If you already know what a stock option is, and realize how they can help you leverage movements in the market, then the next step is to understand the pricing of those options. We will take a look at the Black Scholes option pricing model. But before we do, you need to understand that options prices are very subjective. The Black Scholes model is just a tool to guide you on theoretical options pricing. Black Scholes is probably the most popular option pricing model, but there are many others to choose from.

To determine an options theoretical price, the black scholes model uses the following parameters:

  • underlying price of the stock
  • strike price of the option
  • time to maturity
  • volatility
  • * risk free rate of return

The actual Black-Scholes Formula Is:

C0 = S0N(d1) - Xe-rTN(d2)

Where:
d1 = [ln(S0/X) + (r + σ2/2)T]/ σ √T
d2 = d1 - σ √T
C0 = option value
S0 = stock price
N(d) = the probability that a random draw from a standard normal distribution will be less than (d).
X = exercise price
e = 2.71828
r = risk-free interest rate
T = time to option’s maturity, in years
ln = natural logarithm function
σ = standard deviation of the annualized continuously compounded rate of return on the stock

That’s a lot to take in, and certainly a lot of work to calculate by hand. But the good news is that you don’t have to. Many online brokerages have black scholes calculators built directly into their option chains. Some of them also highlight which market option prices are above or below theoretical pricing models.

Another option for computing and studying option values is to utilize Microsoft Excel and the visual basic language to build your own option pricing tool set. This can also be a lot of work, but yet again there is good news. The work has already been done for you, and you can just purchase a license to the visual basic code. I recommend purchasing the following book, which includes a CD containing all the visual basic option pricing code you will need. You can use the code as is, which is very functional, or build even more sophisticated applications utilizing the visual basic functions included. The book can be easily purchased by clicking the cover image link below:

Option Pricing Models and Volatility Using Excel-VBA (Wiley Finance)
Option Pricing Models and Volatility Using Excel-VBA (Wiley Finance) by Fabrice Douglas Rouah

A sample Excel screenshot is shown below: