The Option Model
This chapter will be an introduction of the option model. Too often, would-be option traders get confused by all of the complicated mathematical formulas used to describe option models. I am going to try and simplify the way you view an option model, by converting your observation to a single simple formula that will work with all liquid options.
Games of Chance
First a little background on the mathematical models that were used to create options. The first model was introduced in a paper published by Fischer Black and Myron Scholes in 1973. The math is quite complicated, but it basically describes a bell-shaped curve, Figure 7.1, in which the highest degree of uncertainty exists at the current market price; the ATM call and puts each have a 50 percent chance of being in the money at expiration. Therefore, the uncertainty decreases as price moves higher or lower from the current price. As options go deeper in the money, the probability that they will end up with a 1.00 delta continues to increase until it reaches a point at which there is no premium left in the option. That price is referred to as parity. At this time, the option will react to the underlying asset tick for tick to the upside (or downside for a put) and may be used as a surrogate for the underlying asset. If the market were to reverse, the option would eventually lose deltas and would not ...