Yu Lian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 81-84). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.4 / Chapter 3 --- An Index Tracking Model with Downside Chance Risk Mea- sure --- p.12 / Chapter 3.1 --- Statement of the Model --- p.13 / Chapter 3.2 --- Efficient Frontier --- p.16 / Chapter 3.3 --- Application of the Downside Chance Index Tracking Model --- p.29 / Chapter 3.4 --- Chapter Summary --- p.34 / Chapter 4 --- Index Tracking Models with High Order Moment Downside Risk Measure --- p.35 / Chapter 4.1 --- Statement of the Models --- p.35 / Chapter 4.2 --- Mean-Downside Deviation Financial Index Tracking Model --- p.38 / Chapter 4.3 --- Chapter Summary --- p.45 / Chapter 5 --- Numerical Analysis --- p.45 / Chapter 5.1 --- Data Analysis --- p.45 / Chapter 5.2 --- Experiment Description and Discussion --- p.48 / Chapter 5.2.1 --- Efficient Frontiers --- p.48 / Chapter 5.2.2 --- Monthly Expected Rate of Return --- p.50 / Chapter 5.3 --- Chapter Summary --- p.52 / Chapter 6 --- Summary --- p.54 / Chapter A --- List of Companies --- p.57 / Chapter B --- Graphical Result of Section 5.2.1 --- p.61 / Chapter C --- Graphical Result of Section 5.2.2 --- p.67 / Chapter D --- Proof in Chapter 3 and Chapter4 --- p.73 / Bibliography --- p.81

Liquidity, often defined as the ability of markets to absorb large transactions without much effect on prices, plays a central role in the functioning of financial markets. This dissertation aims to investigate the implications of liquidity from several different perspectives, and can help to close the gap between theoretical modeling and practice. In the first part of the thesis, we study the implication of liquidity costs for systemic risks in markets cleared by multiple central counterparties (CCPs). Recent regulatory changes are trans- forming the multi-trillion dollar swaps market from a network of bilateral contracts to one in which swaps are cleared through central counterparties (CCPs). The stability of the new framework de- pends on the resilience of CCPs. Margin requirements are a CCP’s first line of defense against the default of a counterparty. To capture liquidity costs at default, margin requirements need to increase superlinearly in position size. However, convex margin requirements create an incentive for a swaps dealer to split its positions across multiple CCPs, effectively “hiding” potential liquidation costs from each CCP. To compensate, each CCP needs to set higher margin requirements than it would in isolation. In a model with two CCPs, we define an equilibrium as a pair of margin schedules through which both CCPs collect sufficient margin under a dealer’s optimal allocation of trades. In the case of linear price impact, we show that a necessary and sufficient condition for the existence of an equilibrium is that the two CCPs agree on liquidity costs, and we characterize all equilibria when this holds. A difference in views can lead to a race to the bottom. We provide extensions of this result and discuss its implications for CCP oversight and risk management. In the second part of the thesis, we provide a framework to estimate liquidity costs at a portfolio level. Traditionally, liquidity costs are estimated by means of single-asset models. Yet such an approach ignores the fact that, fundamentally, liquidity is a portfolio problem: asset prices are correlated. We develop a model to estimate portfolio liquidity costs through a multi-dimensional generalization of the optimal execution model of Almgren and Chriss (1999). Our model allows for the trading of standardized liquid bundles of assets (e.g., ETFs or indices). We show that the benefits of hedging when trading with many assets significantly reduce cost when liquidating a large position. In a “large-universe” asymptotic limit, where the correlations across a large number of assets arise from a relatively few underlying common factors, the liquidity cost of a portfolio is essentially driven by its idiosyncratic risk. Moreover, the additional benefit from trading standardized bundles is roughly equivalent to increasing the liquidity of individual assets. Our method is tractable and can be easily calibrated from market data. In the third part of the thesis, we look at liquidity from the perspective of market microstructure, we analyze the value of limit orders at different queue positions of the limit order book. Many modern financial markets are organized as electronic limit order books operating under a price- time priority rule. In such a setup, among all resting orders awaiting trade at a given price, earlier orders are prioritized for matching with contra-side liquidity takers. In practice, this creates a technological arms race among high-frequency traders and other automated market participants to establish early (and hence advantageous) positions in the resulting first-in-first-out (FIFO) queue. We develop a model for valuing orders based on their relative queue position. Our model identifies two important components of positional value. First, there is a static component that relates to the trade-off at an instant of trade execution between earning a spread and incurring adverse selection costs, and incorporates the fact that adverse selection costs are increasing with queue position. Second, there is also a dynamic component, that captures the optionality associated with the future value that accrues by locking in a given queue position. Our model offers predictions of order value at different positions in the queue as a function of market primitives, and can be empirically calibrated. We validate our model by comparing it with estimates of queue value realized in backtesting simulations using marker-by-order data, and find the predictions to be accurate. Moreover, for some large tick-size stocks, we find that queue value can be of the same order of magnitude as the bid-ask spread. This suggests that accurate valuation of queue position is a necessary and important ingredient in considering optimal execution or market-making strategies for such assets.

Chu, Ho. / "December 2009." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 99-111). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of Mutual Fund Investment --- p.1 / Chapter 1.2 --- Research Motivation --- p.4 / Chapter 1.3 --- List of Contributions --- p.9 / Chapter 1.4 --- Thesis Structure --- p.12 / Chapter 2 --- Literature Review --- p.14 / Chapter 2.1 --- Traditional Measurement Approaches --- p.14 / Chapter 2.1.1 --- Jensen's Alpha --- p.16 / Chapter 2.1.2 --- Treynor Index --- p.19 / Chapter 2.1.3 --- Sharpe Ratio --- p.21 / Chapter 2.1.4 --- Other Measures --- p.23 / Chapter 2.1.4.1 --- M2 Measure --- p.23 / Chapter 2.1.4.2 --- Multifactor Models --- p.25 / Chapter 2.1.4.3 --- Morningstar's RAR --- p.27 / Chapter 2.1.5 --- Shortcomings of Traditional Measures --- p.30 / Chapter 2.2 --- Data Envelopment Analysis --- p.33 / Chapter 2.2.1 --- Brief Introduction --- p.33 / Chapter 2.2.2 --- Research Review on Fund Performance Mea-surement --- p.37 / Chapter 2.2.3 --- Limitations of Basic DEA Models --- p.42 / Chapter 3 --- DEA Methodology and Formulation --- p.47 / Chapter 3.1 --- CCR and BCC Model --- p.48 / Chapter 3.2 --- Problem of Slacks and DEA efficiency --- p.52 / Chapter 3.3 --- Slacks-based Measure --- p.55 / Chapter 3.4 --- Variables with Negative Values --- p.57 / Chapter 3.5 --- Range Directional Measure --- p.59 / Chapter 3.6 --- Modified Slacks-Based Measure --- p.62 / Chapter 4 --- Empirical Study and Discussions --- p.65 / Chapter 4.1 --- Data Source and Tools for Measurement --- p.65 / Chapter 4.2 --- Model Variables Defined --- p.67 / Chapter 4.3 --- Comparison of MSBM Performance Measure to Other Measures --- p.73 / Chapter 4.4 --- Comparison of Hong Kong MPFs with Different Categories --- p.78 / Chapter 5 --- Conclusions and Future Work --- p.90 / Bibliography --- p.99

Zhou, Tu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 61-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.0 / Chapter 1.1 --- Motivation and Objective --- p.0 / Chapter 1.2 --- Major Contribution --- p.2 / Chapter 1.3 --- Thesis Organization --- p.4 / Chapter 2 --- Measurement of Relationship between financial time series --- p.5 / Chapter ´ب2.1 --- Linear Correlation --- p.5 / Chapter 2.1.1 --- Pearson Correlation Coefficient --- p.6 / Chapter 2.1.2 --- Rank Correlation --- p.6 / Chapter 2.2 --- Mutual Information --- p.7 / Chapter 2.2.1 --- Approaches of Mutual Information Estimation --- p.10 / Chapter 2.3 --- Copula --- p.12 / Chapter 2.4 --- Analysis from Experimental Data --- p.14 / Chapter 2.4.1 --- Experiment 1: Nonlinearity --- p.14 / Chapter 2.4.2 --- Experiment 2: Sensitivity of Outliers --- p.16 / Chapter 2.4.3 --- Experiment 3: Transformation Invariance --- p.20 / Chapter 2.5 --- Chapter Summary --- p.23 / Chapter 3 --- Clustered Dynamic Conditional Correlation Model --- p.26 / Chapter 3.1 --- Background Review --- p.26 / Chapter 3.1.1 --- GARCH Model --- p.26 / Chapter 3.1.2 --- Multivariate GARCH model --- p.29 / Chapter 3.2 --- DCC Multivariate GARCH Models --- p.31 / Chapter 3.2.1 --- DCC GARCH Model --- p.31 / Chapter 3.2.2 --- Generalized DCC GARCH Model --- p.32 / Chapter 3.2.3 --- Block-DCC GARCH Model --- p.32 / Chapter 3.3 --- Clustered DCC GARCH Model --- p.34 / Chapter 3.3.1 --- Minimum Distance Estimation (MDE) --- p.36 / Chapter 3.3.2 --- Clustered DCC (CDCC) based on MDE --- p.37 / Chapter 3.4 --- Clustering Method Selection --- p.40 / Chapter 3.5 --- Model Estimation and Testing Method --- p.42 / Chapter 3.5.1 --- Maximum Likelihood Estimation --- p.42 / Chapter 3.5.2 --- Box-Pierce Statistic Test --- p.44 / Chapter 3.6 --- Chapter Summary --- p.44 / Chapter 4 --- Experimental Result and Applications on CDCC --- p.46 / Chapter 4.1 --- Model Comparison and Analysis --- p.46 / Chapter 4.2 --- Portfolio Selection Application --- p.50 / Chapter 4.3 --- Value at Risk Application --- p.52 / Chapter 4.4 --- Chapter Summary --- p.55 / Chapter 5 --- Conclusion --- p.57 / Bibliography --- p.61

The thesis consists of three independent topics, each of which is discussed in an individual chapter. The first chapter considers a multiperiod optimal transport problem where distributions μ0, . . . , μn are prescribed and a transport corresponds to a scalar martingale X with marginals Xt ∼ μt. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence–Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if μ0 is atomless, but not in general. In the one-period case n = 1, these transports reduce to the Left-Curtain coupling of Beiglbo ̈ck and Juillet. In the multiperiod case, the bivariate marginals for dates (0,t) are of Left-Curtain type, if and only if μ0, . . . , μn have a specific order property. The general analysis of the transport problem also gives rise to a strong duality result and a description of its polar sets. Finally, we study a variant where the intermediate marginals μ1,...,μn−1 are not prescribed. The second chapter studies the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n → ∞. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as “large n” equilibria. The third chapter studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset’s payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The unique equilibrium price is characterized by a weakly coupled system of linear parabolic equations which shows that holding and liquidity costs play dual roles. We derive the leading-order asymptotics for small transaction and holding costs which give further insight into the equilibrium and the consequences of illiquidity.

This thesis is about (a) money supply being determined by banking behaviour, or by the behaviour of central banks and (b) the influence of money supply on bank stock returns. That money is endogenously determined is a proposition of post-Keynesian (PK) economists suggesting that money supply is determined by the behaviour of commercial banks as banks adjust money creation in response to credit demands by the public. This theory challenges the monetarist view of exogenous money supply, where the central bank is said to control money supply. This thesis examines how, under the credit-creation behaviour of banks, the money supply affects bank stock returns in a multi-equation model.

published_or_final_version / Economics and Finance / Master / Master of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

 This thesis aims to investigate the effects of mean reversion on dynamic corporate finance decisions and stock pricing. In Chapter 1, a continuous-time real option model of mature firm that produces product with exogenous mean reverting price is developed to study the firm’s optimal exit and leverage policies. Simulation results show that both liquidation and bankruptcy triggers are negatively related to the long run price levels, while the speed of mean reversion interacts with the long run price level to affect the firm’s exit decisions in two opposite directions depending on the level’s relative magnitude to total operating expenses (the firm’s instantaneous operation costs plus coupon payments). Regarding the leverage policy, apart from showing the static tradeoff result that firm uses more debts when the current revenues are high, the model exhibits at high long run price levels low-debt scenarios that are analogous to the pecking order prediction, suggesting that both static tradeoff and pecking order effects coexist under a mean reversion environment. Because equity values increase more vigorously with prices than debt values do, the tradeoff effect is overwhelmed and the resulting optimal leverage ratios are generally decreasing with the current price levels. Chapter 2 extends the model in Chapter 1 to derive the closed-form expression of the firm’s equity beta. Because expected stock returns are linearly related to the equity beta by model assumption, several implications to the cross-sectional behaviors of stock returns are obtained. First, it is predicted that firms with mean reverting characteristics should earn lower average returns than others without. The model further reveals the coexistence of positive book-to-market and leverage premiums to stock returns. Most importantly, due to the possession of bankruptcy option by equity holders, high distress risk stocks are expected to earn lower average returns than otherwise similar but low distress risk stocks. This provides an extra dimension to study the ‘distress premium puzzle’. Finally to verify the model predictions, empirical tests using historical market and accounting data from CRSP and COMPUSTAT are conducted, and supportive results are generally obtained. / published_or_final_version / Economics and Finance / Doctoral / Doctor of Philosophy

Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy