Using GDP Growth Differences as Drift in a Currency GBM

Summary

The document raises a modeling question about simulating a currency pair with geometric Brownian motion when the asset is assumed to respond to relative economic performance. It proposes using the difference between the two countries’ GDP growth rates as the drift at each time step, while setting aside volatility and other market influences. The focus is whether this choice is mathematically consistent with GBM and whether it could be appropriate in practice.

The document presents the proposed model and its assumptions but contains no answer, empirical analysis, or evidence that GDP growth differentials predict exchange-rate drift. It is therefore useful as a framing of the distinction between a mathematically permissible drift specification and a defensible real-world model. Any practical application would need to define how GDP data enters the process and validate the relationship against exchange-rate behavior, while accounting for omitted drivers and measurement timing.

Key ideas

• A GBM drift can be specified as a time-varying input in a proposed simulation.
• The question proposes using the difference in two countries’ GDP growth rates as currency drift.
• Mathematical compatibility alone does not establish that a drift assumption is empirically useful.
• The document offers no validation or answer about real-world forecasting performance.

Tags

# What is the relevant application of mathematics?


# What is the relevant application of mathematics?












I want to model an asset (like a currency) that is sensitive to relative economic performance between two countries, which can be measured by GDP (for example). This is a very simple case with many assumptions. My question only pertains to the maths behind this:

```
Can drift be modelled in Geometric Brownian Motion
```

If you were to randomly simulate the price path of such an asset (e.g. USDCHY – driven by relative economic performance in China and the US, which can be measured by GDP), would it be appropriate to model it using Geometric Brownian Motion where the drift, for each timestep, is defined by the simple difference between GDP growth rates? (disregarding vol or anything else).

Just wondering, in principal, if this violates any convention or model assumption.

Do you think this would be appropriate to use in real life?

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