published_or_final_version / Economics and Finance / Doctoral / Doctor of Philosophy

Presale of residential units refers to putting the units on sale before they are completed. The value of presale to the developer comes from the flexibility of timing the presale launch so as to optimize the expected payoff. We model the developer's optimal launch timing as a real option, and the purchaser's series of presale payments with the flexibility to default as compound options. By assuming a stochastic property price process, we derive model frameworks that a risk-averse developer should adopt in launching the presale under single and multiple payment schemes. The frameworks solve the optimal conditions, contract structures, and prices for the launch. We then extend the model to optimize developers' payoffs in monopolistic and imperfect market equilibria. Finally, by assuming a jump-diffusion demand shock process and based on game theoretic approach, we derive sub-game Nash equilibrium optimal strategies that determine when and at what price developers should launch for presale with stochastic or deterministic rare market events. All the models thus derived are subject to probabilities of purchaser defaults, which will happen if the contract prices are too high when compared to market prices. Our model frameworks confirm that the launch option values increase with increases in price growth rates and variances, but decrease in risk-free rates. Furthermore, developers tend to delay the launch when good events are anticipated, while launching presale earlier at lower prices in times of expected bad events. The equilibrium strategies also provide an alternative explanation to oversupply in property markets. We further illustrate effects of rare events on presale launching strategies through government intervention (particularly public housing and housing subsidies) and output flow uncertainty in competitive equilibrium. Our general optimal strategic models are robust in a few aspects. First, we include the time factor that is crucial for some real options. Second, only slight adjustments are required to cope with market changes, or jumps. Finally, the strategies thus derived can be extensively and flexibly applied to other real options which incur multi-stage contingent payoffs, and whose price processes are characterized by stochastic jump-diffusion process. / Lai Neng. / "October 2000." / Source: Dissertation Abstracts International, Volume: 62-01, Section: A, page: 0270. / Supervisor: Ko Wang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 184-192). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / School code: 1307.

Choi Tsz Wang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review of Structural Models --- p.5 / Chapter 2.1 --- The Merton model --- p.5 / Chapter 2.2 --- The default barrier model of Black and Cox --- p.7 / Chapter 3 --- Estimating the Merton model --- p.10 / Chapter 3.1 --- The Variance Restriction (VR) method --- p.10 / Chapter 3.2 --- The Maximum Likelihood estimation (ML) method --- p.12 / Chapter 3.3 --- Comparison between VR and ML methods --- p.13 / Chapter 4 --- Implications of Using the Proxy in Default Barrier Estimation --- p.15 / Chapter 4.1 --- Rejection of SC framework --- p.16 / Chapter 4.2 --- Positive barrier implication --- p.17 / Chapter 4.3 --- Barier over debt implication --- p.17 / Chapter 4.4 --- Numerical illustration --- p.19 / Chapter 5 --- The Proposed Framework --- p.22 / Chapter 5.1 --- Maximum likelihood estimation --- p.23 / Chapter 5.2 --- Barrier-to-debt ratio specification --- p.25 / Chapter 5.3 --- Simulation checks --- p.26 / Chapter 5.4 --- Comments on the performance of α --- p.29 / Chapter 6 --- Estimation with Empirical Data --- p.33 / Chapter 6.1 --- Description of data --- p.33 / Chapter 6.2 --- Empirical results --- p.35 / Chapter 7 --- Conclusion --- p.41 / References --- p.43

Chan Chun Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 63-66). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Volatility Smile and Stochastic Volatility Models --- p.6 / Chapter 2.1 --- Volatility Smile --- p.6 / Chapter 2.2 --- Stochastic Volatility Model --- p.9 / Chapter 2.3 --- Multiscale Stochastic Volatility Model --- p.12 / Chapter 3 --- Lookback Options --- p.14 / Chapter 3.1 --- Lookback Options --- p.14 / Chapter 3.2 --- Lookback Spread Option --- p.15 / Chapter 3.3 --- Dynamic Fund Protection --- p.16 / Chapter 3.4 --- Floating Strike Lookback Options under Black-Scholes Model --- p.17 / Chapter 4 --- Floating Strike Lookback Options under Multiscale Stochastic Volatility Model --- p.21 / Chapter 4.1 --- Multiscale Stochastic Volatility Model --- p.22 / Chapter 4.1.1 --- Model Settings --- p.22 / Chapter 4.1.2 --- Partial Differential Equation for Lookbacks --- p.24 / Chapter 4.2 --- Pricing Lookbacks in Multiscale Asymtoeics --- p.26 / Chapter 4.2.1 --- Fast Tirnescale Asymtotics --- p.28 / Chapter 4.2.2 --- Slow Tirnescale Asymtotics --- p.31 / Chapter 4.2.3 --- Price Approximation --- p.33 / Chapter 4.2.4 --- Estimation of Approximation Errors --- p.36 / Chapter 4.3 --- Floating Strike Lookback Options --- p.37 / Chapter 4.3.1 --- Accuracy for the Price Approximation --- p.39 / Chapter 4.4 --- Calibration --- p.40 / Chapter 5 --- Other Lookback Products --- p.43 / Chapter 5.1 --- Fixed Strike Lookback Options --- p.43 / Chapter 5.2 --- Lookback Spread Option --- p.44 / Chapter 5.3 --- Dynamic Fund Protection --- p.45 / Chapter 6 --- Numerical Results --- p.49 / Chapter 7 --- Conclusion --- p.53 / Appendix --- p.55 / Chapter A --- Verifications --- p.55 / Chapter A.1 --- Formula (4.12) --- p.55 / Chapter A.2 --- Formula (4.22) --- p.56 / Chapter B --- Proof of Proposition --- p.57 / Chapter B.1 --- Proof of Proposition (4.2.2) --- p.57 / Chapter C --- Black-Scholes Greeks for Lookback Options --- p.60 / Bibliography --- p.63

Gao, Fei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 52-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Option Pricing with GARCH --- p.1 / Chapter 1.2 --- Mean Reversion in GARCH --- p.3 / Chapter 1.3 --- Thesis Setting --- p.4 / Chapter 2 --- Literature Review --- p.5 / Chapter 2.1 --- GARCH Model --- p.5 / Chapter 2.2 --- Locally Risk-Neutral Valuation --- p.8 / Chapter 2.3 --- Conditional Esscher Transform --- p.9 / Chapter 3 --- The Model --- p.12 / Chapter 3.1 --- The Mean-Reverting GARCH Model --- p.12 / Chapter 3.2 --- The Characteristic Functions --- p.15 / Chapter 3.3 --- Identification of Pricing Measures --- p.21 / Chapter 3.3.1 --- Conditional Esscher Transform --- p.21 / Chapter 3.3.2 --- Our Proposed Change of Measure --- p.25 / Chapter 4 --- Option Pricing --- p.30 / Chapter 4.1 --- Fast Fourier Transform --- p.30 / Chapter 4.2 --- Option on Futures : --- p.32 / Chapter 4.3 --- Numerical Analysis --- p.35 / Chapter 5 --- Empirical Analysis - Application to the crude oil market --- p.37 / Chapter 5.1 --- Description of data --- p.37 / Chapter 5.2 --- Estimation --- p.38 / Chapter 5.3 --- Comparisons --- p.40 / Chapter 6 --- Summary and Future work --- p.42 / Chapter 7 --- Appendix --- p.43 / Bibliography --- p.52

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Bao, Zhenhua. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.5 / Chapter 2.1 --- Review of the Models --- p.6 / Chapter 2.1.1 --- Black-Scholes-Merton Model --- p.6 / Chapter 2.1.2 --- Merton's Jump Diffusion Model --- p.8 / Chapter 2.1.3 --- Stochastic Volatility Jump Diffusion Model --- p.10 / Chapter 2.1.4 --- Constant Elasticity of Variance (CEV) Model --- p.13 / Chapter 2.2 --- Kou´ةs Double Exponential Jump Diffusion Model --- p.16 / Chapter 2.2.1 --- The Model Formulation --- p.16 / Chapter 2.2.2 --- The Merits of the Model --- p.17 / Chapter 2.2.3 --- Preliminary Results --- p.20 / Chapter 2.2.4 --- Extant Results on Option Pricing under the Model --- p.21 / Chapter 2.3 --- The Laplace Transform and Its Inversion --- p.24 / Chapter 2.3.1 --- The Laplace Transform --- p.24 / Chapter 2.3.2 --- One-dimensional Euler Laplace Transform Inversion Algorithm --- p.25 / Chapter 2.3.3 --- Two-dimensional Euler Laplace Transform Inversion Algorithm --- p.28 / Chapter 2.4 --- Monte Carlo Simulation for Double Exponential Jump Diffusion --- p.32 / Chapter 3 --- Pricing Double Barrier Option via Laplace Transform --- p.34 / Chapter 3.1 --- Double Barrier Option and the First Passage Time --- p.35 / Chapter 3.2 --- Preliminary Results --- p.35 / Chapter 3.3 --- Laplace Transform of the First Passage Time --- p.38 / Chapter 3.4 --- Pricing Double Barrier Option via Laplace Transform --- p.50 / Chapter 4 --- Numerical Results --- p.54 / Chapter 5 --- Conclusion --- p.57

Zheng, Fangbing. / "September 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 32-33). / Abstracts in English and Chinese.

Lo, Yu Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 66-70). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.8 / Chapter 2.1 --- Mean-reverting Model --- p.8 / Chapter 2.2 --- Volatility Smile --- p.11 / Chapter 2.3 --- Stochastic Volatility Model --- p.13 / Chapter 2.4 --- Multiscale Stochastic Volatility Model --- p.15 / Chapter 3 --- The Heston Stochastic Volatility --- p.17 / Chapter 3.1 --- The Model --- p.17 / Chapter 3.1.1 --- The Characteristic Function --- p.18 / Chapter 3.2 --- European Option Pricing --- p.24 / Chapter 3.2.1 --- Plain Vanilla Options --- p.25 / Chapter 3.2.2 --- Implied Volatility --- p.28 / Chapter 3.2.3 --- Other Payoff Functions --- p.30 / Chapter 3.3 --- Trinomial Tree: Exotic Option Pricing --- p.31 / Chapter 3.3.1 --- Sub-tree for the volatility --- p.33 / Chapter 3.3.2 --- Sub-tree for the asset --- p.34 / Chapter 3.3.3 --- Non-zero Correlation --- p.37 / Chapter 3.3.4 --- Calibration to Future prices --- p.38 / Chapter 3.3.5 --- Numerical Examples --- p.39 / Chapter 4 --- Multiscale Stochastic Volatility --- p.42 / Chapter 4.1 --- Model Settings --- p.42 / Chapter 4.2 --- Pricing --- p.44 / Chapter 4.3 --- Simulation studies --- p.54 / Chapter 5 --- Conclusion --- p.59 / Appendix --- p.61 / Chapter A --- Verifications --- p.61 / Chapter A.l --- Proof of Lemma 3.1.1 --- p.61 / Chapter B --- Black-Scholes Greeks --- p.64 / Bibliography --- p.66

University of Macau / Faculty of Science and Technology / Department of Mathematics