Testing GBM Assumptions for Annual Commodity Price Simulations
Summary
The document considers whether annual commodity-price observations can be used in Monte Carlo simulations based on geometric Brownian motion (GBM), and whether observed annual log returns should be normally distributed. One response explains that GBM assumes normally distributed log returns; if the observed return distribution departs substantially from normality, simulated prices may not match the historical distribution. The questioner mentions using Shapiro–Wilk tests, but no test results are supplied.
A second response stresses that suitability depends on the simulation’s purpose. Pricing or hedging requires an appropriate risk-neutral framework and information tailored to the specific instrument or analysis; historical price observations alone may not provide it. For position-risk analysis, empirical returns or another distribution that fits the data may be more suitable, and the sampling interval should match the intended holding period. The source does not establish that annual data is inherently invalid or that a normality test alone determines reliability. Its sample spans 1900–1950, and the responses note that this unusual period and the intended application require closer examination.
Key ideas
- GBM assumes normally distributed log returns, so strong departures can make simulated price distributions inconsistent with observations.
- The document reports that Shapiro–Wilk tests were being considered, but gives no test results.
- The choice of model depends on whether the simulation is for pricing, hedging, or position-risk analysis.
- Risk analysis may use empirical returns or a distribution fitted to the observed data.
- Data frequency should fit the holding period and purpose of the analysis.
Tags
Full text
# Distribution of data for GBM # Distribution of data for GBM I am running some Monte Carlo simulations with GBM on time series of commodity prices. First of all, the price data is annual between 1900-1950. I would firstly like to know if it is bad practice to apply GBM simulations on annual data, as normally, daily stock prices are used. Furthermore, since the GBM log-returns are normally distributed, I would like to know if this fact requires my data (that is the estimated annual "log-returns" of the commodities) to have a normal distribution. I am doing Shapiro-Wilk tests to see if this is the case. However, I am uncertain if it theoretically is required to have normally distributed data to apply GBM if I want reliable results. ## Answer by ZRH (score 1) https://quant.stackexchange.com/a/43853 By using GBM, you take the implicit assumption that log returns are normally distributed. So if you had a commodity where the distribution of log returns is significantly deviating from normal, you would produce results inconsistent with the observed price distributions. That said, I am not aware of any commodity that exhibits non-GBM behaviour. What are you looking at specifically ? ## Answer by Richi Wa (score 0) https://quant.stackexchange.com/a/43865 What do you want to with your Monte Carlo simulation? The time period 1900 - 1950 is quite strange ... this must be some special analysis that you try to do. MY answer applied for the general situation of historical data: - Do you want to calculate a price or hedge? - Or do you want to look at the risk of a position? For 1: you need a risk neutral measure and I assume that your data basis will by no means help you. You would need to read up on the literature for the specific pricing or hedging. For 2: Why would you use GBM? Why don't you look at the empirical distribution or some parametric distribution that fits your observed distribution closely? Again I wonder if your data base is appropriate what you try to do. If you want to assess the risk of a positions that you do in and out daily you should look at daily data.
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