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2009•edoc Publication server (Humboldt University of Berlin)Open access

Models for Interest Rates and Interest Rate Derivatives

Sun, Li

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Abstract

This thesis gives an introduction to the principles of modern interest rate theory. After covering the basic tools for working in an environment with stochastic interest rates, we introduce different models for the term structure. The principals of risk neutral pricing are introduced and the Black model is derived. Closed form bond valuation equations are derived for the Cox, Ingersoll and Ross (CIR) model. Short examples of calibration of the Vasicek, CIR and LIBOR market model are given.

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This thesis gives an introduction to the principles of modern interest rate theory. After covering the basic tools for working in an environment with stochastic interest rates, we introduce different models for the term structure. The principals of risk neutral pricing are introduced and the Black model is derived. Closed form bond valuation equations are derived for the Cox, Ingersoll and Ross (CIR) model. Short examples of calibration of the Vasicek, CIR and LIBOR market model are given.

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Available abstract

This thesis gives an introduction to the principles of modern interest rate theory. After covering the basic tools for working in an environment with stochastic interest rates, we introduce different models for the term structure. The principals of risk neutral pricing are introduced and the Black model is derived. Closed form bond valuation equations are derived for the Cox, Ingersoll and Ross (CIR) model. Short examples of calibration of the Vasicek, CIR and LIBOR market model are given.

Key concepts: Vasicek model, Interest rate, LIBOR market model, Short-rate model, Rendleman–Bartter model, Libor, Cox–Ingersoll–Ross model, Yield curve

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