published_or_final_version / Statistics / Master / Master of Philosophy

This thesis investigates the fundamental assumptions made in recent continuous-time equilibrium models of the term structure of interest rates. It finds that the number and the stochastic processes of state variables are strikingly different from those assumed in the literature. It develops a three-factor empirical term structure model, based on 22 years of cross-maturity time series data. The results show that the price differences, between the well-known Vasicek, and Cox, Ingersoll and Ross models and the three-factor empirical model, for interest-rate sensitive securities are of substantial economic significance.

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Thesis (M.Com.(Finance)--University of the Witwatersrand, Faculty of Commerce, Law and Management, School of Economic and Business Sciences, 2016. / This study sets out to investigate whether the Taylor Rule provides better the forecasts of the future short-term interest rates than the yield curve in the South African market. For the Taylor Rule we use OLS and use the open-market forward-looking Taylor Rule to forecast interest rates. For the yield curve, simple linear interpolation is used to derive forecast. We find that in the short term, forecasted one-month ahead interest rates closely track the actuals interest rates for both models. At longer horizons, there are larger deviations of forecasts from the actual. The RMSE analyses support the Taylor Rule as a superior forecasting model in all forecasting horizons. / MT2017

利率模型廣泛應用於利率衍生品的定價。為了吻合實證利率的分佈和隱含波動率，一種可能的辦法是用Lévy過程替換Hull- White模型中的布朗隨機變量的利率模型，但是這種方法很難實施。本文建立了一種有效的網絡數值方法對利率進行估測。利用Lévy過程的馬爾可夫性質， FFT網絡實質上是多項樹模型的擴展。這種數值方法的優勢在於一直固定不變的狀態點，對現時利率期限結構的超級校準以及基於對Lévy過程的特徵方程的快速傅裡葉變換(FFT) 去恢復概率密度函數以實現轉移概率的計算過程。這種網絡數值方法對利率衍生品的定價與利率樹類似。對利率上限期權和交換期權的解析解和數值解的比較表明網絡數值方法是準確和有效的。FFT網絡還可以對百慕達式利率交換期權以及美式期權進行定價。最後， FFT網絡被擴展去適應路徑依賴變量，因此，能對利率依賴的結構性票據進行定價，比如目標贖回票據和範團積息結構票據。 / Short rate models are widely used in valuing interest rate derivatives. To fit empirical distribution of interest rates and implied volatility, a possible way is to replace Brownian motion by a Lévy process in short rate models. However, this approach is difficult to implement. This thesis establishes an efficient network approach for interest rate valuation. The FFT-network is essentially an extension of multinomial tree model, taking advantage of the Markov property of Lévy processes. Its fixed and unchanged states at all time, super-calibration ability to the current term structure, and elegant computation procedure for transition probabilities using the fast Fourier transform (FFT) from the characteristic function of Lévy processes make it attractive and distinct from other numerical methods. The interest rate derivatives value is determined in a way similar to that of the tree approach. The comparison between the closed-form solution of interest rate caplets and swaptions and the numerical results under the network demonstrates that the proposed network is accurate and efficient. In addition, the FFT-network can also be used to pricing the Bermudan swaption and American-style option. Finally, the FFT-network is expanded to accommodate path-dependent variables, and hence can be used for pricing some path-dependent structured notes, such as the target redemption notes and range of accrual notes. / Detailed summary in vernacular field only. / Xu, Zhuolu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 91-93). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.4 / Chapter 2.1 --- Elementary techniques --- p.4 / Chapter 2.1.1 --- Characteristic function --- p.4 / Chapter 2.1.2 --- Cumulant generating function --- p.5 / Chapter 2.1.3 --- Fourier Transform --- p.6 / Chapter 2.1.4 --- Fast Fourier Transform (FFT) --- p.8 / Chapter 2.2 --- Lévy Processes --- p.10 / Chapter 2.2.1 --- Definition --- p.10 / Chapter 2.2.2 --- Lévy-Khintchine --- p.11 / Chapter 2.2.3 --- Lévy Processes in Interest Rate --- p.13 / Chapter 2.3 --- Hull-White Model --- p.13 / Chapter 2.3.1 --- Model setup --- p.14 / Chapter 2.3.2 --- Interest rate caps --- p.15 / Chapter 2.3.3 --- European Swaptions --- p.16 / Chapter 2.3.4 --- A Tree-building procedure --- p.19 / Chapter 3 --- HW-Lévy Model --- p.20 / Chapter 3.1 --- Model Setup --- p.20 / Chapter 3.2 --- The Characteristic Function --- p.22 / Chapter 3.3 --- Analytic result on interest rate derivatives --- p.26 / Chapter 4 --- Valuation: FFT Network Model --- p.35 / Chapter 4.1 --- Drawbacks of Tree Approach --- p.35 / Chapter 4.2 --- FFT Network Setup --- p.37 / Chapter 4.3 --- Transition Probability Matrix --- p.38 / Chapter 4.4 --- Yield Curve Fitting --- p.42 / Chapter 4.5 --- Pricing Algorithm under FFT Network --- p.45 / Chapter 4.5.1 --- European Interest Rate Derivatives Pricing --- p.45 / Chapter 4.5.2 --- Bermudan Interest Rate Derivatives Pricing --- p.49 / Chapter 5 --- Extended FFT Network for Path-dependent Structured Notes --- p.55 / Chapter 5.1 --- Extended FFT-netwok --- p.55 / Chapter 5.2 --- Target Redemption Notes (TARN) --- p.61 / Chapter 6 --- Numerical Study --- p.69 / Chapter 6.1 --- Numerical Scheme --- p.69 / Chapter 6.2 --- Numerical Examples --- p.74 / Chapter 7 --- Conclusion --- p.89 / Bibliography --- p.91

Wong, Tsz-Lim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 48-51). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Reduced-Form Model --- p.5 / Chapter 2.1 --- Information and Probabilistic Framework --- p.6 / Chapter 2.2 --- Poisson and Cox Process --- p.6 / Chapter 2.3 --- The Building Blocks of Pricing --- p.8 / Chapter 2.4 --- Comparing the Recovery Models --- p.10 / Chapter 3 --- General Equilibrium Model --- p.12 / Chapter 3.1 --- State Variables --- p.12 / Chapter 3.2 --- Investment Opportunities --- p.14 / Chapter 3.3 --- Preferences --- p.15 / Chapter 3.4 --- The Term Structure of Defaultable Bonds --- p.17 / Chapter 4 --- Methodologies --- p.24 / Chapter 5 --- SNP and EMM --- p.27 / Chapter 5.1 --- SNP Density --- p.27 / Chapter 5.2 --- EMM Estimation --- p.29 / Chapter 6 --- Empirical Results --- p.31 / Chapter 6.1 --- Data Description --- p.31 / Chapter 6.2 --- Estimation Results --- p.33 / Chapter 7 --- Conclusion --- p.42 / Chapter A --- Extended Nelson and Siegel Model --- p.44 / Chapter B --- Moment-Matching of the CIR Model --- p.46 / Bibliography --- p.48

Lai, Ka Lun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 75-77). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Multivariate Threshold Time Series Model --- p.14 / Chapter 2.1 --- The Multivariate TAR Models --- p.14 / Chapter 2.2 --- Testing for Nonlinearity --- p.15 / Chapter 2.3 --- Model Selection and Estimation --- p.22 / Chapter 2.4 --- Bivariate TAR Models --- p.26 / Chapter 2.5 --- Applications --- p.27 / Chapter Chapter 3 --- Comparative Study of Interest Rates --- p.34 / Chapter 3.1 --- Background --- p.34 / Chapter 3.2 --- The Importance of Modelling Interest Rates --- p.40 / Chapter 3.3 --- The Scope of Study --- p.41 / Chapter 3.4 --- Major Findings --- p.42 / Chapter Chapter 4 --- Conclusion --- p.71 / Reference --- p.80

Chow, Chui Ngan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 76-79). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Interest Rate Models --- p.6 / Chapter 2.1 --- Short Rate Models --- p.7 / Chapter 2.2 --- Heath-Jarrow-Morton Framework --- p.8 / Chapter 2.3 --- Bond Market Models (BMM) --- p.9 / Chapter 3 --- Mortality Models --- p.13 / Chapter 3.1 --- Deterministic Survival Functions --- p.13 / Chapter 3.2 --- Stochastic Mortality Models --- p.15 / Chapter 4 --- Guaranteed Annuity Options under BMM --- p.16 / Chapter 4.1 --- Model Settings --- p.17 / Chapter 4.1.1 --- Financial Variables --- p.17 / Chapter 4.1.2 --- Mortality --- p.19 / Chapter 4.2 --- Guaranteed annuity option --- p.21 / Chapter 4.3 --- Numerical results --- p.23 / Chapter 4.3.1 --- Simulation Study --- p.24 / Chapter 4.3.2 --- Empirical results --- p.29 / Chapter 5 --- Longevity Bond Market Models --- p.34 / Chapter 5.1 --- Model Settings --- p.35 / Chapter 5.1.1 --- Theoretical Settings --- p.35 / Chapter 5.1.2 --- Risk-free Bonds and Longevity Bonds --- p.36 / Chapter 5.2 --- Applications on Potential Mortality-Linked Products --- p.41 / Chapter 5.3 --- Numerical Results --- p.45 / Chapter 5.3.1 --- Simulation Settings --- p.46 / Chapter 5.3.2 --- Simulation Results --- p.49 / Chapter 6 --- Conclusion --- p.53 / Chapter A --- Equation Derivation --- p.56 / Chapter A.l --- Proof for Proposition (4.2.1) --- p.56 / Chapter A.2 --- Proof for Proposition (4.2.2) --- p.58 / Chapter A.3 --- Proof for Proposition (5.3.1) --- p.61 / Chapter A.4 --- Proof for Proposition (5.3.2) --- p.66 / Chapter B --- Results --- p.71 / Chapter B.l --- Valuation Results for GAO under BMM --- p.71 / Chapter B.1.1 --- Simulation Situations --- p.71 / Chapter B.1.2 --- Calibration Results --- p.72 / Chapter B.1.3 --- Valuation Results --- p.74

published_or_final_version / Economics and Finance / Doctoral / Doctor of Philosophy

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