Liquidity management of foreign exchange reserves in continuous time

a r t i c l e i n f o JEL classification: C1 C11 E5 F3 Keywords: Foreign exchange reserves Liquidity management Gamma process In order to cope with daily foreign currency exchange payments or trades and avoid liquidity crisis, central banks need to maintain the liquidity of foreign exchange reserves. In this paper, we develop a Foreign Exchange Reserves Liquidity Management (FERLM) model based on stochastic process by introducing a foreign exchange factor. We also generate a feasible target proportion of the liquidity reserve to total foreign exchange reserves, by seeking the balance between capital gains of holding foreign exchange reserves and losses of liquidity insufficiency. With the gradual deepening of economic globalization and the violent increasing of international trades, the impact of exchange rate flexibility upon the level of foreign exchange reserves is growing in recent years. Given the potential influence on economy and financial stability, the issue of efficient foreign exchange reserves management should be of considerable importance. Especially in the 21st century, big expansion takes place in the scales of foreign exchange reserves in most countries , therefore the liquidity problems of foreign exchange reserves are becoming much more vital. Consequently, central banks have to pay more attention to reasonable allocation of foreign exchange reserves. Among different central banks, the management methods of foreign exchange reserves are different. For example, the foreign exchange rate policy of China is mandatory settlement of exchange. Foreign currency inflows are collected to the central bank, and become foreign exchange reserves. Moreover, because the exchange rate of China is not completely free floating, keeping the foreign exchange rate stabilization is not the main aim of the central bank. For this kind of counties as China, the foreign exchange reserves management method of central banks is approximately similar to the deposit management of commercial banks which can be divided into two categories. One is to invest for obtain gains and to prevent from the foreign exchange devaluation. As far as the way of investment is concerned, many scholars gave their own answers (Joachim et al. (2006), Topaloglou et al. (2008), etc.). The other is to maintain the liquidity to deal with daily payments and exchange transitions. Sufficient liquidity could reduce the risk of shortage liquidity, ensure the safety of financial system, and improve the economic development steadily. However, the excessive liquidity of foreign exchange reserves may also bring high holding costs. …