Stock Option Pricing
Stock Options Pricing 101
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Nov 11, 2006 - 10:02:00 PM

How do options get their price? This is a complex subject beyond the scope of what we're doing here, but it is important to have a basic idea. Market makers use computer models usually based from 'The Black-Scholes' pricing model. This model uses the following inputs to determine an option price:

• Stock Price

• Strike Price

• Time remaining until expiration expressed as a percent of a year

• Current risk-free interest rate

• Volatility measured standard deviation

To put some perspective on the subject, let's put the mathematics aside and approach this from a business viewpoint. If we're a buyer of a call option we have limited risk and the potential for a large return. If we're the seller we have limited return and the potential for a large loss. So, if we're the seller what factors would be important to us when determining the premium we would want to charge for writing this option? Let's take a look at the factors we would want to consider below:

Volatility: The more volatile the underlying security is, the more likely the seller can suffer a loss. So, the seller protects themselves by charging a higher premium. Therefore, the higher the volatility increase, the higher the price of the option.

Time to Expiration: The longer the time between when the seller sells the option and the options expirations date, the higher the probability the seller can suffer a loss. This being the case, the seller will protect himself. He does this by charging more. Therefore, the longer the option has before it expires, the higher the price of the option will be.

Sellers Return: The seller wants to make a reasonable rate of return on his investment. The more risk he takes the higher he will expect this return to be. So, the higher the return expected by the seller, the higher the option price will generally be.

The Greeks: The Greeks are a set of statistical values, expressed as percentages that help determine what options to buy and what strategies to use. We'll use Delta and Vega to help determine which options to purchase, but we'll also provide a brief definition of some other measurements.

Delta: Delta is a measure of how the price of an option will move in correspondence to a movement of the price in the underlying stock. If a call option has a delta of .5 and the stock rises by a dollar the option will rise by .50 [$1 * .5]. The stock itself has a delta of 1 and an 'in-the-money' option (option with an intrinsic value) approaches expiration it's delta will approach 1.

In our Microsoft example, let's say the call option we purchased for 3.10 had a delta of .95 and the stock increased $2.50. This means the option will rise in price to 5.48 [3.10 + (2.50*.95)]. If we purchased a put option for $2.10 and this put had a delta of -.95 and the stock fell by $2.50 -- our out would now be worth $4.48 [$2.10 + (-2.50*-.95)].

Vega: Another component of determining options price is the volatility of the underlying security. Vega measures the sensitivity of option value to change in volatility. Vega indicates an absolute change in option value for a one percent change in volatility. For example, a Vega of .070 means an option's value will increase by .070 if the volatility percentage is increased by 1.0, or decreased by .070 if the volatility percentage is decreased by 1.0.

Theta: The definition of an option includes a time constraint. Part of the value of the option is based upon how long it is before the option will expire. The seller will require greater premium the longer he must take on the risk. On the buyers side this means that his assets are depreciating. Theta measures the change in the option value for a one-day reduction in time to expiration.

Gamma: Gamma is the sensitivity of Delta in relation to a movement of the underlying stock. For example, a Gamma change of 0.150 means the delta will increase by 0.150 if the price of the stock increases or decreases by $1.0.

Rho: One of the components of determining an options price is the interest rate. If we're the option seller we would want to be compensated for taking a risk. The interest rate is one factor that determines how much compensation we will get. Rho is the sensitivity of option value to change in interest rate. Rho indicates the change in option value for a one percent change in the interest rate. For example, a Rho of .05 means the option's value will increase by .05 if the interest rate is decreased by 1.0.

Open Interest: Open interest is the number of outstanding options at each strike price being traded.
We suggest trading stocks that average an absolute minimum of 250,000 (preferably 500,000) shares traded daily. The reason you want a minimum of 250,000 daily volume is that there's usually not enough liquidity in the open interest of the options to make a safe options trade.