The BlackScholes model for calculating the premium of an option was introduced in 1973 in a paper entitled, "The Pricing of Options and Corporate Liabilities" published in the Journal of Political Economy. The formula, developed by three economists – Fischer Black, Myron Scholes and Robert Merton – is perhaps the world's most wellknown options pricing model. Black passed away two years before Scholes and Merton were awarded the 1997 Nobel Prize in Economics for their work in finding a new method to determine the value of derivatives (the Nobel Prize is not given posthumously; however, the Nobel committee acknowledged Black's role in the BlackScholes model).
The BlackScholes model is used to calculate the theoretical price of European put and call options, ignoring any dividends paid during the option's lifetime. While the original BlackScholes model did not take into consideration the effects of dividends paid during the life of the option, the model can be adapted to account for dividends by determining the exdividend date value of the underlying stock.
The model makes certain assumptions, including:
 The options are European and can only be exercised at expiration
 No dividends are paid out during the life of the option
 Efficient markets (i.e., market movements cannot be predicted)
 No commissions
 The riskfree rate and volatility of the underlying are known and constant
 Follows a lognormal distribution; that is, returns on the underlying are normally distributed.
The formula, shown in Figure 4, takes the following variables into consideration:
 Current underlying price
 Options strike price
 Time until expiration, expressed as a percent of a year
 Implied volatility
 Riskfree interest rates
Figure 4: The BlackScholes pricing formula for call options. 
The model is essentially divided into two parts: the first part, SN(d1), multiplies the price by the change in the call premium in relation to a change in the underlying price. This part of the formula shows the expected benefit of purchasing the underlying outright. The second part, N(d2)Ke^(rt), provides the current value of paying the exercise price upon expiration (remember, the BlackScholes model applies to European options that are exercisable only on expiration day). The value of the option is calculated by taking the difference between the two parts, as shown in the equation.
The mathematics involved in the formula is complicated and can be intimidating. Fortunately, however, traders and investors do not need to know or even understand the math to apply BlackScholes modeling in their own strategies. As mentioned previously, options traders have access to a variety of online options calculators and many of today's trading platforms boast robust options analysis tools, including indicators and spreadsheets that perform the calculations and output the options pricing values. An example of an online BlackScholes calculator is shown in Figure 5; the user must input all five variables (strike price, stock price, time (days), volatility and risk free interest rate).
Figure 5: An online BlackScholes calculator can be used to get values for both calls and puts. Users must enter the required fields and the calculator does the rest. Calculator courtesy www.tradingtoday.com 

Trading
Understanding the BlackScholes Model
The BlackScholes model is a mathematical model of a financial market. From it, the BlackScholes formula was derived. The introduction of the formula in 1973 by three economists led to rapid ... 
Trading
NYIF Instructor Series: Black Scholes Model
In this short instructional video Anton Theunissen explains the Black Scholes model. 
Trading
Circumvent Limitations of BlackScholes Model
Mathematical or quantitative modelbased trading continues to gain momentum, despite major failures like the financial crisis of 200809, which was attributed to the flawed use of trading models. ... 
Trading
How To Build Valuation Models Like BlackScholes (BS)?
Want to build a model like BlackScholes? Here are the tips and guidelines for developing a framework with the example of the BlackScholes model. 
Trading
The Anatomy of Options
Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio. 
Trading
Understanding How Dividends Affect Option Prices
Learn how the distribution of dividends on stocks impacts the price of call and put options, and understand how the exdividend date affects options. 
Trading
Dividends, Interest Rates And Their Effect On Stock Options
Learn how analyzing these variables are crucial to knowing when to exercise early. 
Trading
Breaking Down The Binomial Model To Value An Option
Find out how to carve your way into this valuation model niche. 
Markets
How & Why Interest Rates Affect Options
The Fed is expected to change interest rates soon. We explain how a change in interest rates impacts option valuations. 
Trading
The "True" Cost Of Stock Options
Perhaps the real cost of employee stock options is already accounted for in the expense of buyback programs.