INTERNATIONAL RESERVE MANAGEMENT: A DRIFT†SWITCHING REFLECTED JUMP†DIFFUSION MODEL

Ning Cai and Xuewei Yang

Mathematical Finance, 2018, vol. 28, issue 1, 409-446

Abstract: We study the cost of shocks, that is, jump risk, with respect to reserve management when the reserve process is formulated as a drift†switching jump diffusion with a reflecting barrier at 0. Inspired by the Brownian drift switching model, our model results in a more realistic dynamic behavior of international reserves than the buffer stock model. The new model can capture both the jump behavior in reserve dynamics and the leptokurtic feature of the increment distribution which has a higher peak and two asymmetric heavier tails than the normal distribution. Through the selection of an initial distribution that reflects certain steady state behaviors, the reserve process becomes a regenerative process. This selection enables us to derive a closed†form expression for the total expected discounted cost of managing reserves, thus helping us to numerically find management strategies that minimize costs. The numerical results show that shocks at the reserve level have a significant effect on reserve management strategies and that model misspecification can result in nonnegligible additional costs.

Date: 2018
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