This paper studies numerical method for approximation of the Libor rate model driven by the Levy noise. We start with the Libor model based directly on the forward rate process. Within this modeling approach we can derive the explicit prices for swaps and swaptions. We use the implicit Euler...

This manuscript gives introduction to parabolic Partial Differential Equations (PDE) in one-dimensional case. It recalls the notion and main limitations of Black-Scholes model and establishes the Black-Scholes formula. It recalls the standard machinery of solving the parabolic PDE which is...

These lecture notes summarize standard machinery of an advanced course on Mathematics of Arbitrage. This note is based on material developed in a series of papers published in recent years by Prof. Walter Schachermeyer. The notes must be understood as a complementary material to the book of F....

This manuscript reviews standard classes of Libor Market models and discusses their numerical approximation machinery. It gives introduction to non-defaultable, defaultable models, Levy-forced models and affine Libor models

his lecture notes summarizes standard machinery of an advanced course on Stochastic Portfolio Theory, presents techniques for analysis of portfolio dynamics and equity market structure. This notes is based on material developed in a series of papers published in recent years by Prof. Ioannis...