The maximum value of a call or put option could be any value between zero and the difference between the underlying price and exercise price. By establishing lower bounds, we are able to tighten the range so that at expiration, the minimum value of a call and a put is zero.

  • The maximum value of a call option is: max (0, underlying price - exercise price).
  • The maximum value of a put option is max (0, exercise price - underlying price).
Remember that the maximum value of a call option is the greater of zero or, its underlying price minus the exercise price. On the other hand, the maximum value of a put option is the greater of zero, or its exercise price minus the underlying price.

The maximum and minimum values for American calls are explained by the following formula:

Formula 15.7

Notice that the lower bounds for an American call option are the same as the lower bounds for a European call option.

Now, for an American put option, the lower bounds are slightly different:

Formula 15.8

European Calls
Because European options can only be exercised on a specific date (unlike American options, which can be exercised at any time before or at expiration), we need to perform extra manipulations to determine the lower bound. We will skip these manipulations here because it is unlikely that you will be asked to know this on your upcoming exam. The formula is as follows:

Formula 15.9

Where: co = current call value, S0 = current price of underlying asset, X = strike price, r = risk-free rate of interest, and T = time to expiration (# days/365)

European Puts
The lower bounds for European puts is are follows:

Formula 15.10

Straddles and Strangles

Related Articles
  1. Trading

    4 Reasons To Hold Onto An Option

    There are times when an investor shouldn't exercise an option. Find out when to hold and when to fold.
  2. Trading

    Three Ways to Profit Using Put Options

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

    Three Ways to Profit Using Call Options

    A brief overview of how to provide from using call options in your portfolio.
  4. Trading

    Dividends, Interest Rates And Their Effect On Stock Options

    Learn how analyzing these variables are crucial to knowing when to exercise early.
  5. Trading

    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.
  6. Trading

    Options Hazards That Can Bruise Your Portfolio

    Learn the top three risks and how they can affect you on either side of an options trade.
  7. Trading

    Getting Acquainted With Options Trading

    Learn more about stock options, including some basic terminology and the source of profits.
  8. Trading

    American Vs. European Options

    These two options have many similar characteristics, but it's the differences that are important.
  9. Trading

    Understanding How Dividends Affect Option Prices

    Learn how the distribution of dividends on stocks impacts the price of call and put options, and understand how the ex-dividend date affects options.
  10. Financial Advisor

    The Best Strategies to Manage Your Stock Options

    We look at strategies to help manage taxes and the exercise of incentive and non-qualified stock options.
Frequently Asked Questions
  1. Who determines interest rates?

    In countries using a centralized banking model, interest rates are determined by the central bank. In the first step of interest ...
  2. 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, ...
  3. What is the Financial Services Sector?

    A diverse group of companies, beyond banks and credit unions, comprises the financial services sector.
  4. 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 ...
Trading Center