The Valuation of Deposit Insurance in an Arbitrage-free Basel II Consistent Framework

This paper analyzes the joint influence of the quality of a bank's loan portfolio, the bank's maturity gap and its deposit rate policy on the value of deposit insurance in an arbitrage-free Basel II consistent framework. We develop and apply a two-stage structural model of a bank where deposit insurance is a European put option on the loan portfolio, the default of each loan is driven by the borrower's asset value and interest rates are stochastic. Modeling the firms' asset values by conditional independent three-factor geometric Brownian motions and applying forward measure techniques, we obtain semi-analytical solutions of arbitrage-free deposit insurance premiums for sufficiently large and homogenous loan portfolios. We show for realistic parameter combinations that the correlation within the loan portfolio and the bank's maturity gap can have a material impact on fair deposit insurance premiums. Furthermore, we find that fair deposit insurance premiums can depend negatively on the borrowers' default risk when the bank faces a maturity gap. The fair deposit insurance premium for a bank holding defaultable loans can even be lower than for a bank investing in default-free bonds