Yu Qing. / Thesis submitted in: November 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 65-68). / Abstracts in English and Chinese. / Acknowledgements --- p.i / Abstract --- p.ii / 摘要 --- p.iii / Table of Contents --- p.iv / List of Tables --- p.vi / List of Figures --- p.vi / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Literature Review --- p.4 / Chapter 2.1 --- Theoretical Model --- p.4 / Chapter 2.2 --- Empirical Investigation --- p.9 / Chapter 2.2.1 --- Choice of The Functional Form --- p.9 / Chapter 2.2.2 --- Choice of Variables --- p.13 / Chapter 2.2.3 --- Estimation of Supply and Demand Functions --- p.16 / Chapter 2.2.4 --- Test of Heteroskedasticity --- p.17 / Chapter 2.2.5 --- Test of Multicollinearity --- p.18 / Chapter 2.2.6 --- Application of The Hedonic Price Model to Developing Countries --- p.20 / Chapter 2.3 --- Concluding Remarks --- p.21 / Chapter Chapter 3 --- Introduction of The Housing Market in Guang Zhou --- p.23 / Chapter 3.1 --- Development and Current Situation --- p.23 / Chapter 3.2 --- Some Caveats --- p.26 / Chapter Chapter 4 --- Empirical Results --- p.30 / Chapter 4.1 --- The Data --- p.30 / Chapter 4.1.1 --- Dependent Variable --- p.34 / Chapter 4.1.2 --- Locational Variables --- p.34 / Chapter 4.1.3 --- Structural Variables --- p.35 / Chapter 4.1.4 --- Neighbourhood Variables --- p.37 / Chapter 4.2 --- The Results --- p.38 / Chapter 4.2.1 --- Regression Results and Possible Interpretation --- p.40 / Chapter 4.2.2 --- Test of Multicollinearity --- p.48 / Chapter 4.2.3 --- Test of Heteroscedasticity --- p.50 / Chapter 4.2.4 --- Test of Alternative Functional Forms --- p.55 / Chapter 4.3 --- Possible Sources of Estimation Bias --- p.57 / Chapter 4.4 --- Concluding Remarks --- p.59 / Chapter Chapter 5 --- Conclusion --- p.61 / References --- p.65

Cheng, Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 91-96). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Accumulator in a Nutshell --- p.1 / Chapter 1.1.2 --- Criticism over Accumulators --- p.3 / Chapter 1.1.3 --- Significance of Research over Accumulators --- p.4 / Chapter 1.1.4 --- Contribution of this Research --- p.5 / Chapter 1.2 --- Literature Review --- p.6 / Chapter 1.2.1 --- Literature on Option Pricing Theory --- p.6 / Chapter 1.2.2 --- Literature on Occupation Time Derivatives and Accumulators --- p.9 / Chapter 1.2.3 --- Accumulators as Occupation Time Deriva- tives --- p.14 / Chapter 1.3 --- Structure of this Thesis --- p.16 / Chapter 2 --- Theoretical Foundation --- p.17 / Chapter 2.1 --- Black Scholes Framework --- p.18 / Chapter 2.1.1 --- The Model --- p.18 / Chapter 2.1.2 --- Girsanov's Theorem --- p.20 / Chapter 2.1.3 --- Simulation --- p.21 / Chapter 2.2 --- Heston Framework --- p.22 / Chapter 2.2.1 --- Motivation to Extend to Heston Model --- p.22 / Chapter 2.2.2 --- The Model --- p.23 / Chapter 2.2.3 --- The Monte Carlo Method --- p.25 / Chapter 3 --- Pricing under Black-Scholes Framework --- p.30 / Chapter 3.1 --- Structure One (Suspension Feature) --- p.30 / Chapter 3.1.1 --- Introduction --- p.30 / Chapter 3.1.2 --- Model --- p.32 / Chapter 3.1.3 --- Sensitivity Tests --- p.35 / Chapter 3.1.4 --- Simulation Results --- p.38 / Chapter 3.2 --- Structure Two (Knock-out Feature) --- p.40 / Chapter 3.2.1 --- Introduction --- p.40 / Chapter 3.2.2 --- Model --- p.41 / Chapter 3.2.3 --- Sensitivity Tests --- p.45 / Chapter 3.2.4 --- Simulation Results --- p.48 / Chapter 3.3 --- Structure Three (Knock-out & Double Commit- ment Feature) --- p.50 / Chapter 3.3.1 --- Introduction --- p.50 / Chapter 3.3.2 --- Model --- p.51 / Chapter 3.3.3 --- Sensitivity Tests --- p.56 / Chapter 3.3.4 --- Simulation Results --- p.58 / Chapter 4 --- Extension: Pricing under Heston Framework --- p.59 / Chapter 4.1 --- Structure One --- p.59 / Chapter 4.1.1 --- Pricing of the Contract --- p.59 / Chapter 4.2 --- Structure Two and Three --- p.61 / Chapter 4.2.1 --- Simulation Results --- p.62 / Chapter 4.3 --- Heston Parameters Estimates --- p.63 / Chapter 5 --- Discussion --- p.66 / Chapter 5.1 --- Volatility of Accumulators --- p.66 / Chapter 5.2 --- Instability in the Model Parameters --- p.69 / Chapter 5.3 --- Premium over Accumulators --- p.71 / Chapter 5.4 --- Return of the Accumulator Products --- p.72 / Chapter 6 --- Future Work & Conclusion --- p.75 / Chapter 6.1 --- Future Work --- p.75 / Chapter 6.2 --- Conclusion --- p.76 / Chapter A --- Other Parameters Estimation --- p.77 / Chapter B --- Sample Contracts --- p.80 / Chapter B.1 --- Equity Accumulator --- p.80 / Chapter B.2 --- Commodity Accumulator --- p.80 / Chapter B.3 --- FX-Linked Accumulation --- p.80 / Bibliography --- p.91

American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.

published_or_final_version / Real Estate and Construction / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Economics and Finance / Doctoral / Doctor of Philosophy

A research report presented in partial fulfilment (50%) of the requirements for the degree of Master of Commerce in Business Economics (Finance) in the School of Economic and Business Sciences at the University of Witwatersrand, Johannesburg, 6 October 2017 / This study tests the efficacy of the liquidity variables of Liu (2006) in determining the existence of a liquidity premium on the South African market and finds evidence of a significant liquidity effect. This factor is determined to be robust and to proxy for a different underlying effect than the Fama-French (1992) effects and the market risk premium. The analysis is performed through portfolio sorts and tests for difference of portfolio means, as well as both a univariate and multivariate regression analysis. The sample period covers 16 years from 2000 to 2015. The relationship between size and liquidity is clear, however liquidity is found to be separate from the size effect. This study recommends the use of a liquidity-augmented model for the analysis of asset returns in South Africa. / GR2018

Master of Commerce (Finance) in the Finance Division, School of Economic and Business Sciences at the University of the Witwatersrand, Johannesburg, 6 September 2017 / The aim of this study is to investigate the relationship between market liquidity changes on the Johannesburg Stock Exchange (JSE), and the market’s degree of efficiency. Market efficiency is characterised in terms of two philosophies: Fama’s (1970) Efficient Markets Hypothesis, and Shiller’s (1981; 2003) informational efficiency designation. Efficiency was tested using measures of return predictability, a random walk benchmark, and price volatility; liquidity was measured using market turnover. The tests were conducted on JSE Top 40 shares across three regimes, spanning January 2012 – June 2016. The regimes are demarcated by two structural breaks in the JSE’s microstructure: the 2012 trading platform upgrade, and the 2014 colocation centre launch. The results show that past order imbalances are a significant predictor of daily returns, although the significance of this predictability has dissipated over time. Return predictability is not influenced by liquidity. In fact, there is evidence that illiquidity weakens return predictability. Prices were closer to random walk benchmarks during the third regime. In consideration of informational efficiency, during the latter two regimes price volatility is greater during trading versus non-trading hours. This is coupled with an emergence of nonlinear return dependence, which is indicative of greater mispricing. Thus, over the three regimes, market efficiency improved in the sense of the EMH, but informational efficiency deteriorated. The study contributes to the field by: introducing an inverse measure of market efficiency; providing insight into the measure’s time variation and relation to liquidity; and demonstrating that market efficiency tests should incorporate its dual meanings, enabling richer understanding of their intersection. / GR2018

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. / For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. / For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods. / 本論文為金融衍生產品定價的兩類問題作出了研究。第一類是自由邊界問題，它可以制定一個受制於自由邊界條件的偏微分方程式(PDE)，雖然當中自由邊界條件的函數形式是已知的，但自由邊界的位置是未知的，只能通過為實際解施加連續性條件作隱式確定。這裡為兩個具體問題進行了研究，分別是固定利率按揭合約(fixed-rate mortgages)定價和方差恆彈性模型的美式期權(CEV American options)定價。第二類是多維問題，它涉及到多個相關隨機變量及他們引申出的多維PDE。這裡為一個典型例子進行了研究，稱為籃子差異期權(basket-spread options)，其基礎資產價格由相關的幾何布朗運動驅動。我們為這三個問題提出了解析近似解。 / 對於上述的自由邊界問題，我們提出了一項參數移動邊界來近似模仿未知的自由邊界，使原來的自由邊界問題轉化為移動邊界問題，從而提出一種解析近似解。控制移動邊界的參數是通過滿足近似解的一階導數連續性條件來定。得到了解析近似解令當中的衍生產品定價和避險參數能有效快速地計算出，相比於有限差分法(finite-difference method)，精度保持了但計算時間顯著降低。再透過應用一個多階段方案，將移動邊界重鑄成一項分段光滑的連續函數，能有系統地將近似解的結果逼近有限差分法的結果。 / 對於上述的多維問題，我們從Kirk(1995)的二維差異期權(spread option)近似解定價公式推廣到多維的籃子差異期權。由於最終的定價公式是封閉形式，所有避險參數也從而得到封閉式近似解。從一些模擬例子顯示出，近似解的定價和避險參數，與通過數值積分法(numerical integration)或蒙地卡羅模擬法(Monte Carlo simulation)獲得的基準值比較，只有小於百分之一的誤差。此外，透過利用一種期權價格和相關基礎變量的概率分佈關係，我們進一步推論出一項籃子差異變量的近似解分佈函數，這可應用到任何多維幾何布朗運動的線性組合變量分佈。最後，我們提出一種隱式攝動方法，把定價誤差減少高達一百倍，跟現有的近似解定價方法相比，這是其中一種最健全和準確的籃子差異期權定價方法。 / Lau, Chun Sing = 自由邊界和多維的金融衍生產品定價問題 : 解析近似解 / 劉振聲. / Thesis Ph.D. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 174-186). / Abstracts also in Chinese. / Title from PDF title page (viewed on 12, September, 2016). / Lau, Chun Sing = Zi you bian jie he duo wei de jin rong yan sheng chan pin ding jia wen ti : jie xi jin si jie / Liu Zhensheng. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

An important problem in mathematical finance is to develop option pricing models that are able to capture implied volatility “smile” or “skew” commonly observed in financial markets. Many existing models are based on time-homogeneous Markov processes and they often have difficulty in calibrating implied volatilities across both strikes and maturities. In this dissertation, we develop two parsimonious and analytically tractable option pricing models to evaluate VIX options and crack spread options, respectively. Our modeling approach is based on additive subordination, which is a natural generalization of classical Bochner’s subordination. Probabilistically, additive subordination corresponds to a stochastic time change with respect to an independent additive subordinator. To model the VIX dynamics, we timechange a non-affine mean-reverting 3/2 diffusion with an independent additive subordinator to capture its empirical features, such as mean reversion and jumps, as well as upward-sloping implied volatility skew in VIX options. Moreover, we develop a parsimonious and analytically tractable two-factor model for crude oil and its refined product to evaluate crack spread option, where each factor is an additive subordinate Cox-Ingersoll-Ross process. This model captures key empirical features of individual commodities, such as mean-reversion and jumps, as well as of their spread. Analytical formulas for related options prices under each model are derived via an eigenfunction expansion approach. Empirical results show that our models have great flexibility in calibrating implied volatilities across strikes and maturities of each underlying with excellent performance. Our results suggest that additive subordination is a useful technique that allows one to construct a large family of jump-diffusions and/or pure jump processes with rich time- and state-dependent local characteristics, which are suited for parsimoniously reproducing empirical features with analytical tractability. / 金融數學中的一個重要問題是建立能夠捕獲金融市場普遍觀察到的隱含波動率微笑現象的期權定價模型。許多現存的模型基於時間齊次的馬爾可夫過程且這些模型一般難以同時校準具有各種執行價格和到期時間的隱含波動率。在此博士論文中，我們建立了兩個簡潔且易於分析的期權定價模型，分別用於定價VIX期權和裂變價差期權。我們的建模方法基於additivesubordination，該方法是經典的Bochner的Subordination方法的自然延伸。從概率論上講，additive subordination定義了一個關於additive subordinator的隨機時間變換。為了對VIX的動態變化建模，我們對一個具有非仿射均值回复的3/2擴散過程進行時間變換來捕獲VIX的相關性質，如均值回复和跳躍，以及VIX期權中的向上偏的隱含波動率曲線。進一步，我們對原油和其成品油創建了一個簡潔的且易於分析的俩因子模型來定價裂變價差期權，其中每一個因子都是一個additive subordinate Cox-Ingersoll-Ross過程。這個模型可以捕獲每個油品價格的關鍵屬性，如均值回复和跳躍，以及其他之間的價差。每個模型下的相應期權價格的解析公式通過特偵函數展開的方式求解得到。實證研究表明我們的模型具有較好的靈活性，在校準每個期權品種的隱含波動率曲面方面都具有非常好的表現。我們的研究結果也表明additive subordination是一個非常有用的方法。它可以用於創建一大類具有時間和狀態相依特偵的跳躍擴散或純跳過程，這些過程可用於簡便的建模一些實證特徵且便於分析。 / Li, Jing. / Thesis Ph.D. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 129-142). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only.

Heung Ling-lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 81-82). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iv / Chapter Chapter1: --- Introduction --- p.1 / Chapter Chapter2: --- Review of binomial schemes and trinomial schemes --- p.4 / Chapter Chapter3: --- Binomial/trinomial scheme from the viewpoint of quadrature --- p.12 / Chapter Chapter4: --- Binomial/trinomial schemes from Gaussian quadrature formula --- p.16 / Chapter Chapter5: --- New Schemes from other quadrature formula --- p.27 / Chapter Chapter6: --- Multinomial scheme --- p.35 / Chapter Chapter7: --- Numerical results --- p.41 / Chapter Chapter8: --- Conclusion --- p.47 / Appendix --- p.49 / Bibliography --- p.81