Inflation-linked products and optimal investment with macro derivatives [Elektronische Ressource] / Taras Beletski

Fachbereich Mathematik M.Sc. Taras Beletski INFLATION-LINKED PRODUCTS AND OPTIMAL INVESTMENT WITH MACRO DERIVATIVES Vom Fachbereich Mathematik der Technischen Universität Kaiserslautern zur Verleihung des akademischen Grades Doktor der Naturwissenschaften (Doctor rerum naturalium, Dr. rer. nat.) genehmigte Dissertation Datum der Disputation: 5. Dezember 2006 1. Gutachter: Professor Dr. Ralf Korn 2. Gutachter: Professor Dr. Angelika May D 386 TO MY DEAR MUM AND DAD ABSTRACT In this thesis diverse problems concerning inflation-linked products are dealt with. To start with, two models for inflation are presented, including a geometric Brownian motion for consumer price index itself and an extended Vasicek model for inflation rate. For both suggested models the pricing formulas of inflation-linked products are derived using the risk-neutral valuation techniques. As a result Black and Scholes type closed form solutions for a call option on inflation index for a Brownian motion model and inflation evolution for an extended Vasicek model as well as for an inflation-linked bond are calculated. These results have been already presented in Korn and Kruse (2004) [17].