Sound deposit insurance pricing using a machine learning approach

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. © 2019 by the author. Licensee MDPI, Basel, Switzerland

Machine Learning in Insurance

Machine learning is a relatively new field, without a unanimous definition. In many ways, actuaries have been machine learners. In both pricing and reserving, but also more recently in capital modelling, actuaries have combined statistical methodology with a deep understanding of the problem at hand and how any solution may affect the company and its customers. One aspect that has, perhaps, not been so well developed among actuaries is validation. Discussions among actuaries’ “preferred methods” were often without solid scientific arguments, including validation of the case at hand. Through this collection, we aim to promote a good practice of machine learning in insurance, considering the following three key issues: a) who is the client, or sponsor, or otherwise interested real-life target of the study? b) The reason for working with a particular data set and a clarification of the available extra knowledge, that we also call prior knowledge, besides the data set alone. c) A mathematical statistical argument for the validation procedure

Designing sound deposit insurances

Deposit insurances were blamed for encouraging the excessive risk taking behavior during the 2008 financial crisis. The main reason for this destructive behavior was “moral hazard risk”, usually caused by inappropriate insurance policies. While this concept is known and well-studied for ordinary insurance contracts, yet needs to be further studied for insurances on financial positions. In this paper, we set up a simple theoretical framework for a bank that buys an insurance policy to protect its position against market losses. The main objective is to find the optimal insurance contract that does not produce the risk of moral hazard, while keeping the bank's position solvent. In a general setup we observe that an optimal policy is a multi-layer policy. In particular, we obtain a close form solution for the optimal insurance contracts when a bank measures its risk by either Value at Risk or Conditional Value at Risk. We show the optimal solutions for these two cases are two-layer policies. © 2017 Elsevier B.V