The option chart for call options will often look very similar to the spot market chart, except in cases where the spot market falls dramatically. Either the call option chart or the put option chart will be equal to zero when Days are equal to zero. The Option Calculator is an application that allows you to see the effects of price, time, and volatility on the price of an option.
The second section allows you to set and choose the time horizons that are to be calculated and shown on the graph.
The Black-Scholes 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 Black-Scholes model is used to calculate the theoretical price of European put and call options, ignoring any dividends paid during the option's lifetime.
Figure 5: An online Black-Scholes calculator can be used to get values for both calls and puts. While the original Black-Scholes 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 ex-dividend date value of the underlying stock. Click the New Chart button to create and display a new spot market price simulation (the corresponding option value chart is explained below).
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 Black-Scholes model). The second part, N(d2)Ke^(-rt), provides the current value of paying the exercise price upon expiration (remember, the Black-Scholes model applies to European options that are exercisable only on expiration day).
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.
The value of the option is calculated by taking the difference between the two parts, as shown in the equation.
An example of an online Black-Scholes 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). Damola, check out the can dynamically createBullish option calculator - free software for those.
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