Definition
Put-call parity is a principle related to the pricing of options. According to this concept, the price of a call option (which is a right to buy a certain asset), combined with a certain amount of cash, should equal the price of a put option (which is a right to sell the asset), plus the actual price of the asset itself. If any inequality occurs between these values, it creates an opportunity for risk-free profit through arbitrage.
Key Takeaways
- Put-Call Parity defines a relationship between the prices of European put and call options with the same underlying asset, strike price, and expiration dates. This concept assists in maintaining equilibrium and preventing arbitrage chances in the financial market.
- According to Put-Call Parity, the price of a call option implies a certain fair price for the corresponding put option and vice versa. This principle is founded on law of one price, asserting that two items with the same value should essentially trade at the same price.
- Violations to the put-call parity represent an opportunity for riskless profit. However, with the inclusion of transaction costs or dividends, the parity may not hold exactly. Therefore, most trading strategies exploiting deviations from put-call parity focus on potential marginal benefits.
Importance
Put-Call Parity is a crucial concept in finance because it defines a price relationship between put options, call options, and the underlying asset.
This relationship is important as it allows traders and investors to create synthetic positions using different combinations of the underlying assets and options, facilitating arbitrage opportunities.
If the Put-Call Parity does not hold due to price discrepancies in the market, it can lead to arbitrage opportunities; this means traders can potentially take advantage of price differences for a risk-free return.
It also assists in pricing options, aiding in valuating European options, and ensuring the fair pricing of options.
Thus, understanding Put-Call Parity is vital to efficient market operation and effective trading strategies.
Explanation
Put-Call Parity is a critical concept in options pricing which establishes a relationship between the price of European put and call options of the same class, that is, with the same underlying asset, strike price, and expiration date. It serves as a tool for arbitrageurs to identify mispriced options in the market and take advantage of risk-free profit opportunities which may emerge from price discrepancies.
Without the concept of put-call parity, options would be inaccurately priced, leading to potential inefficiencies in the markets. In a simplified sense, put-call parity implies that holding a short put and long call position should equate to a risk-free interest rate, as it replicates a strategy to invest in a risk-free bond.
This relationship becomes a pillar for the determination of the fair value of an option and allows investors to hedge their options holdings effectively. Without the put-call parity, the options market would lack equilibrium, leading to significant price distortions, essentially creating inconsistencies in the financial markets.
Thus, put-call parity plays a key role in maintaining fair and orderly operations in options markets.
Examples of Put-Call Parity
Example 1: Stock InvestmentsConsider an investor who buys a call option for company XYZ’s stock at a $50 strike price, expiring in six months. Simultaneously, he also sells a put option for the same company’s stock at a $50 strike price, also expiring in six months. The investor is confident that the stock price will rise. If it does, he will exercise the call option and purchase the stock at $50, while the put option will expire worthless – effectively profiting from the call option. If the price falls, his put option will be exercised, forcing him to buy the stock at the strike price of $
Essentially, the investor protected himself from downside risk while gaining on upside potential, thereby establishing Put-Call Parity.
Example 2: Currency MarketConsider a currency trader who thinks the exchange rate of EUR/USD will be unstable in the near future. The trader takes a put option on EUR/USD at the strike price of
20 expiring in three months, and sells a call option on EUR/USD at the same strike price and expiration date. The trader receives the premium from selling the call option while paying for the put option. If the EUR/USD rate does indeed fluctuate heavily, regardless of whether it goes up or down, the trader will benefit from one of the two options, thus hedging his risk and demonstrating Put-Call Parity.
Example 3: Commodity MarketImagine a wheat farmer who is not sure about the prices of wheat in the future market. The farmer buys a call option on wheat futures contracts at $5 per bushel and simultaneously sells a put option at the same strike price of $5 per bushel. If wheat prices rise above $5, the farmer will exercise the call option and buy the futures contracts at $5 per bushel, and gain from the higher market prices. If the prices fall below $5, he has to buy the contracts at $5 due to the put option, protecting himself from the further downside. Thus, the farmer has ensured Put-Call Parity through hedging against future price volatility.
FAQ on Put-Call Parity
What is Put-Call Parity?
Put-Call Parity is a principle in options pricing that defines the relationship between the price of European put and call options of the same class, having the same underlying security, strike price and expiration date. It is an important concept of the options market for traders to understand.
How does the Put-Call Parity work?
The Put-Call Parity states that concurrently holding a short European put and long European call of the same class will generate the same return as holding one forward contract on the same underlying asset, with the same expiration, and a forward price equal to the option’s strike price. If these positions have different cash flows, an arbitrage opportunity will present itself.
What is the Put-Call Parity formula?
The formula for Put-Call Parity is C + PV(X) = P + S. Where C is the price of the European call option, P is the price of the European put option, S is the spot price or current market value of the underlying asset, X is the strike price of the option, and PV(X) is the present value of the strike price (X), discounted from the date of expiry at an appropriate risk-free rate.
Why is the Put-Call Parity important?
The Put-Call Parity concept offers valuable insights for trading and hedging. It aids traders to price options, enables them to create synthetic positions using options, and also helps in identifying arbitrage opportunities in the market.
Does Put-Call Parity hold for American options?
Put-Call Parity principle does not always apply to American options because they can be exercised before the expiration date which opens up many more possibilities for the price of the underlying asset.
Related Entrepreneurship Terms
- Option Pricing
- Strike Price
- Expiration Date
- Arbitrage
- Market Efficiency
Sources for More Information
- Investopedia: This site offers a comprehensive resources explaining a variety of finance terms, including Put-Call Parity.
- Khan Academy: A free, online educational platform that may offer lessons or tutorials regarding Put-Call Parity.
- Corporate Finance Institute: Offers courses and resources in financial analysis and finance-related topics such as Put-Call Parity.
- The Balance: A personal finance website which provides informative articles on a wide range of topics, including understanding Put-Call Parity.
