How Are Options Values Calculated?

Main Factors Determining Option Price

While a number of factors figure into option prices, stock option premiums are primarily affected by the movement of the underlying stock. Black and Scholes won the Nobel Economic Prize for their model that determines the theoretical fair price of an option. The six factors enumerated by B&S are figured by markets into the price of a stock option are:

¨     Stock price

¨     The option’s strike price

¨     Time left until expiration

¨     The stock’s historical volatility

¨     Interest rates (minor effect)

¨     Dividends (minor effect)

  1. Stock price is the major factor, by far, affecting the option’s price. Changes in stock price can profoundly affect the price of options on the stock.
  2. Strike price has a bearing on the option price, on how much of the price is intrinsic vs. time value, the option’s delta, and other factors. Generally, the farther away the strike price is from the stock price, the less time value the option will have.
  3. Time to expiration is the time remaining before the option expires. Because of time decay, option time value decreases as expiration approaches, until it is reduced to intrinsic value (if any) at or close to expiration. However, ATM and OTM calls rarely go to zero before expiration; maybe $0.05, but never zero. The major option price decay occurs in last 30 days before expiration, as noted above. ITM options can trade for less than intrinsic value (below parity), but usually not by more than a few pennies. Professional traders, whose trading costs are virtually nil, could arbitrage sub-parity calls by buying the call and selling the stock, pocketing as profit the below-parity amount.

Premium compression – This is a term meaning that the further out in time an option’s expiration, the lower the premium per month quoted.

Example: A call 6 months out will not have 6 times the premium of the current-month call. It may not carry even 3 times the current-month premium. The further out in time the expiration date, the more the premium will be “compressed” compared to the price of the same-strike option for the current month.

  1. Stock volatility – this is the stock’s historical price volatility – the standard deviation of price variations – over a fixed period of time, usually one year. The more volatile the stock, the more likely it is to move, which should increase the price of its options. Black-Scholes fair-price computations performed by different persons will usually show different results, because they assign different values to stock volatility.

To a much lesser extent, option prices are affected by:

  1. Interest rates have hardly any effect on real prices. However, they are used in Black-Scholes option valuation computations.
  2. Stock dividends also have very little effect on prices, since they are considered to be “baked” into the stock’s price by market forces. However, if a stock’s price falls significantly, as happened in the period from October 2008 through March 2009, dividend yields skyrocket (of course assuming that the dividend did not change), dividends may assume a larger role in the pricing of options. It is difficult, however, to know how much of a role dividend plays in that event, especially with stock volatility so high during this time.

Other Factors Affecting Option Price

As a practical matter, there are a few other factors that the market grinds into an option’s price, some of which are very important:

  • Current stock prices of similar companies
  • Supply and demand for the underlying stock
  • The option’s liquidity (volume)
  • Supply and demand for the option
  • The market’s expectation of future events affecting the underlying stock *
  • The market’s expectation of the stock’s future direction *

* Significant news events and expectation of market direction are the major factors, other than actual stock price movements, that affect the option’s price and certainly are the ones that drive implied volatility – and thus result in a high amount of time value in option premiums.

The last two items (market expectations) interact rather directly with supply and demand for the option. For hedging purposes alone, large companies normally will show significant volume and open interest in the option series close to the money; both of which decrease as the strike gets further from the money. However, volume and open interest frequently will be heavier in those series that are in the direction of anticipated stock movement, reflecting increased speculation activity.