Put-call parity is the relationship that must exist between the prices of European put and call options that both have the same underlier, strike price and expiration date. (Put-call parity does not apply to American options because they can be exercised prior to expiry.) This relationship is illustrated by arbitrage principles that show that certain combinations of options can create positions that are the same as holding the stock itself. These option and stock positions must all have the same return; otherwise, an arbitrage opportunity would be available to traders.

A portfolio comprising a call option and an amount of cash equal to the present value of the option's strike price has the same expiration value as a portfolio comprising the corresponding put option and the underlier. For European options, early exercise is not possible. If the expiration values of the two portfolios are the same, their present values must also be the same. This equivalence is put-call parity. If the two portfolios are going to have the same value at expiration, they must have the same value today, otherwise an investor could make an arbitrage profit by purchasing the less expensive portfolio, selling the more expensive one and holding the long-short position to expiration.

Any option pricing model that produces put and call prices that don't satisfy put-call parity should be rejected as unsound because arbitrage opportunities exist.

For a closer look at trades that are profitable when the value of corresponding puts and calls diverge, refer to the following article: Put-Call Parity and Arbitrage Opportunity.

There are several ways to express the put-call parity for European options. One of the simplest formulas is as follows:
 

Formula 15.11
c + PV(x) = p + s

Where:
c = the current price or market value of the European call
x = option strike price
PV(x) = the present value of the strike price 'xeuropean' discounted from the expiration date at a suitable risk-free rate
p = the current price or market value of the European put
s = the current market value of the underlyer

The put-call parity formula shows the relationship between the price of a put and the price of a call on the same underlying security with the same expiration date, which prevents arbitrage opportunities. A protective put (holding the stock and buying a put) will deliver the exact payoff as a fiduciary call (buying one call and investing the present value (PV) of the exercise price).
 

Note: There are much more sophisticated formulas for analyzing put-call relationships. For the exam, you should know that a protective put = fiduciary call (asset + put = call + cash).

Portfolio insurance is very similar to a "fiduciary call" (lending + call). The amount of lending is set so that return of principal plus interest by the payoff date exactly equals the floor.

Effect of Cash Flows on Put-Call Parity and the Lower Bounds

Related Articles
  1. Investing

    What is Put-Call Parity?

    Put-call parity describes the relationship that must exist between European put and call options with the same expiration date and strike prices.
  2. Trading

    Put-Call Parity and Arbitrage Opportunity

    These trades are profitable when the value of corresponding puts and calls diverge.
  3. Trading

    Forecasting Market Direction With Put/Call Ratios

    Options are not only trading instruments but also predictive tools that can help us gauge the feelings of traders.
  4. Investing

    Understanding Risk Parity

    Risk parity is an investment strategy that focuses on the allocation of risk across a portfolio.
  5. Trading

    Leading Indicators Of Behavioral Finance

    Discover how put-call ratios and moving averages can be used to analyze investor behavior.
  6. Investing

    Explaining Interest Rate Parity

    Interest rate parity exists when the expected nominal rates are the same for both domestic and foreign assets.
  7. Investing

    Explaining Uncovered Interest Rate Parity

    Uncovered interest rate parity is when the difference in interest rates between two nations is equal to the expected change in exchange rates.
  8. Trading

    Three Ways to Profit Using Put Options

    A brief overview of how to profit from using put options in your portfolio.
  9. Trading

    Getting Acquainted With Options Trading

    Learn more about stock options, including some basic terminology and the source of profits.
Frequently Asked Questions
  1. What's the Best Way to Contact Warren Buffett?

    Learn how to contact Warren Buffett and what kinds of contact is most likely to receive a response from him or from his company, ...
  2. What is the Financial Services Sector?

    A diverse group of companies, beyond banks and credit unions, comprises the financial services sector.
  3. Who are Whole Foods' (WFM) main competitors?

    Whole Foods' main competitors are Sprouts Farmers Markets and Trader Joe's. However, the recent acquisition by Amazon my ...
  4. What caused the Stock Market Crash of 1929 that preceded the Great Depression?

    Find out what led to the stock market crash of 1929, which in turn led to the Great Depression. It sparked a nearly 90% loss ...
Trading Center