This page is written for those who already have some understanding
of options, but if you are a beginner, you are advised to study this page
(after digesting the contents of the page on
basic concepts). The page on
volatility
, written for the experienced options trader, is also important in
order to increase your understanding of options and to help you to have
a clearer understanding of how options are priced in the marktplace.
What is the theoretical value of an option and how is it
determined?
When
you buy or sell an option, a profit or loss results from
that trade. If you were to make that same trade under identical
conditions many times, then the
theoretical value (fair value)
of the option is the price that would
result your breaking even (excluding commissions). In
order to have an edge, the trader wants to buy options below their
fair value, or sell them above the fair value. If you consistently
overpay for options, or sell them for too little, the probability
of your making winning trades is diminished.
The value of an option is based on several factors.
A pricing model is then applied to these factors to calculate
the theoretical value. Such a pricing mechanism for options
became widely available when Myron Scholes and Fisher
Black developed the Black-Scholes model for pricing
equity options. This occurred at about the time options began trading
on an exchange (CBOE) in 1973. There have been refinements
to this model over the years, but it is still in widespread use.
In order to apply the model, the
following data has to be input:
stock price
: The higher the stock price, the more a call
is worth. (The less a put is worth.)
strike price
: The
higher the strike price, the less a call ( the more a put) is worth. The
right to purchase the stock for a cheaper price is worth more than the
right to buy it at a higher price.
time to expiration
: The more time left before the option
expires, the more any option is worth.
interest rate
: The higher the interest rate, the more
the call (less the put) is worth. This is because a call
buyer uses less cash to buy the call than he would use to buy
stock, and the difference can be invested to earn interest.
The more interest earned, the more a call buyer is willing to pay for
the option.
dividend
: An option holder is not entitled to cash dividends,
and dividends reduce the price of the stock (when the stock goes ex-dividend,
the stock price is decreased by the amount of the dividend). The
higher the dividend, the less a call is worth, and the more a put
is worth.
volatility
: The is the only one of the factors that is
not known. (Of course dividends, interest rates, stock prices
and time to expiration are constantly changing, but they are
known at the time the option transaction is made.) The volatility
used in the model is an
estimate
of the potential price movement that will occur during
the life of the option. The higher the volatility, the more
any option is worth because a high volatility increases the probability
that the option will make a large favorable move for the holder
of the option (Only a favorable move is considered, because if
the move is unfavorable, the option holder loses nothing extra.
Loss is limited to the price paid for the option.) Since
a change in the volatility estimate changes the value of an option by
a lrge amount, and since this volatility a difficult factor to estimate,
there is often a significant disagreement as to the fair value of
an option.
Volatility,
and how it applies to stock options, is frequently misunderstood. In
order to help
those of you who are first learning about options to have a better understanding
of this very
important topic, a separate page is devoted to
learning about volatility
.
Are theoretical values of an option important for you?
If you are embarking on a strategy that is consistent
over time, such as selling
covered call
options, then it is not necessary for you to be overly concerned
with the theoretical value of an option each time you sell options.
The reason is that sometimes you will receive more than an option
is worth when you sell it, and at other times, you will receive less than
it is worth. Over an extended period of time, this should result
in your receiving an approximation of fair vailue for the options you
sell.
If you are considering buying or selling options on an
irregular basis, then the price at which your transaction occurs is of
much greater importance. A discussion of why this is true follows.
Before we get to that, this is an appropriate time to point out
that we strongly recommend conservative options strategies. Although
the more speculative strategies involving stock options are capable of
producing some very exciting returns, most of the time they result in
a loss of money. Frequently, that loss is 100% of the capital invested
in the position. We feel so strongly about recommending a conservative
approach when using stock options, we have written a
book
on the subject.
Why theoretical values are important
Trading
an option without regard to its theoretical value, or how that
value is determined, is giving up your best chance to become
a successful trader. Of course, if you know for certain which
way a stock is going to move, then it probably does not matter that
you pay far more for an option than it is worth. For those
of us without such insight, being aware of the fair value of an option
is essential.
Trading with knowledge of theoretical values can save a trader large
amounts of money over his trading career. Sometimes you can enter an
order to buy or sell an option and the
premium
paid (or received) will be reasonable. There are often times
however, when the premium levels are extremely high or low. This
can occur when a major news event, such as an earnings report, is
pending (premiums are high), when the market in the stock has been
dull and no news is expected (premiums are low), or even when a person
with a major influence on market movement (Federal Reserve chairman,
for ex.) is about to make a statement. Thus it is not a good
idea to assume that options are always reasonably priced. There
are times when the expectation is universally high that a major
move in the entire market is either imminent, or has just occurred.
When a major move has occurred, there is an increased chance that an additional
major move is imminent. At those times, option premiums reach very
high levels, when compared with historical standards. A trader who generally
buys options has to decide whether it is right to pay these very
high premiums or to sit on the sidelines and wait for a better oportunity.
Similarly those who generally sell options have to decide whether
to be fully invested when option prices are at historically low levels,
or to reduce their trading and wait. Sellers of
uncovered
options also have to be concerned the market may make a major move
in either direction, exposing them to large potential losses.
Knowing how to use option theoretical values can guide the trader (after
he chooses a particular stock) in selecting which particular
option to buy or sell. The observation that one specific
option
series
is much more overvalued (or undervalued) than others
can help a trader initiate a position that not only allows him/her
to have the long or short position he wants, but to do so with
the extra edge that comes from having the position at a favorable
price.
If any
of the terms in the above discussion are not clear to you, see the
glossary
Even though there is a model to calculate the theoretical
value of an option, there is often a great difference of opinion on
what the fair value of an option is. It is this difference of
opinion that helps to create a marketplace.
There are several online sites
that provide an 'options calculator'. We provide
our own, couresty of
Dr. Robert Lum
.
There are internet sites that offer
to sell models for calculating theoretical values. They
are probably too expensive for anyone but a professional
trader.
The calculator provided here is sufficient for most users.
DISCLAIMER: Any gains or losses that result of use, misuse
or non-use of the information provided is the sole responsibility
of the user.
