Carlos Vázquez is full Professor in Applied Mathematics at the Department of Mathematics in the University of A Coruña (Spain) since 2000 and leads the research group M2NICA. He got Graduate degrees in Mathematics and in Economics, as well a Ph.D. in Applied Mathematics from the University of Santiago de Compostela (Spain). He also holds a Doctorat Trosième Cicle from Université Claude Bernard de Lyon. Formerly he has been Associate Professor at University of Vigo and Visiting Professor at Université Claude Bernard de Lyon and Univeristy of Bolonia.
He has published numerous papers in different fields of Applied Mathematics, mainly related to PDEs modeling, analysis and numerical solution of problems arising in different domains of engineering and applied sciences.
In quantitative finance, his expertise mainly concerns to linear and nonlinear PDE formulations of pricing and investment problems, their mathematical analysis, numerical solution and computer implementation.
Carlos is the organizer at UDC of a Master in Industrial Mathematics, jointly delivered with other 4 Spanish universities, where he teaches courses on stochastic numerical methods, mathematical modeling in finance and computational finance. Also he has delivered master and Doctorate level courses in finance at different institutions worldwide.
His personal webpage is: http://dm.udc.es/staff/carlos_vazquez/
The authors present a methodology to generate future scenarios of interest rates for different credit ratings under a real-world probability measure.
This paper's aim is twofold: to introduce a mathematical framework that is sufficiently general and sound to cover the main areas of model risk, and to illustrate how a practitioner can identify the relevant abstract concepts and put them to work.