The Black-Scholes calculator computes the values for Call and/or Put options using various currencies.
INSTRUCTIONS: Enter the following:
Call or Put Value (CPV): The calculator returns the prescribed call or put value in U.S. dollars (USD). However, the user can automatically convert this to other currency units via the pull-down menu including European Euro, Canadian Dollar, Mexican Peso, Brazilian Real, Russian Rubel, Indian Rupee, Chinese Yuan, Japanese Yen, Swiss Franc, Australian Dollar and the South African Rand,
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 HERE. 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 (HERE. 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 of European-style options over 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: http://www.theguardian.com/science/2012/feb/12/black-scholes-equation-credit-crunch. 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 The Black Swan by Nassim Nicholas Taleb. 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.
Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model. He coined the term "Black–Scholes options pricing model". Merton and Scholes received the 1997 Nobel Prize in Economics for their work. Though ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy.