International Reserve Management: A Drift-Switching Reflected Jump-Diffusion Model

We study the cost of shocks, i.e., jump risk, in reserve management when reserve process is formulated as a drift switching jump-diffusion with a reflecting barrier at 0. Inherited from the Brownian drift control model, our model better describes the dynamic behavior of international reserves than does the buffer stock model. The new model can capture both the jump behavior in reserve dynamics and the leptokurtic feature that the increment distribution has a higher peak and two asymmetric heavier tails than does the normal distribution. By selecting an initial distribution that reflects certain steady state behavior, the reserve process becomes a regenerative process. This enables us to derive a closed-form expression for the total expected discounted cost of managing reserves, which in turn facilitates us to find optimal control variables that minimize the cost. Numerical results indicate that the shocks on reserve level have a significant effect on the reserve management strategies, and that model misspecification can result in non-negligible additional cost.