本研究主要探討附保證最低提 (Guaranteed Minimum Withdrawal Benefits, GMWB)的變額(Variable Annuity, VA) 在隨機模型下之定價。保證最低提是變額的一種附加約 (rider) 並在市場下跌的情況下為變額持有人提供保障。它保證持有人在合約期內的總提少於一個預先訂的額，而變額的投資表現。一般，這個保證額相等於變額的初始投資額。本研究的融模型假設投資標的基價格符合對維過程 (exponential Lévy process)，而隨機則符合由維過程驅動的瓦西克模型 (Vasiček model)。融模型中的個維過程的相依結構 (dependence structure) 會由維關結構 (Lévy Copula) 描述。這個方法的好處是可描述同型的相依結構。用一個配合維關結構而有效的蒙地卡模擬方法，我們研究在同相依結構及模型下保證最低提的價值變化。在固定的特別情況下，保證最低提的價值能夠透過卷積方法 (convolution method) 而得到半解析解 (semi-analytical solution) 。最後，我們將本研究中的學模型擴展以研究近期出現由保證最低提演化而成的一種保證產品。這個產品名稱為保證終身提 (Guaranteed Lifelong Withdrawal Benefit, GLWB)，而此產品的到期日則與持有人的壽命相關。 / In this thesis, we study the problem of pricing the variable annuity(VA) with the Guaranteed Minimum Withdrawal Benefits (GMWB) under the stochastic interest rate framework. The GMWB is a rider that can be elected to supplement a VA. It provides downside protection to policyholders by guaranteeing the total withdrawals throughout the life of the contract to be not less than a pre-specied amount, usually the initial lump sum investment, regardless of the investment performance of the VA. In our nancial model, we employ an exponential L´evy model for the underlying fund process and a Vasiček type model driven by a L´evy process for the interest rate dynamic. The dependence structure between the two driving L´evy processes is modeledby the L´evy copula approach whichis exible to model a wide range of dependence structure. An effcient simulation algorithm on L´evy copula is then used to study the behavior of the value of the GMWB when the dependence structure of the two L´evy processes and model parameters Vry. When the interest rate is deterministic, the value of the GMWB can be solved semi-analytically by the convolution method. Finally, we extend our model to study a recent variation of GMWB called Guaranteed Life long Withdrawal Benefits (GLWB) in which the maturity of the GLWB depends on the life of the policyhodler. / Detailed summary in vernacular field only. / Chan, Wang Ngai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 115-121). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Variable Annuity & Guaranteed Minimum Withdrawal Benefit --- p.1 / Chapter 1.2 --- Literature Review --- p.4 / Chapter 1.3 --- Financial Model for GMWB --- p.7 / Chapter 2 --- L´evy Copulas and the Simulation Algorithm --- p.12 / Chapter 2.1 --- Definitions and Theorem --- p.15 / Chapter 2.2 --- Examples of L´evy Copulas --- p.19 / Chapter 2.2.1 --- Independence case --- p.19 / Chapter 2.2.2 --- Complete Dependence --- p.20 / Chapter 2.2.3 --- The Clayton L´evy Copula --- p.21 / Chapter 2.3 --- Simulation algorithm for two-dimensional dependent L´evy process --- p.22 / Chapter 3 --- Model Formulation for GMWB --- p.26 / Chapter 3.1 --- Financial Model for GMWB --- p.27 / Chapter 3.2 --- Underlying Fund of VA and the Interest Rate --- p.30 / Chapter 3.3 --- A Special Case of Deterministic Interest Rate --- p.34 / Chapter 4 --- Numerical Implementation --- p.38 / Chapter 4.1 --- The Clayton L´evy Copula --- p.39 / Chapter 4.2 --- The Underlying Fund and the Interest Rate Processes --- p.42 / Chapter 4.3 --- Kendall’s Tau Coefficient --- p.47 / Chapter 4.4 --- The GMWB Option Value --- p.49 / Chapter 4.4.1 --- Control Variate for Simulation --- p.49 / Chapter 4.4.2 --- Simulation Results --- p.51 / Chapter 4.5 --- Deterministic Interest Rate --- p.52 / Chapter 5 --- GMWB Pricing Behavior --- p.56 / Chapter 5.1 --- L´evy model for the underlying fund --- p.57 / Chapter 5.1.1 --- The Skewness --- p.57 / Chapter 5.1.2 --- The Kurtosis --- p.65 / Chapter 5.2 --- The Vasiček model driven by L´evy process --- p.73 / Chapter 5.2.1 --- The Volatility Parameter ôV --- p.73 / Chapter 5.2.2 --- The Mean Reverting Parameter aV --- p.77 / Chapter 5.3 --- Dependence between the underlying fund and rate processes --- p.81 / Chapter 5.3.1 --- The jump direction dependence parameter n{U+1D9C} --- p.83 / Chapter 5.3.2 --- The jump magnitude dependence parameter θ{U+1D9C} --- p.90 / Chapter 6 --- GMWB for Life --- p.96 / Chapter 6.1 --- Model Formulation --- p.98 / Chapter 6.1.1 --- Mortality model --- p.99 / Chapter 6.1.2 --- Financial Model for GLWB --- p.101 / Chapter 6.2 --- GLWB product from John Hancock --- p.103 / Chapter 6.3 --- GLWB Pricing Behavior --- p.104 / Chapter 6.3.1 --- The correlation effect --- p.106 / Chapter 7 --- Conclusion --- p.108 / A Proofs --- p.113 / Chapter A.1 --- Proof of Equation 3.1 --- p.113 / Chapter A.2 --- Proof of Equation 3.3 --- p.114 / Bibliography --- p.115

Liu, Junyi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 76-79). / Abstracts in English and Chinese. / Table of Content / Abstract --- p.i / Acknowledgement --- p.iii / Table of Content --- p.iv / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- "“Race to the bottom""" --- p.1 / Chapter 1.2 --- The New Context of International Trade --- p.2 / Chapter 1.3 --- Related party trade of Hong Kong --- p.4 / Chapter 1.4 --- Transfer Pricing --- p.6 / Chapter Chapter 2 --- The Theory --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Literature Review --- p.10 / Chapter 2.3 --- The Model --- p.16 / Chapter 2.4 --- MNC Manipulation Of Transfer Pricing --- p.20 / Chapter 2.5 --- MNC Manipulation Of Host Country Demand --- p.25 / Chapter 2.6 --- MNC Manipulation Of Explicit Benchmarks On Transfer Prices --- p.28 / Chapter 2.7 --- The Race to the Bottom in International Tax Competition --- p.32 / Chapter 2.8 --- Textbook Model without Transfer Pricing --- p.35 / Chapter 2.9 --- Concluding Remarks --- p.37 / Chapter Chapter 3 --- Empirical Evidence --- p.39 / Chapter 3.1 --- Introduction --- p.39 / Chapter 3.2 --- Related Literature --- p.41 / Chapter 3.3 --- Data and Empirical Specification --- p.44 / Chapter 3.4 --- Empirical Results --- p.51 / Appendix --- p.58 / List of Tables --- p.63 / Table 1 Related Party Trade as a Share of U.S. Imports from Selected Countries and Regions --- p.63 / Table 2 Related Party Trade as a Share of U.S. Exports from Selected Countries and Regions --- p.63 / "Table 3A Top 10 Source Countries for Re-exports via Hong Kong, 2006" --- p.64 / "Table 3B: Top 10 Destinations of Re-exports via Hong Kong, 2006" --- p.64 / Table 4A: Top 10 sources of China's FDI in 2005 --- p.64 / Table 4B: Top 10 sources of China's FDI in 2006 --- p.64 / Table 4C Top 10 sources of China's FDI (January to March 2007) --- p.64 / Table 5 Round Tripping of FDI to the PRC: The Case of U.S. --- p.65 / Table 6 Top 24 Destinations for FDI in 2005 --- p.65 / Table 7 Percentage of foreign firms reporting losses in the PRC --- p.65 / Table 8 43 Countries by region --- p.66 / Table 9 Gross Foreign Productions of U.S. Multinationals by Country from 1997 to 2004 --- p.66 / Table 10 Tax Rates by Country from 1997 to 2004 --- p.67 / Table 11 Original Corruption Index by country from 1997 to 2004 --- p.68 / Table 12 U.S. MNCs' Internal Trade Ratio by country from 1997 to 2004 --- p.69 / Table 13 - OLS Regression of Foreign Productions on Present Tax Rates --- p.70 / Table 14 - OLS Regression of Foreign Productions on Present Tax Rates --- p.71 / Table 15 OLS Regression of Foreign Productions on One-Year-Lag Tax Rate --- p.71 / Table 16 OLS Regression of Foreign Productions on One-Year-Before Tax Rate --- p.72 / Table 17 OLS Regression of Foreign Productions on Corruption A and B --- p.72 / Table 18 OLS Regression of Foreign Productions on Corruption B and C --- p.73 / Table 19 OLS Regression of Tax Rate on Country Dummies --- p.74 / Bibliography --- p.76

In consumption goods markets, we observe both bargaining and searching. However, in this literature, very little work has been done to incorporate both features into one model. This study addresses this problem. In my first chapter, I add a bargaining parameter to a traditional sequential search model and solve for the new equilibrium in this set-up. Then, I do some comparative statics, changing the distribution of the bargaining parameter to see what happens to the equilibrium. Finally, I use the model to explain two seemingly contradicting empirical works in the literature of discrimination in the auto market. Ayres and Siegelman (1995), using data they collected from a controlled experiment, found that the initial offers for the minorities are higher. Yet Goldberg (1996), using consumer expenditure survey data (CES), reported that there is no significant difference between the final prices for minorities and non-minorities. My model reconciles these two results and shows that if minorities have a more dispersed bargaining parameter distribution and if the final transaction prices are the same at the mean level, then the initial offer distribution for the minorities first-order stochastically dominates that for the non-minorities. In my second chapter, I investigate how the bargaining process affects firms’ offer distribution and thus the final price distribution. Based on Varian (1980), I add a bargaining parameter into the model, and solve for the new equilibrium in this set up. Then, I do some comparative statics, changing the distribution of the bargaining parameter to see what would happen to the equilibrium. This model yields the same results as the first chapter. In the third chapter, I applied my theoretical model to the automobile market, and empirically test the model. I used CES data, and my findings support the theoretical model. The minority dummies are not significant in determining the mean level of consumers’ bargaining ability distribution, but are significantly positive in determining the variance of the distribution. / text

The major economic policy issue of the 1980s is inflation. Although economists have been writing about inflation for several decades, little work has been done on the theory of inflation measurement. There is an extensive literature dealing with the statistical aspects of price indices and the inflation phenomenon. However, statistical discussions ignore the economic theory behind inflation measures and inflation discussions fail to address the practical aspect of measurement of inflation. This dissertation develops an inflation measure that overcomes these failings. By combining the principles of price formation found in microeconomic literature with the macroeconomic theory of inflation, an economically appropriate measure of inflation is presented. The measure adopts the Marshallian view that producers fix prices and vary output in response to market conditions. Recognizing that production takes time which leads to uncertainty about the forward delivery market, the measure stresses both labor and material input costs as the prime price determinants. Contracts fix these costs. Current or spot market demand influences prices only in the service sector. This influence is measured and added to the price forming factors determined in oligopoly, monopoly and competitive sectors. The four sectors are combined with a measure of government price influence to generate the measure of inflation. A highly stylized model of this measure is tested monthly for the 1965-78 period. The theoretical measure and the model results are then compared to conventional inflation measures. The CPI, GNP deflator and WPI are discussed and their problems as measures of inflation are assessed. The measure proposed and tested here eliminates much of the sampling bias, substitution bias, and quality bias plaguing the others. Being designed as a measure of inflation in the general price level, the proposed measure actually incorporates the broad economic base necessary for a macroeconomic measure. It provides a useful policy guide for inflation management and an appropriate measure of the policy's success.

The efficiency of revenue management relies on the effectiveness of the strategies it employs. In the competing market nowadays, time has become an important concern at both demand and supply sides. With time-sensitive customers and additional benefits from intertemporal demand shift, we find that the sellers could turn to a time-differentiation based strategy as an effective revenue management tool. Motivated by real-life business issues of Toyota China dealerships, in this thesis, we consider stylized inventory-control models with delivery upgrades, in which the seller allocates its on-hand inventory to price and delivery-time sensitive customers. The seller provides two delivery-time options with different prices. Customers choose the proper purchasing option according to their heterogeneous preferences. The seller has two decisions: inventory commitment and inventory replenishment. The former addresses, within an inventory cycle, how on-hand inventories are allocated between the two classes of customers. The latter addresses, between inventory cycles, how the inventory is replenished. Furthermore, the seller may employ early delivery, namely upgrade, to achieve a higher inventory flexibility. We develop the optimal inventory allocation and upgrade, and inventory replenishment policies, and demonstrate that the optimal control can be characterized by a switching curve. Based on the basic model setting, we extend our analysis to include cases of upgrade cost, stock-out substitution, and capacity constraint. We further discuss the joint pricing and inventory decision. We obtain the form of the optimal joint policy, and show that the two strategies may well complement each other in our setting. When each is applied separately, their performances are also compared. To shed more light on the practical side, finally, we use the Toyota dealership data to calibrate the required parameters, and demonstrate the potential of the optimal inventory allocation and upgrade control. / Liang, Xiaoying. / Advisers: Houmin Yan; Youhua Chen. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 118-124). / 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 Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011. / Imported from http://etd.sun.ac.za / ENGLISH ABSTRACT: In this thesis, we propose to use Levy processes to model the dynamics of asset prices. In the first part, we deal with single asset options and model the log stock prices with a Levy process. We employ pure jump Levy processes of infinite activity, in particular variance gamma and CGMY processes. We fit the log-returns of six stocks to variance gamma and CGMY distributions and check the goodness of fit using statistical tests. It is observed that the variance gamma and the CGMY distributions fit the financial market data much better than the normal distribution. Calibration shows that at given maturity time the two models fit into the option prices very well. In the second part, we investigate the effect of dependence structure to multivariate option pricing. We use the new concept of Levy copula introduced in the literature by Tankov [40]. Levy copulas allow us to separate the dependence structure from the behavior of the marginal components. We consider bivariate variance gamma and bivariate CGMY models. To model the dependence structure between underlying assets we use the Clayton Levy copula. The empirical results on six stocks indicate a strong dependence between two different stock prices. Subsequently, we compute bivariate option prices taking into account the dependence structure. It is observed that option prices are highly sensitive to the dependence structure between underlying assets, and neglecting tail dependence will lead to errors in option pricing. / AFRIKAANSE OPSOMMING: In hierdie proefskrif word Levy prosesse voorgestel om die bewegings van batepryse te modelleer. Levy prosesse besit die vermoe om die risiko van spronge in ag te neem, asook om die implisiete volatiliteite, wat in finansiele opsie pryse voorkom, te reproduseer. Ons gebruik suiwer–sprong Levy prosesse met oneindige aktiwiteit, in besonder die gamma– variansie (Eng. variance gamma) en CGMY–prosesse. Ons pas die log–opbrengste van ses aandele op die gamma–variansie en CGMY distribusies, en kontroleer die resultate met behulp van statistiese pasgehaltetoetse. Die resultate bevestig dat die gamma–variansie en CGMY modelle die finansiele data beter pas as die normaalverdeling. Kalibrasie toon ook aan dat vir ’n gegewe verstryktyd die twee modelle ook die opsiepryse goed pas. Ons ondersoek daarna die gebruik van Levy prosesse vir opsies op meervoudige bates. Ons gebruik die nuwe konsep van Levy copulas, wat deur Tankov[40] ingelei is. Levy copulas laat toe om die onderlinge afhanklikheid tussen bateprysspronge te skei van die randkomponente. Ons bespreek daarna die simulasie van meerveranderlike Levy prosesse met behulp van Levy copulas. Daarna bepaal ons die pryse van opsies op meervoudige bates in multi–dimensionele exponensiele Levy modelle met behulp van Monte Carlo–metodes. Ons beskou die tweeveranderlike gamma-variansie en – CGMY modelle en modelleer die afhanklikheidsstruktuur tussen onderleggende bates met ’n Levy Clayton copula. Daarna bereken ons tweeveranderlike opsiepryse. Kalibrasie toon aan dat hierdie opsiepryse baie sensitief is vir die afhanlikheidsstruktuur, en dat prysbepaling foutief is as die afhanklikheid tussen die sterte van die onderleggende verdelings verontagsaam word.