Put-call parity

Definition

Put-call parity is a financial principle that defines a relationship between the price of European put options and European call options with the same strike price and expiration date. This concept is essential for pricing options correctly and helps investors understand how to hedge their portfolios effectively, connecting option pricing with underlying asset values.

5 Must Know Facts For Your Next Test

1. Put-call parity can be expressed using the formula: $$C - P = S - K e^{-rT}$$, where C is the call option price, P is the put option price, S is the current stock price, K is the strike price, r is the risk-free interest rate, and T is the time to expiration.
2. If put-call parity does not hold, it creates an arbitrage opportunity for traders to profit by exploiting the mispricing between calls and puts.
3. This relationship assumes no dividends are paid on the underlying asset during the life of the options; adjustments are made if dividends are present.
4. The principle of put-call parity is vital for hedging strategies, as it ensures that combinations of options and underlying assets are fairly priced in relation to each other.
5. Put-call parity applies exclusively to European options since they can only be exercised at expiration, while American options allow for exercise before expiration, complicating the pricing relationships.

Review Questions

• How does put-call parity contribute to effective option pricing and hedging strategies?
  • Put-call parity establishes a fundamental relationship between call and put option prices, ensuring they are aligned with the underlying asset's value. By understanding this relationship, traders can identify mispriced options and develop effective hedging strategies. This helps minimize risk in investment portfolios by allowing investors to lock in prices and protect against adverse market movements.
• Discuss how deviations from put-call parity can create arbitrage opportunities in financial markets.
  • When put-call parity does not hold true, it indicates a pricing discrepancy between call and put options that can be exploited through arbitrage. Traders can buy the undervalued option while simultaneously selling the overvalued option to secure a risk-free profit. This process helps to bring option prices back into alignment according to put-call parity, demonstrating its importance in maintaining market efficiency.
• Evaluate the implications of put-call parity for investors trading European options compared to American options.
  • Put-call parity provides a clear framework for pricing European options due to their exercise restrictions at expiration. In contrast, American options complicate this relationship as they can be exercised at any time prior to expiration. This flexibility allows for additional strategies but also means that simple put-call parity relationships may not hold. Investors trading European options can rely more heavily on this principle for accurate pricing and hedging, while those dealing with American options must consider additional factors such as early exercise potential.

Related terms

European Options: Options that can only be exercised at the expiration date, as opposed to American options, which can be exercised at any time before expiration.

Arbitrage: The practice of taking advantage of price differences in different markets to earn a profit, often by simultaneously buying and selling assets.

Strike Price: The predetermined price at which an option can be exercised, representing the price at which the underlying asset can be bought or sold.