Title: Mathematics of the bond market : a Lévy processes approach /
Authors: Barski, Michał; Zabczyk, Jerzy
Year: 2020
Subjects: Bond market Mathematical models.; Finance Mathematical models; Lévy processes; Finance Mathematical models; Lévy processes
Abstract: "Bonds are financial assets issued by governments, central banks or companies. Their holders receive some fixed payments at future dates. The life time of a bond is specified by its maturity - the date when the nominal value of the bond is paid. All previous payments are called coupons and they are usually fixed as fractions of the nominal value of the bond. The payments received by the holder, although fixed, can, however, be influenced by the credit rating of the issuer. This means that in case of the issuer's bankruptcy the promised payments can be reduced or even canceled"--
Contents: Elements of the bond market -- Arbitrage-free bond markets -- Completeness -- Stochastic preliminaries -- Lévy processes -- Martingale representation and Girsanov's theorems -- Fundamentals -- Arbitrage-free HJM markets -- Arbitrage-free forward curves models -- Arbitrage-free affine term structure -- Completeness -- Stochastic equations for forward rates -- Analysis of the HJMM equation -- Analysis of Morton's equation -- Analysis of the Morton-Musiela equation.