Abstract
While the main conceptual issue related to deposit insurances is the moral hazard risk, the main technical issue is inaccurate calibration of the implied volatility. This issue can raise the risk of generating an arbitrage. In this paper, first, we discuss that by imposing the no-moral-hazard risk, the removal of arbitrage is equivalent to removing the static arbitrage. Then, we propose a simple quadratic model to parameterize implied volatility and remove the static arbitrage. The process of removing the static risk is as follows: Using a machine learning approach with a regularized cost function, we update the parameters in such a way that butterfly arbitrage is ruled out and also implementing a calibration method, we make some conditions on the parameters of each time slice to rule out calendar spread arbitrage. Therefore, eliminating the effects of both butterfly and calendar spread arbitrage make the implied volatility surface free of static arbitrage.
Highlights
Banks can lend or invest most of their money deposits
We have provided some conditions that guarantee the absence of static arbitrage; we have everything to fit the proposed quadratic model to implied volatility data
The main objective of this study is to focus on the second issue by correctly pricing deposit insurances via improving the implied volatility calibration
Summary
Banks can lend or invest most of their money deposits. if bank’s borrowers default, the bank’s creditors, depositors, risk loss. In order to protect depositors from this risk, policy makers have promoted deposit insurance schemes that are majorly issued by government run institutions. The major issue due to these type of insurances is that they encourage the risk of moral hazard. While this problem has been studied to some extent in the literature (see Assa (2015) and Assa and Okhrati (2018)), there is another issue relevant to the incorrect contract design and miss-pricing which needs further attention. We first show that the removal of the arbitrage for the policies with no risk of moral hazard is tantamount to the removal of static arbitrage This fact lead us to naturally use machine learning methods to improve the precision of estimation for implied volatility
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