随着全球金融市场的日益创新和不断加剧的竞争，金融产品也变得越来越结构复杂。这些复杂的金融产品，从定价，对冲到风险管理，都对相应的数学技术提出越来越高的要求。在目前运用的技术中，蒙特卡洛模拟方法由于其广泛的适用性而备受欢迎。本篇论文对于在金融工程和工业界都受到广泛关注的两个问题进行研究：局部化以及对于受布朗运动驱动的随机微分方程的精确抽样；布朗河曲，重要性抽样已经对于扩散过程极值的无偏估计。 / 第一篇文章考虑了使用蒙特卡洛模拟方法产生随机微分方程的样本路径。离散化方法是此前普遍使用的近似产生路径的方法：这种方法很容易实施，但是会产生抽样偏差。本篇文章提出一种模拟方法，可用于随机微分方程路径的精确抽样。一个至关重要的发现是：随机微分方程的概率分布可以被分解为两部分的乘积，一部分是标准布朗运动的概率分布，另外一部分是双重随机的泊松过程。基于这样的分解和局部化技术，本篇文章提出一种接受-拒绝算法。数值试验可以验证，这种方法的均方误差-计算时间的收敛速度可以达到O(t⁻¹[superscript /]²)，优于传统的离散化方法。更进一步的优点是：这种方法可以对带边界的随机微分方程进行精确抽样，而带边界的微分方程正是传统离散方法经常遇到困难的情形。 / 第二篇文章研究了如何计算基于扩散过程极值的泛函。传统的离散化方法收率速度很慢。本篇文章提出了一种基于维纳测度分解的无偏蒙特卡洛估计。运用重要性抽样技术和对于布朗运动路径的威廉分解，本篇文章将对于一般性扩散过程的极值的抽样化简为对于两个布朗河曲的抽样。数值试验部分也验证了本篇文章所提方法的准确性和计算上的高效率。 / With increased innovation and competition in the current financial market, financial product has become more and more complicated, which requires advanced techniques in pricing, hedging and risk management. Monte Carlo simulation is among the most popular ones due to its great °exibility. This dissertation contains two problems recently arises and receives much attention from both the financial engineering and simulation communities: Localization and Exact Simulation of Brownian Motion Driven Stochastic Differential Equations; And Brownian Meanders, Importance Sampling and Un-biased Simulation of Diffusion Extremes. / The first essay considers generating sample paths of stochastic differential equations (SDE) using the Monte Carlo method. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This essay presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law of a general SDE can be decomposed into a product of the law of standard Brownian motion and the law of a doubly stochastic Poisson process. An acceptance-rejection algorithm is devised based on the combination of this decomposition and a localization technique. The numerical results corroborates that the mean-square error of the proposed method is in the order of O(t⁻¹[superscript /]²), which is superior to the conventional discretization schemes. Furthermore, the proposed method also can generate exact samples for SDE with boundaries which the discretization schemes usually find difficulty in dealing with. / The second essay considers computing expected values of functions involving extreme values of diffusion processes. The conventional discretization Monte Carlo simulation schemes often converge very slowly. In this paper, we propose a Wiener measure decomposition-based approach to construct unbiased Monte Carlo estimators. Combined with the importance sampling technique and the celebrated Williams' path decomposition of Brownian motion, this approach transforms the task of simulating extreme values of a general diffusion process to the simulation of two Brownian meanders. The numerical experiments show the accuracy and efficiency of our Poisson-kernel unbiased estimators. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Huang, Zhengyu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 107-115). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- SDEs and Discretization Methods --- p.4 / Chapter 1.3 --- The Beskos-Roberts Exact Simulation --- p.15 / Chapter 1.4 --- Major Contributions --- p.19 / Chapter 1.5 --- Organization --- p.26 / Chapter 2 --- Localization and Exact Simulation of SDEs --- p.27 / Chapter 2.1 --- Main Result: A Localization Technique --- p.27 / Chapter 2.1.1 --- Sampling of ζ --- p.33 / Chapter 2.1.2 --- Sampling of Wζ^(T-t) --- p.35 / Chapter 2.1.3 --- Sampling of the Bernoulli I --- p.38 / Chapter 2.1.4 --- Comparison Involving Infinite Sums --- p.40 / Chapter 2.2 --- Discussions --- p.43 / Chapter 2.2.1 --- One Extension: SDEs with Boundaries --- p.43 / Chapter 2.2.2 --- Simulation Efficiency --- p.45 / Chapter 2.2.3 --- Extension to Multi-dimensional SDE --- p.48 / Chapter 2.3 --- Numerical Examples --- p.52 / Chapter 2.3.1 --- Ornstein-Uhlenbeck Mean-Reverting Process --- p.52 / Chapter 2.3.2 --- A Double-Well Potential Model --- p.56 / Chapter 2.3.3 --- Cox-Ingersoll-Ross Square-Root Process --- p.56 / Chapter 2.3.4 --- Linear-Drift CEV-Type-Diffusion Model --- p.62 / Chapter 2.4 --- Appendix --- p.62 / Chapter 2.4.1 --- Simulation of Brownian Bridges --- p.62 / Chapter 2.4.2 --- Proofs of Main Results --- p.64 / Chapter 2.4.3 --- The Oscillating Property of the Series --- p.71 / Chapter 3 --- Unbiased Simulation of Diffusion Extremes --- p.79 / Chapter 3.1 --- A Wiener Measure Decomposition --- p.79 / Chapter 3.2 --- Brownian Meanders and Importance Sampler of Diffusion Extremes --- p.81 / Chapter 3.2.1 --- Exact Simulation of (θT, KT, WT) --- p.83 / Chapter 3.2.2 --- Simulating Importance Sampling Weight --- p.84 / Chapter 3.3 --- Some Extensions --- p.88 / Chapter 3.3.1 --- Variance Reduction --- p.88 / Chapter 3.3.2 --- Double Barrier Options --- p.90 / Chapter 3.4 --- Numerical Examples --- p.94 / Chapter 3.5 --- Appendix --- p.98 / Chapter 3.5.1 --- Brownian Bridges and Meanders --- p.98 / Chapter 3.5.2 --- Proofs of Main Results --- p.101 / Bibliography --- p.107

Thesis (M.Sc.(Mathematics and Applied Mathematics)) -- University of Pretoria, 2008. / Summary in English. Includes bibliographical references.

Doctorat en sciences sociales, politiques et économiques / info:eu-repo/semantics/nonPublished

The Malliavin-Thalmaier formula was introduced for simulation of high dimensional probability density functions. But when this integration by parts formula is applied directly in computer simulations, we show that it is unstable. We propose an approximation to the Malliavin-Thalmaier formula. In this paper, we find the order of the bias and the variance of the approximation error. And we obtain an explicit Malliavin-Thalmaier formula for the calculation of Greeks in finance. The weights obtained are free from the curse of dimensionality.

The diploma thesis is focused on the problems of financial engineering instruments and specific methods for the use of credit instruments in the theories of regional development with special reference to initiative JESSICA. Analytical part contains theoretical and methodological context of the implementation of JESSICA in the UK and Poland. On the basis of the comparison of urban structures and experience with the initiative are assess the backgrounds, conditions and barriers of JESSICA implementation in the Czech Republic. The key added value of the thesis is the estimation of the critical issues for the implementation of JESSICA on a basis of a case study of Moravia-Silesia cohesion region.

Como a volatilidade é a única variável não observada nas fórmulas padrão de apreçamento de opções, o mercado financeiro utiliza amplamente o conceito de volatilidade implícita, isto é, a volatilidade que ao ser aplicada na fórmula de apreçamento resulte no preço correto (observado) das opções negociadas. Por isso, entender como as volatilidades implícitas das diversas opções de dólar negociadas na BM&F, o objeto de nosso estudo, variam ao longo do tempo e como estas se relacionam é importante para a análise de risco de carteiras de opções de dólar/real bem como para o apreçamento de derivativos cambiais exóticos ou pouco líquidos. A proposta de nosso estudo é, portanto, verificar se as observações da literatura técnica em diversos mercados também são válidas para as opções de dólar negociadas na BM&F: que as volatilidades implícitas não são constantes e que há uma relação entre as variações das volatilidades implícitas e as variações do valor do ativo objeto. Para alcançar este objetivo, aplicaremos a análise de componentes principais em nosso estudo. Com esta metodologia, reduziremos as variáveis aleatórias que representam o processo das volatilidades implícitas em um número menor de variáveis ortogonais, facilitando a análise dos dados obtidos. / Volatility is the only unobserved variable in the standard option pricing formulas and hence implied volatility is a concept widely adopted by the financial market, meaning the volatility which would make the formula yield the options real market price. Therefore, understanding how the implied volatility of the options on dollar traded at BM&F, the subject of our study, vary over time is important for risk analysis over dollar option books and for pricing of exotic or illiquid derivatives Our works proposal is to verify if the observations made by the technical literature over several markets could also be applied to the options on dollar traded at BM&F: implied volatilities do vary over time and there is a relation between this variation and the variation of the underlying asset price. In order to fulfill these goals, we will apply principal component analysis in our study. This methodology will help us analyze the data by reducing the number of variables that represent the implied volatility process into a few orthogonal variables.

jointly presented by Lau Chi Yuen, Joseph, Wong Chi Ho. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 92-96). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / Chapter CHAPTER I --- INTRODUCTION --- p.1 / Chapter CHAPTER II --- THE MOTIVATION OF DERTVATIVES TRANSACTIONS --- p.3 / Chapter CHAPTER III --- MAJOR TYPE OF DERIVATIVES TRADING IN EXCHANGE MARKET AND OTC MARKET IN HONG KONG --- p.7 / Exchange Traded Derivatives --- p.7 / Index Option --- p.7 / Strategies of option trading --- p.9 / Ratio covered writing --- p.9 / Bull/Bear Spreads --- p.10 / Butterfly Spreads --- p.11 / Calendar Spreads --- p.12 / Straddle --- p.13 / Strips and Straps --- p.14 / Strangles --- p.14 / Index Future --- p.15 / Spreading Trading --- p.16 / Warrants and Covered Warrants --- p.16 / Other derivatives --- p.19 / OTC (Over-The-Counter) Derivatives --- p.20 / Equity or equity-linked derivatives --- p.20 / Advantages of equity-linked derivatives --- p.20 / Equity-Linked Debt Instruments --- p.21 / Equity Swaps --- p.23 / The Future of Equity Swap Market --- p.27 / Equity options --- p.27 / OTC Stock options --- p.28 / Collar --- p.28 / Spread Call or Put (Capped Call or Put) --- p.29 / Barrier options --- p.30 / Convertible Bonds --- p.31 / OTC Currency Derivatives --- p.31 / Currency Options --- p.32 / Currency Swaps --- p.33 / Currency forwards --- p.33 / Currency Asian Option --- p.33 / Interest Rate Derivatives --- p.34 / Interest rate swap --- p.34 / Interest rate swaptions --- p.35 / Interest rate forward swaps --- p.35 / "Interest rate cap, floor and collar" --- p.35 / Chapter CHAPTER IV --- GROWTH OF ASIAN AND HONG KONG DERIVATIVES MARKET --- p.37 / Bookrunners in Asia --- p.39 / Growth of OTC markets in Asia --- p.41 / Chapter CHAPTER V --- PRICING MODELS FOR THE DERIVATIVES --- p.46 / Black-Scholes differential equation --- p.46 / For HSI call option --- p.47 / For HSI put options --- p.47 / Binomial Trees Model --- p.50 / Valuation of Convertible Bond --- p.50 / Swap Pricing - Banker rs Perspective --- p.51 / Decreasing Profit Margin in Swap Deal --- p.53 / Chapter CHAPTER VI --- THE APPLICATION OF DERIVATIVES IN HONG KONG MARKET --- p.54 / Corporations --- p.54 / Lowering Funding Costs through Arbitrage Opportunity or Issuance of Customized Instruments --- p.55 / Diversifying Funding Sources --- p.55 / Funding Operations in Multiple Countries at Lowest Cost --- p.56 / Managing Foreign Exchange Exposures --- p.56 / Hedging the cost of Issuing Floating-Rate and Fixed-Rate Debt --- p.57 / Hedging the Cost of Anticipated Issuance of Fixed-Rate Debt --- p.58 / Managing Existing Debt of Asset Portfolio --- p.58 / Institutional Investors --- p.59 / Enhancing Yields Through Arbitrage Opportunities --- p.59 / Asset Allocation using Swap --- p.59 / Synthetic Equity --- p.59 / Synthetic FRN --- p.60 / The Benefits of Swap in Asset Management --- p.62 / Eliminate Currency Risk --- p.62 / Managing Risk Exposure with Customized instruments --- p.63 / Individual investors --- p.63 / "Financial Institutions," --- p.64 / Greater Progress in Asian Markets Risk Management Still Lies Ahead --- p.64 / Chapter CHAPTER VII --- RISK MANAGEMENT --- p.65 / Concerns of risk management --- p.65 / "What can be done by the clients," --- p.67 / What can be done by regulators --- p.69 / Chapter CHAPTER VIII --- RISK MANAGEMENT - BANKERS PERSPECTIVE --- p.71 / Reasons for Investment in risk management --- p.71 / Profit by taking more of the right risks --- p.71 / Internationalization of markets --- p.72 / Greater variety and complexity of financial instruments --- p.73 / Risk management in Action --- p.74 / A Common Framework in Risk Management --- p.74 / Identification --- p.74 / Measurement --- p.74 / Management --- p.76 / Measuring Volatility - Past Vs Future --- p.76 / Market Risk Management --- p.78 / Basic Information Views --- p.78 / Trader's View --- p.79 / Accountant's View --- p.79 / Management's View --- p.80 / Simulation to Describe Risks --- p.80 / Reality Check --- p.83 / Reporting in Action --- p.84 / "Risk Management at Large Investment Banks Today," --- p.85 / APPENDIX I SIMULATION OF DELTA HEDGING --- p.88 / BIBLIOGRAPHY --- p.92

In this study, a Prediction Accuracy Based Hill Climbing Feature Selection Algorithm (AHCFS) is created and compared with an Error Rate Based Sequential Feature Selection Algorithm (ERFS) which is an existing Matlab algorithm. The goal of the study is to create a new piece of an algorithm that has potential to outperform the existing Matlab sequential feature selection algorithm in predicting the movement of S&P 500 (^GSPC) prices under certain circumstances. The two algorithms are tested based on historical data of ^GSPC, and Support Vector Machine (SVM) is employed by both as the classifier. A prediction without feature selection algorithm implemented is carried out and used as a baseline for comparison between the two algorithms. The prediction horizon set in this study for both algorithms varies from one to 60 days. The study results show that AHCFS reaches higher prediction accuracy than ERFS in the majority of the cases.

In this era of big data, we often rely on techniques ranging from simple linear regression, structural estimation, and state-of-the-art machine learning algorithms to make operational and financial decisions based on data. This calls for a deep understanding of practical and theoretical aspects of methods and models from statistics, econometrics, and computer science, combined with relevant domain knowledge. In this thesis, we study several practical, data-related problems in the particular domains of sharing economy and financial economics/financial engineering, using appropriate approaches from an arsenal of data-analysis tools. On the methodological front, we propose a new estimator for classic demand estimation problem in economics, which is important for pricing and revenue management. In the first part of this thesis, we study customer preference for the bike share system in London, in order to provide policy recommendations on bike share system design and expansion. We estimate a structural demand model on the station network to learn the preference parameters, and use the estimated model to provide insights on the design and expansion of the system. We highlight the importance of network effects in understanding customer demand and evaluating expansion strategies of transportation networks. In the particular example of the London bike share system, we find that allocating resources to some areas of the station network can be 10 times more beneficial than others in terms of system usage, and that currently implemented station density rule is far from optimal. We develop a new method to deal with the endogeneity problem of the choice set in estimating demand for network products. Our method can be applied to other settings, in which the available set of products or services depends on demand. In the second part of this thesis, we study demand estimation methodology when data has a long-tail pattern, that is, when a significant portion of products have zero or very few sales. Long-tail distributions in sales or market share data have long been an issue in empirical studies in areas such as economics, operations, and marketing, and it is increasingly common nowadays with more detailed levels of data available and many more products being offered in places like online retailers and platforms. The classic demand estimation framework cannot deal with zero sales, which yields inconsistent estimates. More importantly, biased demand estimates, if used as an input to subsequent tasks such as pricing, lead to managerial decisions that are far from optimal. We introduce two new two-stage estimators to solve the problem: our solutions apply machine learning algorithms to estimate market shares in the first stage, and in the second stage, we utilize the first-stage results to correct for the selection bias in demand estimates. We find that our approach works better than traditional methods using simulations. In the third part of this thesis, we study how to extract a signal from option pricing models to form a profitable stock trading strategy. Recent work has documented roughness in the time series of stock market volatility and investigated its implications for option pricing. We study a strategy for trading stocks based on measures of their implied and realized roughness. A strategy that goes long the roughest-volatility stocks and short the smoothest-volatility stocks earns statistically significant excess annual returns of 6% or more, depending on the time period and strategy details. Standard factors do not explain the profitability of the strategy. We compare alternative measures of roughness in volatility and find that the profitability of the strategy is greater when we sort stocks based on implied rather than realized roughness. We interpret the profitability of the strategy as compensation for near-term idiosyncratic event risk. Lastly, we apply a heterogeneous treatment effect (HTE) estimator from statistics and machine learning to financial asset pricing. Recent progress in the interdisciplinary area of causal inference and machine learning has proposed various promising estimators for HTE. We take the R-learner algorithm by [73] and adapt it to empirical asset pricing. We study characteristics associated with standard factors, size, value and momentum through the lens of HTE. Our goal is to identify sub-universes of stocks, ``characteristic responders", in which size, value or momentum trading strategies perform best, compared with the performance had they been applied to the entire universe. On the other hand, we identify subsets of ``characteristic traps" in which the strategies perform the worst. In our test period, the differences in average monthly returns between long-short strategies restricted to ``characteristic responders" and ``characteristic traps" range from 0.77% to 1.54% depending on treatment characteristics. The differences are statistically significant and cannot be explained by standard factors: a long-short of long-short strategy generates alpha of significant magnitude from 0.98% to 1.80% monthly, with respect to standard Fama-French plus momentum factors. Simple interaction terms between standard factors and ex-post important features do not explain the alphas either. We also characterize and interpret the characteristic traps and responders identified by our algorithm. Our study can be viewed as a systematic, data-driven way to investigate interaction effects between features and treatment characteristic, and to identify characteristic traps and responders.

abstract: The lack of food safety in a grower's produce presents the grower with two risks; (1) that an item will need to be recalled from the market, incurring substantial costs and damaging brand equity and (2) that the entire market for the commodity becomes impaired as consumers associate all produce as being risky to eat. Nowhere is this more prevalent than in the leafy green industry, where recalls are relatively frequent and there has been one massive E. coli outbreak that rocked the industry in 2006. The purpose of this thesis is to examine insurance policies that protect growers from these risks. In doing this, a discussion of current recall insurance policies is presented. Further, actuarially fair premiums for catastrophic revenue insurance policies are priced through a contingent claims framework. The results suggest that spinach industry revenue can be insured for $0.02 per carton. Given the current costs of leafy green industry food safety initiatives, growers may be willing to pay for such an insurance policy. / Dissertation/Thesis / M.S. Agribusiness 2013