Theoretical value—what a concept! A trader plugs six numbers into a
pricing model, and it tells him what the option is worth, right? Well, in
practical terms, that’s not exactly how it works. An option is worth what the
market bears. Economists call this price discovery. The price of an option is
determined by the forces of supply and demand working in a free and open
market. Herein lies an important concept for option traders: the difference
between price and value.
Price can be observed rather easily from any source that offers option
quotes (web sites, your broker, quote vendors, and so on). Value is
calculated by a pricing model. But, in practice, the theoretical value is really
not an output at all. It is already known: the market determines it. The trader
rectifies price and value by setting the theoretical value to fall between the
bid and the offer of the option by adjusting the inputs to the model.
Professional traders often refer to the theoretical value as the fair value of
the option.
At this point, please note the absence of the mathematical formula for the
Black-Scholes model (or any other pricing model, for that matter).
Although the foundation of trading option greeks is mathematical, this book
will keep the math to a minimum—which is still quite a bit. The focus of
this book is on practical applications, not academic theory. It’s about
learning to drive the car, not mastering its engineering.
The trader has an equation with six inputs equaling one known output.
What good is this equation? An option-pricing model helps a trader
understand how market forces affect the value of an option. Five of the six
inputs are dynamic; the only constant is the strike price of the option in
question. If the price of the option changes, it’s because one or more of the
five variable inputs has changed. These variables are independent of each
other, but they can change in harmony, having either a cumulative or net
effect on the option’s value. An option trader needs to be concerned with the
relationship of these variables (price, time, volatility, interest). This
multidimensional view of asset pricing is unique to option traders.