CIR Process Boundary Condition - Quant Trader Interview Question
Difficulty: Hard
Category: Stochastic Calculus
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Topics: stochastic-calculus, cir-process, interest-rate-models, boundary-behavior
Problem Description
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
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