Stock Option Pricing
Option Pricing Models
By Frank Kneipher
Jan 28, 2007 - 8:39:00 PM

These models are mathematical formulas used in determining theoretical values for option contracts. Professional option traders commonly use these models to make bid and ask prices on a timely basis during the trading, to keep the prices of calls and puts in proper numerical relationship, and for monitoring and adjusting their risk. Some individual investors find these models useful when considering a price to buy or sell an option contract. Option pricing models generally require six inputs: underlying price, strike price, time to expiration, interest rates, dividend amount and volatility.

The term "fair value" (also "theoretical value") refers to a theoretical option price generated by an option pricing model. Because pricing models require an assumption about an underlying stock or index's future volatility as input, values produced by these formulas are ultimately subjective.

Volatility is fluctuation, not direction, of stock price movement. It represents the standard deviation of day-to-day price changes, expressed as an annualized percentage.

Option traders are generally interested in two types of volatility: historical and implied.

• An underlying stock's historical volatility represents its actual price fluctuation as observed over a specific period in the past.
  
• An option's implied volatility (as derived from an option pricing calculator or displayed on many option chains) represents a forecast of the underlying stock's volatility as implied by the option's price in the marketplace. In other words it is the volatility measurement that would be needed as input into a pricing model to generate a theoretical value the same as the options current market price.

It is often asked why an option change in price didn?t change as much as the underlying stock.  You should expect only deep in-the-money calls and puts to change in price as much as the underlying stock. A theoretical sensitivity of option value to underlying stock price movement can be quantified by an option's "delta," generated by an option pricing model, which can range from 0 to 1.00. At-the-money calls and puts have deltas around .50, which implies an expected change in option price by .50 (or 50%) of underlying stock price change. Deep in-the-money options may have deltas up to 1.00, implying an expected change in option price of up to 100% the change in stock price. Out-of-the-money calls and puts have deltas less than .50, down to a low of 0. Deltas may be generated by an option pricing calculator.

Lets not forget about liquidity.  Liquidity is a trading environment characterized by high trading volume.  Liquid markets commonly have narrow spreads between the bid and ask prices, and the ability to accept larger orders without significant price changes.  Always keep in mind that Index and Equity Options with poor liquidity will serve as a disadvantage to the trader due to wider bid ask spreads and less favorable fills.  We should always consider the liquidity issue prior to getting involved in the trading of Options in these areas.

Happy Trading

Frank Kneipher

FKPRINTS1@YAHOO.COM