The Valuation of Deposit Insurance with Risk Using Fourier Transform

Deposit insurance is a tool to stabilize a banking system. In deposit insurance, the insured risk is the risk of the bank's failure to fulfill its obligations to the customer because of its revoked license. The application of a flat rate deposit insurance system will lead to moral hazard problems, and cause a banking crisis as the banks get involved to risky activities. To anticipate this, it is necessary to design a deposit insurance premium which calculating the different risk levels of each bank. One method that can be used is Fourier transforms. The purpose of this study is to obtain a deposit insurance with risk premium model from the Black-Scholes Model by using Fourier transform. Based on the simulation results, the research found the value of volatility and interest rate is directly proportional to the value of deposit insurance premiums, as well as the value of debt obligations. The high value of deposit insurance premiums is also influenced by the value of dividends, however the value of insurance premiums has changed insignificantly prior to n period, therefore the value of deposit insurance premiums from zero to n period has changed insignificantly.