medium · Quantitative Finance stochastic
When modeling a pairs trade, a researcher finds that the spread is cointegrated.
Why is the OU process used to model this spread instead of Geometric Brownian Motion (GBM)?
- GBM is non-stationary and its variance grows linearly with time.
- GBM's price process can never mathematically go negative.
- The OU process lets the model capture volatility clustering.
- GBM carries a zero drift only when evaluated under the risk-neutral measure.
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