Heath-Jarrow-Morton model serves as a tool for modeling forward rates and valuation of interest rate sensitive securities. It is used by various financial institutions for the valuation and hedging of interest rate derivatives, as well as arbitrageurs seeking arbitrage opportunities.
The master's thesis presents single-period discrete HJM model, its extension to multiperiod model and HJM LIBOR model. Model assumptions, conditions for no arbitrage that determine pseudo probabilities, comparison of pseudo and actual probabilities, evolution of zero-coupon bond prices and risk-neutral valuation of interest rate financial instruments are given. The emphasis is on valuing interest rate caps and floors, which serve as a hedge against interest rate risk. The extension of the one-factor model to several factors is shown. The multi-period discrete HJM model can be used as an approximation to the continuous HJM model. It is necessary to reduce the size of the time steps and select the appropriate parameters for the discrete model, so that the latter will be the best possible approximation for the HJM LIBOR model.
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