How to use Probability Calculators with Options Trades

Introduction

One of the most common mistakes novice options traders make is to only take into account
the risk/reward ratio of an options trade without considering the probabilities involved in the
specific trade.

It is not uncommon to hear such a trader comment on the fact that the trade has ‘unlimited
profit’ potential while the maximum loss is limited to the amount paid for the option. This is in
fact a common catchphrase used by some brokers to recruit new options buyers.

If the prospective options buyer knew that there was in some cases only a 5% or 10% chance
the trade would turn profitable, such a trader might have made a different decision. This is
why it is so important to learn how to use a probability calculator early in your options trading
career.

Probability calculator

Fig. 8.22 show what a typical probability calculator looks like. There is more than one
website where traders can get free versions of this type of software, called Monte Carlo
Probability Calculators.

Fig. 8.22

What this does is, given the price and the volatility of the underlying asset and the expiration
date and strike price(s) of the option(s), calculate the probability of certain events taking
place, e.g. that the asset price will expire above or below the strike price.

In this example one would therefore enter the current price of the underling under Asset
Price. The Upside Price and Downside Price = the strike prices of the call or put options
involved. A trader who simply wants to buy a call option should enter the strike price in the
Upside Price field and simply enter ‘1’ in the Downside Price field.

Then enter the Expiration Date of the option in the appropriate field. The Volatility is usually
provided by the broker and should go into the appropriate field. When one clicks on Calculate
the programme calculates the rest.

The result will look something like fig. 8.22(d) below.

Fig. 8.22(d)

The most important result here for the options buyer and seller is the percentage probability
that the price will close beyond the upside (call options) or the downside (put options). In this
example there is only a 5.11% probability that the option would expire In the Money; bad
news for the options buyer and good news for the options seller.

A point to ponder

There is more to this than it seems though. What is very important to remember, especially for
options sellers, is that the trade has to be managed. One can’t simply leave a Naked Put or a
Naked Call until it goes deep ITM.

It is therefore also important to look at the possibility that the price would ever exceed the
strike price (to the upside or downside) without necessarily expiring beyond that level. In Fig.
8.22(d) we see that the probability that the price would ever exceed the strike price to the
upside is 8.26%. While this is still relatively low, it is more than 50% higher than the likelihood
of the price actually expiring beyond this level.

The options seller might therefore have to buy back the option at a loss more often than
expected, because once the price of the underlying asset exceeds the strike price the option
is ITM and it could be exercised.