Wait until calculator button appears. *Sometimes You Need To Press Refresh*

The MonteCarlo Simulation Boyle (1977) which for its stochastic (*random distribution of probabilities*) process here,
uses a **random** variation from a standard normal distribution.

That is it simulates a Wiener process but of course is built on the geometric Brownian motion of a natural logarithm for
the underlying asset.

The Monte Carlo simulation is often used when no closed-form solution is available

In general it can be used to price most types of **European** Options.

You may wish to further research the work of J. Barraquand and D. Martineau (1995)

"Numerical Valuation of High Dimensional Multivariate American Securities"

Journal of Financial and Quantitative Analysis, 30(3), 383-405

for potential American Option pricing.

The Monte Carlo simulation is rather computer intensive.

Any models are thus better in machine code such as ( C or C++ )

The works of Brotherton-Ratcliffe (1994): "Monte Carlo Monitoring", Risk Magazine December 1994

covers a technique to speed the simulation calculation which needs many thousands of iterations to price with suitable accuracy.

An excellent reference point is: The Art of Computer Programming, D.E. Knuth 2nd edition

Strategies for Quasi-Monte Carlo by Bennett L. Fox

SIM-OPT Consulting, Boulder, CO, USA

Book Series: INTERNATIONAL SERIES IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE : Volume 22

Which is described as follows:

*
Strategies for Quasi-Monte Carlo builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC).
One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension,
while the other variables collectively are relatively insignificant.
Another is smoothing.
The book provides many illustrations of both keys, in particular for problems involving Poisson processes or Gaussian processes.
RQMC beats grids by a huge margin. With low effective dimension, RQMC is an order-of-magnitude more efficient than standard Monte Carlo.
With, in addition, certain smoothness - perhaps induced - RQMC is an order-of-magnitude more efficient than deterministic QMC.
Unlike the latter, RQMC permits error estimation via the central limit theorem.
For random-dimensional problems, such as occur with discrete-event simulation,
RQMC gets judiciously combined with standard Monte Carlo to keep memory requirements bounded.
*
ISBN 0-7923-8580-2

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.