How Options are Priced

We take our first look at how options are priced.

The pricing of options is based on the probabilty of outcome. In other words- the odds.
Because one can be an option buyer or an option seller, also called an option writer, options are necessariliy priced on probability, or it would be possible for a trader engage in riskless arbitrage. In other words, if options were not priced based on probability of outcome, it would be possible for a trader to place offsetting trades, and make a profit without any risk of losing money that exceeds the profit one could make from a risk free investment, such as a bank account or a bond.

Options are priced by making some general assumptions about the markets, and then using some basic tools from statistics to determine the probability or odds of whether the option will or will not be profitable, and, if the option is profitable, a probabilty distribution of how profitable the option will be.

There are only 5 Inputs to the price of an option (or 6 if the stock has a dividend):

The first is the current price of the stock.

The second input is the Strike Price, which is the pre-set buy or sell price that you are locking in.

The 3rd input for pricing an option is the amount of time left until the option expires. It should make sense that if there is more time left until the option expires, then there is more time for the price of the stock to possibly move to where the option is profitable.

The 4th input is the current the risk free rate. The risk free rate is the rate one can get on a risk free investment such as a US government bond. Because money can be invested risk free into a bank account or a government bond, the interest that one would earn in a risk free investment is considered the time value of money. If one places money into an investment that contains risk, such as buying a stock or an option, then one has to consider the money they could have earned in a risk free investment during that time.

An option’s strike price is the future value of the Strike Price when the option expires. That value must be discounted to the present value using the time value of money. In other words, the interest that one could earn in a risk free investment between the time the option is purchased, and the time the option expires, is subtracted off of the the strike price. This discounts the Strike Price to the present value. The most common used rate for the Risk Free rate is the US 10 Year Treasury Rate.

The last part of option pricing is the volatility of the Periodic Daily Returns. This is the rate of change or percent that the stock increases and decreases each day, not the change in dollar amount.

It should make sense that the higher the volatility, in other words the more the price goes up and down each day, the higher likelihood that the price of the stock will move in the favor of the option holder.

Volatility is the largest factor in determining option pricing.