Deposit Insurance Pricing By Considering Reinsurance And Its Application

Since the1980s, systemic banking crisis spread to the whole world. The depositinsurance, as one of the three pillars of financial safety nets, had made an importantcontribution to resist bank runs, protect the legitimate rights of depositors andmaintain the financial market’s stability of a country, even the global. However, withthe growing trend of financial globalization, the risks faced by banks are getting larger,more and more losses come from sudden events, such as the Barings Bank incident,United Kingdom Northern Rock events and so on. So we will find a phenomenon thata single holding limited assets’ deposit insurance company seems weak in the face ofsuch a huge loss.In order to address this problem, the reinsurance is introduced to the depositinsurance field in this article, in accordance with the division of insurance losses,insurance are divided into primary insurance company and reinsurance company, theoriginal insurance company’s underwriting losses don’t exceed a ceiling, theexceeding part borne by reinsurers. We designed two models, the first model assumesthat bank assets’ motor process follows a geometric Brownian motion, we useactuarial method to deduce the original insurance and reinsurance pricing formulas onthis premise; In the second model, in order to make the distribution of assets morefitting thick tail spikes, we consider using Possion jump diffusion process to fit bankassets’ motor process, and using actuarial method to deduce the original insurance andreinsurance pricing formulas on this premise. In the empirical link, this article choosesR-V model to derive the value and the volatility of bank assets indirectly, andcomparing the results with no reinsurance under the same stochastic process. For thesecond model, we estimate the parameters of jump-diffusion model with themaximum likelihood estimation method in the paper, then bring parameter values intothe pricing formulas and get the original insurance’s and reinsurance’s numericalresults, similarly we also compare the results with no reinsurance under the samejump-diffusion process.