The Black-Scholes calculator computes the values for Call and Put Options based on the Black-Scholes equation.
INSTRUCTIONS: Choose units and enter the following:
Black-Scholes Call / Put Value (BSV): The calculator returns the call and put value in U.S. dollars (USD). However, these can be automatically converted to other currencies via the pull down menu. Currency values are updated based on the market every two minutes.
The Black-Scholes equation is based on a partial differential equation that was developed as a model of the financial market. A Wikipedia article on the Black-Scholes equation can be found. This equation is a useful approximation to determine the benefit of purchasing the option and has been tested against two of the algorithms found at espenhaug.org ( . However, users should independently confirm their calculations before relying on this or any other equation to make financial decisions.
The Black–Scholes equation, a partial differential equation, gives a theoretical estimate of the price ofover time. The Black-Scholes equation employs the technique of constructing a risk neutral portfolio that replicates the returns of holding an option and produces a closed-form solution for a European option's theoretical price at maturity.
The value of a call option for a non-dividend-paying stock exercised after the specified time, T, is given:
Call Value = `N(d_1)*S - N(d_2) * X * e^(-r*T)`
The value of a put option based on put-call parity is given
Put Value = `X*e^(-r*T) - S * "Call Value"` = `N(-d_2) * X * e^(-r*T) - N(-d_1)*S`
where `d_1` and `d_2` are given as:
`d_1` = `1/(v*sqrt(T))*[ln(S/X) + (r + v^2/2) *T]` and
`d_2` = `d_1 - v*sqrt(T)`
For these equations:
Before using the Black-Scholes equation for your own estimations, you should read the following article:. This article takes a look at what caused the 1987 banking debacle and suggests that it was caused by the misuse of the Black-Scholes formula. Pay particular attention to the mention of the bestseller by . This book looks at the natural phenomena of how extreme events cause even the most robust estimation theory to fail, which is important to remember when doing estimates for investment purposes.
was the first to publish a paper expanding the mathematical understanding of the options pricing model. He coined the term "Black–Scholes model". Merton and Scholes received the 1997 for their work. Though ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy.