Premiums of Deposit Insurance with Maximum Limit Under the Black-Scholes Model
Abstract
Deposit insurance is an important mechanism in protecting bank customers from the risk of bankruptcy and providing a sense of security for their savings. Under deposit insurance, customers will still receive a refund of their funds up to a certain limit determined by the deposit insurance agency. This research aims to construct a formula to calculate the premium of deposit insurance with a given upper claim limit. To the best of the authors' knowledge, this article is the first study that gives a formula for deposit insurance premiums with a coverage limit. First, we present a theorem that shows the equivalence between the claim of deposit insurance with coverage limit with the payoff of two put options. Secondly, under the assumption that the asset follows Geometric Brownian Motion, we determine the fair price of the premium of deposit insurance. The main research findings indicate that the sum of two Black-Scholes options with different strike prices can be used to determine the premium value of deposit insurance while considering the applied coverage limits. Finally, we simulate some sensitivity analysis to gain a deeper understanding on the impact of several important variables on the magnitude of premium. Based on sensitivity analysis, it is found that the premium value is inversely proportional to interest rates and directly proportional to asset price volatility.
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