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CIR Process Boundary Condition

Hard · Stochastic Calculus · Quant Trader interview question · stochastic-calculus, cir-process, interest-rate-models, boundary-behavior

You are modeling the short-term interest rate using the Cox-Ingersoll-Ross (CIR) process: $dr_t = \kappa (\theta - r_t) dt + \sigma \sqrt{r_t} dW_t$ where: $r_t$ is the short-term interest rate at time $t$ $\kappa$ is the rate of mean reversion $\theta$ is the long-term mean level of the interest rate $\sigma$ is the volatility $dW_t$ is a standard Brownian motion Under what condition on the parameters $\kappa$, $\theta$, and $\sigma$ will the interest rate $r_t$ remain strictly pos