Pricing of Embedded Options in Bank Deposits and Loans Based on Jump-Diffusion Interest Rate Model

Abstract

The marketization of interest rate is an inevitable requirement for China’s financial reform and joining the WTO to connect with the international financial market. It is also an important link to improve the marketization degree of China’s financial system. The marketization of interest rate in China is gradually advancing according to its preset mode. In the process of interest rate marketization, an unavoidable problem is that while the interest rate marketization gives the commercial banks the autonomy of capital pricing, the fluctuation of interest rate is more and more frequent. However, due to the fluctuation of interest rate, the loan as the main assets of commercial banks will be prepayed by borrowers, and the time deposit as the main liabilities of commercial banks will be withdrawn by depositors in advance; that is, embedded options are implied in asset liability items, which makes it difficult for commercial banks to accurately calculate the actual interest margin of deposits and loans and manage the interest rate risk. Therefore, it is of great significance to identify and price such embedded option value. On the basis of identifying and decomposing the embedded options in deposit and loan of commercial banks, according to the change characteristics of deposit and loan interest rate of Chinese commercial banks, this paper chooses jump-diffusion interest rate model to describe the change of benchmark interest rate of deposit and loan in China and demonstrates the advantages of this model compared with other models. Based on Monte Carlo simulation technology, the embedded options of five-year fixed deposit and ten-year prepayable loan in China are priced. On this basis, it points out that the real interest margin of commercial bank’s deposit and loan should be the nominal interest margin minus the value of deposit and loan’s embedded options. In the process of interest rate risk management, we should pay attention to the existence of embedded options and carry out effective management.