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:
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:
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)
The lower bounds for European puts is are follows:
TradingA brief overview of how to profit from using put options in your portfolio.
TradingA brief overview of how to provide from using call options in your portfolio.
TradingThere are times when an investor shouldn't exercise an option. Find out when to hold and when to fold.
TradingThe adage "know thyself"--and thy risk tolerance, thy underlying, and thy markets--applies to options trading if you want it to do it profitably.
TradingLearn the top three risks and how they can affect you on either side of an options trade.
TradingLearn more about stock options, including some basic terminology and the source of profits.
TradingLearn how to buy calls and then sell or exercise them to earn a profit.
TradingLearn how the distribution of dividends on stocks impacts the price of call and put options, and understand how the ex-dividend date affects options.
TradingThese two options have many similar characteristics, but it's the differences that are important.