## 02 May 2008

### Basic Options Pricing

As we noted earlier, options are derivatives, and are so called because they derive their value from their underlying instrument. Determining the value of options had always been problematic up until the point when in the early 70’s, Fischer Black and Myron Scholes developed the “Black Scholes Option Pricing Model”. The model has been refined and improved over time with alternative equations such as the “Cox, Ross & Rubinstein Binomial Model” being the more usual model used for American style stock options these days.

I shall use the generic term of “Option Pricing Model”, or OPM as proxy unless specifically mentioned otherwise.

I submit that only mathematicians would be interested in the actual formula, and by the miracle of technology we have software to compute this for us non-mathematicians. There is much available on the web on the topic if you’re so inclined.

At this point I would like to introduce a piece of software to you, that I use for pricing and producing payoff diagrams (or risk graphs as they are sometimes known) and will be used extensively throughout this course. It is free for the evaluation version and at less than \$100 for the full version it is very inexpensive. I have no financial interest in the product and there are other modelers that are equally useful.

It is the Hoadley Options Strategy Modeler and is available for download at http://hoadley.net/options/strategymodel.htm. All instructions in how to use the software are at the site. I consider it an essential tool for analyzing trades, particularly for those who learn more visually-spatially than by pure abstract. Its real value becomes apparent in analyzing multi-legged spread trades.

The OPM considers six variables or “inputs” in order to generate a price for an option. They are:

1. The price of the underlying
2. The strike price
3. The time till expiry
4. Risk free interest rates
5. Dividends, if any
6. Volatility

At any point in time, the first five inputs are known unequivocally. However for the sixth input, volatility, it is the future volatility of the underlying that must be known. This of course is impossible, so a volatility projection must be made. I will be discussing volatility in depth in a later section.

But here are some general rules of thumb that you can use as a guide, before we get to more in-depth pricing principles:

• Higher prices mean higher call prices.
• Higher prices mean lower put prices
• Lower prices mean lower call prices
• Lower prices mean higher put prices
• More time till expiry means higher option prices
• Higher volatility means higher option prices

Please not that these are general principles and there are several dynamics that can effect the above and I would like to cover some other principles before continuing on with option pricing.