Yield Curves and Forward Curves for Diffusion Models of Short Rates

Description

This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students. Front Matter ....Pages i-xxiv The Processes of Short-Term Interest Rates and Their Probability Densities (Gennady A. Medvedev)....Pages 1-18 The Term Structure of Interest Rates (Gennady A. Medvedev)....Pages 19-26 The Vasiček Model (Gennady A. Medvedev)....Pages 27-39 The Cox–Ingersoll–Ross Model (Gennady A. Medvedev)....Pages 41-69 The Duffie–Kan One-Factor Model (Gennady A. Medvedev)....Pages 71-91 The Duffie–Kan Two-Factor Models (Gennady A. Medvedev)....Pages 93-114 The Three Factor Models (Gennady A. Medvedev)....Pages 115-125 Another Version of the Term to Maturity Variable (Gennady A. Medvedev)....Pages 127-140 The Nelson–Siegel–Svensson No-Arbitrage Yield Curve Model (Gennady A. Medvedev)....Pages 141-177 Quadratic Models of Yield in a Risk-Neutral World (Gennady A. Medvedev)....Pages 179-199 Polynomial Models of Yield Term Structure (Gennady A. Medvedev)....Pages 201-227 Back Matter ....Pages 229-230