Created
April 19, 2015 08:27
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Geometric Brownian motion
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| sigma = 0.3 | |
| mu = 0.06 | |
| N = 1000 | |
| flag = 0 | |
| lambda = c(0.01, 0.05, 0.1, 0.5, 1) | |
| xs = c(5) | |
| Xs = matrix(5, nrow = 5, ncol = N) | |
| zs = rnorm(N) | |
| for (i in 2:N) | |
| { | |
| xs[i] = xs[i-1] + (mu - 0.5*sigma*sigma)/N + sigma*sqrt(1/N)*zs[i] | |
| } | |
| for (j in 1:5) | |
| { | |
| for (i in 2:N) | |
| { | |
| n = rpois(1, lambda[j]*1/N) | |
| M = 0 | |
| if(n != 0) | |
| { | |
| flag <<- flag+1 | |
| ys = 0.1*rnorm(n, mean = 0, sd = 1)+1 | |
| M = 0 | |
| for (k in 1:n) | |
| M = M + log(ys[k]) | |
| } | |
| Xs[j, i] = Xs[j,i-1] + (mu-0.5*sigma*sigma)/N + sigma*sqrt(1/N)*zs[i] + M | |
| } | |
| } | |
| yM = max(max(xs), max(Xs)) | |
| ym = min(min(xs), min(Xs)) | |
| plot(xs, cex = 0.05, type="l", ylim=c(ym, yM)) | |
| lines(1:N, Xs[1,1:N], col="red") | |
| lines(1:N, Xs[2,1:N], col="blue") | |
| lines(1:N, Xs[3,1:N], col="green") | |
| lines(1:N, Xs[4,1:N], col="violet") | |
| lines(1:N, Xs[5,1:N], col="orange") |
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