Abstract
The primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy process-driven models of banking reserves in order to address the problem of hedging deposit withdrawals from such institutions by means of reserves. Here reserves are related to outstanding debt and acts as a proxy for the assets held by the bank. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank's provisioning strategy, respectively. A discussion of the main risk management issues arising from the optimization problem mentioned earlier forms an integral part of our paper. This includes the presentation of a numerical example involving a simulation of the provisions made for deposit withdrawals via treasuries and reserves.
Highlights
We apply the quadratic hedging approach developed in [1] to a situation related to bank deposit withdrawals
The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank’s provisioning strategy, respectively
The main risks that can be identified are reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank’s provisioning strategy, respectively
Summary
We apply the quadratic hedging approach developed in [1] to a situation related to bank deposit withdrawals. In order to derive a hedging strategy for a bank reserve-dependent depository contract we require the generalized GKW decomposition for both its intrinsic value and the product of the inverse of Treasuries and the arbitrage free value of the sum of the cohort deposits. We accomplish this by assuming that the bank takes deposits (from a certain cohort of depositors with prespecified characteristics) as a single lump sum at the beginning of a specified time interval and holds it until withdrawal some time later.
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