Black-Scholes European Options Pricing

MonteCarlo Simulation

Inputs Start Date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Maturity Date Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Days Remaining   366 Risk Free Rate Stock Volatility Current Price Exercise Price Dividend Yield Number of Simulations   Outputs Start Date: 02/04/{Start Year} Maturity Date: 02/04/{Maturity Year} Option Price Call Option 10.5278 Put Option 9.8369     Simulated Call 13.2033 Simulated Put 10.6666   Calculations   Time to Maturity (yrs) 1.0027   d1 0.1772   d2 -0.1232   Normalized d1 0.5703   Normalized d2 0.451   Normalized -d1 0.4297   Normalized -d2 0.549   N*(d1) 0.3927 Greeks Greeks for: Call Put Delta 0.5703 -0.4297 Gamma 0.0159 0.0159 Theta 16.2193 22.3459 Vega 38.7768 38.7768 Rho 38.3963 -46.7444

http://www.global-derivatives.com

Original Excel / VBA version contributed by Kevin Cheng (Apr 28, 2003)
Web based (PHP) version contributed by Randy Casburn (Jan 28, 2005)
randy@randycasburn.com
with great help from PHPMathLib from Paul Meager (et. al.)

*NOTE:  In the Excel version this field is updated in real time as the simulations are run. 
That's not possible in a server-side technology such as PHP without being really, really ugly.  Besides...
I would rather see it used as a precision adjustment
provided through iterative re-entry.

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GD-MCS.php
ProbabilityDistribution.php
NormalDistribution.php
SpecialMath.php
NumericalConstants.php