Online Local Volatility Calibration by Convex Regularization with Morozov's Principle and Convergence Rates

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to considering both the local volatility surfaces and their corresponding prices as indexed by the observed underlying stock price as time goes by in appropriate function spaces. The resulting parameter to data map is defined in appropriate Bochner-Sobolev spaces. Under this framework, we prove key regularity properties. This enable us to build a calibration technique that combines online methods with convex Tikhonov regularization tools. Such procedure is used to solve the inverse problem of local volatility identification. As a result, we prove convergence rates with respect to noise and a corresponding discrepancy-based choice for the regularization parameter. We conclude by illustrating the theoretical results by means of numerical tests.Comment: 23 pages, 5 figure

The impact of COVID-19 vaccination delay: A data-driven modeling analysis for Chicago and New York City.

BACKGROUND: By the beginning of December 2020, some vaccines against COVID-19 already presented efficacy and security, which qualify them to be used in mass vaccination campaigns. Thus, setting up strategies of vaccination became crucial to control the COVID-19 pandemic. METHODS: We use daily COVID-19 reports from Chicago and New York City (NYC) from 01-Mar2020 to 28-Nov-2020 to estimate the parameters of an SEIR-like epidemiological model that accounts for different severity levels. To achieve data adherent predictions, we let the model parameters to be time-dependent. The model is used to forecast different vaccination scenarios, where the campaign starts at different dates, from 01-Oct-2020 to 01-Apr-2021. To generate realistic scenarios, disease control strategies are implemented whenever the number of predicted daily hospitalizations reaches a preset threshold. RESULTS: The model reproduces the empirical data with remarkable accuracy. Delaying the vaccination severely affects the mortality, hospitalization, and recovery projections. In Chicago, the disease spread was under control, reducing the mortality increment as the start of the vaccination was postponed. In NYC, the number of cases was increasing, thus, the estimated model predicted a much larger impact, despite the implementation of contention measures. The earlier the vaccination campaign begins, the larger is its potential impact in reducing the COVID-19 cases, as well as in the hospitalizations and deaths. Moreover, the rate at which cases, hospitalizations and deaths increase with the delay in the vaccination beginning strongly depends on the shape of the incidence of infection in each city

Additional file 1 of On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil

Supplementary file 1. The Supplementary Materials contain additional figures and tables