Derivatives - Put-Call Parity

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. Options & Futures

    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. Options & Futures

    Put-Call Parity And Arbitrage Opportunity

    Look at trades that are profitable when the value of corresponding puts and calls diverge.
  3. Economics

    Interest Rate Arbitrage Strategy: How It Works

    Changes in interest rates can give rise to arbitrage opportunities that, while short-lived, can be very lucrative for traders who capitalize on them.
  4. Options & Futures

    Three Ways to Profit Using Put Options

    A brief overview of how to profit from using put options in your portfolio.
  5. Options & Futures

    Getting Acquainted With Options Trading

    Learn more about stock options, including some basic terminology and the source of profits.
  6. Options & Futures

    Three Ways to Profit Using Call Options

    A brief overview of how to provide from using call options in your portfolio.
  7. Options & Futures

    The Basics of Options Profitability

    The adage "know thyself"--and thy risk tolerance, thy underlying, and thy markets--applies to options trading if you want it to do it profitably.
  8. Investing Basics

    Understanding Risk Parity

    Risk parity is an investment strategy that focuses on the allocation of risk across a portfolio.
  9. Options & Futures

    Going Long On Calls

    Learn how to buy calls and then sell or exercise them to earn a profit.
  10. Trading Strategies

    A Guide Of Option Trading Strategies For Beginners

    Options offer alternative strategies for investors to profit from trading underlying securities, provided the beginner understands the pros and cons.
RELATED TERMS
  1. Put-Call Ratio

    A ratio of the trading volume of put options to call options. ...
  2. Put-Call Parity

    A principle that defines the relationship between the price of ...
  3. Reverse Conversion

    A finance and risk management technique based on a put-call parity ...
  4. Parity

    1. In general, a situation of equality. Parity can occur in many ...
  5. Put On A Call

    One of the four types of compound options, this is a "put" option ...
  6. Conversion Arbitrage

    An options trading strategy employed to exploit the inefficiencies ...
RELATED FAQS
  1. Where can traders and investors find most recent Put-Call indicator ratios and charts?

    Learn about how the put-call ratio is calculated and interpreted, and discover where traders and analysts can obtain current ... Read Answer >>
  2. How is the Put-Call Ratio calculated and where does the information come from?

    Discover how major exchanges and financial websites, such as the Chicago Board of Exchange, compile data for their respective ... Read Answer >>
  3. Why is the Put-Call Ratio important for investors and economists for tracking market ...

    Discover why the put-call ratio is considered a useful measure for investors and economists when they are determining market ... Read Answer >>
  4. What is the put-call ratio and why should I pay attention to it?

    The put-call ratio is a popular tool specifically designed to help individual investors gauge the overall sentiment (mood) ... Read Answer >>
  5. ABC shares are currently trading at $27.00, and they are expected to pay a dividend ...

    The correct answer is d) According to Put-Call Parity: (Stock Price) + (Put) - (Call) = PV(X) + PV(D) 27.00 + 1.50 - c = ... Read Answer >>
  6. How are call options priced?

    Learn how aspects of an underlying security such as stock price and potential for fluctuations in that price, affect the ... Read Answer >>
Hot Definitions
  1. Labor Market

    The labor market refers to the supply and demand for labor, in which employees provide the supply and employers the demand. ...
  2. Demand Curve

    The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity ...
  3. Goldilocks Economy

    An economy that is not so hot that it causes inflation, and not so cold that it causes a recession. This term is used to ...
  4. White Squire

    Very similar to a "white knight", but instead of purchasing a majority interest, the squire purchases a lesser interest in ...
  5. MACD Technical Indicator

    Moving Average Convergence Divergence (or MACD) is a trend-following momentum indicator that shows the relationship between ...
  6. Over-The-Counter - OTC

    Over-The-Counter (or OTC) is a security traded in some context other than on a formal exchange such as the NYSE, TSX, AMEX, ...
Trading Center