The Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It’s commonly used to represent noise or financial development with a random component.
The geometric brownian motion can be calculated to visualize certain bounds (in quantiles) to hint about the absolute range.
For calculation following parameters are required:
- µ (mu): mean percentage
- σ (sigma): variance
- t: time period
- v: Initial value
The extension to the regular calculation uses:
m: Value increase per time period (in my case monthly value)
breaks: Quantile breaks to calculate the bounds
Code to calculate the values:
| import org.apache.commons.math3.distribution.NormalDistribution; | |
| import java.time.LocalDate; | |
| import java.util.*; | |
| import static java.lang.Math.sqrt; | |
| import static java.lang.Math.exp; | |
| public class WienerProcess { | |
| /** | |
| * Run the Wiener process for a given period and initial amount with a monthly value that is added every month. The | |
| * code calculates the projection of the value, a set of quantiles and the brownian geometric motion based on a | |
| * random walk. | |
| * | |
| * @param mu mean value (annualized) | |
| * @param sigma standard deviation (annualized) | |
| * @param years projection duration in years | |
| * @param initialValue the initial value | |
| * @param monthlyValue the value that is added per month | |
| * @param breaks quantile breaks | |
| * @return a List of double arrays containing the values per month for the given quantile breaks | |
| */ | |
| public static List<double[]> getProjection(double mu, double sigma, int years, int initialValue, | |
| int monthlyValue, double[] breaks) { | |
| double periodizedMu = mu / 12; | |
| double periodizedSigma = sigma / Math.sqrt(12); | |
| int periods = years * 12; | |
| List<double[]> result = new ArrayList<double[]>(); | |
| for (int i = 0; i < periods; i++) { | |
| double value = initialValue + (monthlyValue * i); | |
| NormalDistribution normalDistribution = new NormalDistribution(periodizedMu * (i + 1), | |
| periodizedSigma * sqrt(i + 1)); | |
| double bounds[] = new double[breaks.length]; | |
| for (int j = 0; j < breaks.length; j++) { | |
| double normInv = normalDistribution.inverseCumulativeProbability(breaks[j]); | |
| bounds[j] = value * exp(normInv); | |
| } | |
| result.add(bounds); | |
| } | |
| return result; | |
| } | |
| } |
by Applying the values:
- mu: 0.05 (or 5%)
- sigma: 0.1 (or 10%)
- initial value: 7000
- monthly increase: 100
- time period: 6 years
results in the following chart:
The code is available from Github. It ships with a Swing GUI to enter values and to draw a chart based on the calculation. https://gist.github.com/mp911de/464c1e0e2d19dfc904a7
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