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   365 Risk Free Rate Stock Volatility Current Price Exercise Price Dividend Yield Number of Simulations   Outputs Start Date: 09/06/{Start Year} Maturity Date: 09/06/{Maturity Year} Option Price Call Option 10.5126 Put Option 9.8287     Simulated Call 7.7378 Simulated Put 5.2076   Calculations   Time to Maturity (yrs) 1   d1 0.1767   d2 -0.1233   Normalized d1 0.5701   Normalized d2 0.4509   Normalized -d1 0.4299   Normalized -d2 0.5491   N*(d1) 0.3928 Greeks Greeks for: Call Put Delta 0.5701 -0.4299 Gamma 0.0159 0.0159 Theta 16.2805 22.408 Vega 38.6885 38.6885 Rho 38.2964 -46.6303

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