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% Copyright 2015 The MathWorks, Inc. function [m,mtrue,s,strue] = gbmSim(mu,sigma) % Discrete approximation to geometric Brownian motion % % [m,mtrue,s,strue] = gbmSim(mu,sigma) computes the % simulated mean, true mean, simulated standard deviation, % and true standard deviation based on the parameters mu and sigma. numReplicates = 1000; numSteps = 100; y0 = 1; t1 = 1; dt = t1 / numSteps; y1 = y0*prod(1 + mu*dt + sigma*sqrt(dt)*randn(numSteps,numReplicates)); m = mean(y1); s = std(y1); % Theoretical values mtrue = y0 * exp(mu*t1); strue = mtrue * sqrt(exp(sigma^2*t1) - 1); end