Statistical Monte Carlo simulation methods are useful for many purposes including estimation of prices (values) of financial securities and derivatives. Derivatives Expert includes easy to use Monte Carlo simulation functionality to do exactly this, and more. 

A few examples of utilising the Monte Carlo simulation functionality of Derivatives Expert is shown below.

A Monte Carlo Simulation example

This opens the relevant package.

Needs["DerivativesExpert`StatisticalTools`"]

This simulates 10 prices at time 1 year from spot (now), given a spotprice of 100, an annual interest rate of 5.5 percent, an annual volatility rate of 14.5 percent and no dividends.

Simulate[Price[100,1,5.5,14.5,0],10]

This gives a simulation of the possible prices at time 1 year using the same parameters as above. 5000 prices are simulated. The result is the "distribution" of the time-at-maturity financial asset prices, e.g. a stock or bond, that is assumed to follow a log-normal distribution.

Histogram[Simulate[Price[100,1,5.5,14.5,0],5000]]

Visual Look

This is one way to visually look at the properties of Simulate[ Price[]]. The value of theta is varied from 1/25 to 1 with steps of 1/25. At each step 500 values are simulated. Note that for larger theta, the larger becomes the spread between simulated observations i.e. the minimum and the maximum values becomes greater (in absolute terms).

data3 =Flatten[Table[Simulate[Price[110,T,5.5,20,0],500],{T,N[1/25],1,N[1/25]}]];

ListPlot[data3, PlotRange->All, Axes->{False,True}]

Equidistant Trading Times

This simulates 3 price paths from spot to time 1 year. The given spotprice is 100, the annual interest rate is 5.5 percent, the annual volatility rate is 14.5 percent and there is no dividends. Dimension and trading times are of type Integer. This simulates 3 price paths each having 10 equidistant points along the path.

Simulate[PricePath[100,1,5.5,14.5,0,10],3]

This plots 3 price paths that have the same characteristics as the example above but having 250 trading times along the price paths instead of 10. The financial asset, e.g. a stock or bond, is assumed to follow a log-normal random walk.

pp=Simulate[PricePath[100,1,5.5,14.5,0,250],3];
plots=(ListPlot[#1,Joined->True,PlotRange->All,DisplayFunction->Identity]&)/@pp;
Show[plots,DisplayFunction->$DisplayFunction]