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Three studies on the Libor Market Model

The purpose of this thesis is to further current knowledge of the Libor Market Model (LMM) in terms of more efficient implementation and extension to include non-lognormally distributed rates. The performance of LMM in pricing and hedging performance of Bermudan swaptions is also compared with Hull-White, Black-Karasinski, and Swap Market Model (SMM) from an Asset-Liability-Management (ALM) perspective. The first study develops an efficient method for LMM implementation and pricing of Bermudan swaption. Following Derick, Stapleton and Stapleton (2005), we constructed recombining binomial trees for the term structure of forward Libor rate using the method developed by Ho, Stapleton and Subrahmanyam (1995). The contribution of this study is twofold: first, we list the assumptions on the volatility under which LMM can be implemented by the recombining tree method. Second, we perform extensive numerical studies I to compare the European and Bermudan swaption prices produced from the rec01pbining tree with those from the Monte Carlo simulation. Our findings lead us to conclude that our recombining tree LMM could be very useful for pricing exotic interest rate derivatives with early exercise feature. Since the Monte Carlo simulation method is more suited for path-dependent options, \~e conclude that the recombining tree method is a useful tool to complement the Monte Carlo simulation method in pricing exotic interest rate derivatives. T~e second study compares the pricing and hedging performance of the LMM against two spot-rate models, namely Hull-White and Black-Karasinski, and the more recent swap market model from an Asset-Liability-Management (ALM) perspective. In contrast to previous studies in the literature, our emphasis here is on ALM and we use hedging performance on Bermudan swaptions to proxy risk management outcome of a portfolio of long term mortgage loans. The focus here is on the differences between the four models (viz. HW, BK, LMM and SMM) instead of the absolute pricing or hedging error of the individual model. The contribution of this study is twofold: first, we are the first to compare the hedging performance of Bemmdan swaptions for a new set of models, viz.,.HW, BK, SMM and LMM. Second, we perform the test in two currencies from an ALM perspective so that our results are valuable in the decision-making of the ALM division of international financial institutions. The third study extends the LMM to relax the assumption of lognormally distributed forward rates. The probabilities of the tree are modified to include different non-lognormal. distributions. The new model is very easy to implement with the addition of one extra parameter to the standard
Date January 2008
CreatorsGuan, Zhenke
PublisherUniversity of Manchester
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation

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