medium · Quantitative Finance

In the Vasicek model dr_t = κ(θ - r_t) dt + σ dW_t, what happens to the short rate r_t as the parameter κ increases?

1. The short rate is prevented from ever becoming negative.
2. The volatility of the short rate increases significantly.
3. The long-run level θ itself begins to fluctuate.
4. The rate returns to the long-run level θ more quickly.

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