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IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices

Which statement about a mean-reverting Ornstein-Uhlenbeck model for an interest rate dr = a(mu - r)dt + sigma dW (a > 0) is correct?

The long-run distribution is normal with mean mu and variance sigma squared over two a. The process is Gaussian so it can go negative, and its expectation drifts from the starting value towards mu.

  1. AThe long-run variance of r grows without bound
  2. Br is always positive
  3. CThe long-run distribution of r is normal with mean mu and variance sigma^2/(2a)Correct
  4. DThe long-run variance is sigma^2/a
  5. Expected value of r equals r0 at all times

Explanation

The stationary distribution of the OU process is normal with mean mu and variance sigma^2/(2a). Variance does not grow without bound, and r can be negative because it is Gaussian. The expected value moves from r0 towards mu.

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