders can spot deviations indicating mispricing. Such differences may signal potential arbitrage opportunities where buying the underpriced portfolio and selling the overpriced one can generate risk-free profits.
Interest rates influence the present value of the strike price in the Put-Call Parity formula. The strike price is discounted by the risk-free rate over the option's time to expiration, meaning higher rates reduce the present value and affect the relationship between call and put prices.
