Put-Call Parity

Definition

Put-call parity is a fundamental principle in options pricing that defines a relationship between the prices of European call and put options with the same strike price and expiration date. It establishes that the price of a call option, when combined with the present value of the strike price, should equal the price of a put option plus the current stock price. This relationship helps ensure that arbitrage opportunities are minimized, making it vital in the pricing models used to value options, especially in binomial pricing frameworks.

5 Must Know Facts For Your Next Test

1. Put-call parity can be expressed mathematically as: $$C - P = S - K e^{-rT}$$, where C is the call price, P is the put price, S is the current stock price, K is the strike price, r is the risk-free rate, and T is the time to expiration.
2. This principle applies specifically to European options because they can only be exercised at expiration, which simplifies the relationship between call and put prices.
3. If put-call parity does not hold, it creates arbitrage opportunities where traders can exploit price discrepancies between options and the underlying asset.
4. Understanding put-call parity is crucial for using binomial option pricing models, as it helps set the prices of options consistently across different scenarios.
5. Put-call parity assumes no transaction costs and that investors can borrow and lend money at the risk-free rate, which are key considerations in theoretical models.

Review Questions

• How does put-call parity ensure that arbitrage opportunities are minimized in options trading?
  • Put-call parity ensures that there is a consistent relationship between call and put option prices, which prevents mispricing in the market. When this relationship holds, any discrepancies would allow traders to exploit arbitrage opportunities by simultaneously buying and selling the appropriate combinations of stocks and options. This behavior leads to corrections in prices until they align with the established parity condition, thus minimizing potential riskless profits.
• Discuss how put-call parity applies specifically to European options and why this distinction is important.
  • Put-call parity applies specifically to European options because these options can only be exercised at their expiration date. This characteristic allows for a clear-cut relationship between call and put prices since no early exercise feature complicates pricing. In contrast, American options can be exercised at any time before expiration, which introduces additional variables and makes it difficult for put-call parity to hold strictly. Therefore, recognizing this distinction helps traders understand how to apply pricing models effectively.
• Evaluate how put-call parity might impact your strategy when using a binomial option pricing model for evaluating potential investments.
  • When using a binomial option pricing model, understanding put-call parity is essential for creating accurate pricing inputs and managing investment strategies effectively. By ensuring that your calculated call and put prices adhere to the put-call parity relationship, you can validate your model's outputs and make informed decisions regarding hedging or speculative strategies. If the prices deviate from this relationship, it could indicate market inefficiencies or potential investment opportunities. Thus, leveraging this principle enhances both pricing accuracy and strategic positioning in your investment decisions.

Related terms

European Options: Options that can only be exercised at expiration, unlike American options which can be exercised at any time before expiration.

Arbitrage:

The practice of taking advantage of price differences in different markets to generate a profit with minimal risk.

Strike Price: The predetermined price at which an option can be exercised, which is essential in determining option value.