Abdolrahim Badamchizadeh

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.

A queuing system with two incongruent arrivals and services is considered. Two kinds of customers enter the system by Poisson process and the service times are assumed to have general distribution. After first kind service completion, it may feedback to repeat the first service, leave the system or go to give second service. The same policy is applied for the other kind of customer. All stochastic processes involved in this system are independent. We derive the probability generating function for each kind and for the system that yield the performance measures. Some numerical approaches examined the validity of the results.

Implied volatility modeling is the future anticipation of price fluctuation and so has a crucial role in option pricing. Machine learning approach can be applied as a great tool to modeling implied volatility and predicting the corresponding future d