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

No abstract available.

Numerical methods form an important part of the pricing of financial derivatives and especially in cases where there is no closed form analytical formula. We begin our work with an introduction of the mathematical tools needed in the pricing of financial derivatives. Then, we discuss the assumption of the log-normal returns on stock prices and the stochastic differential equations. These lay the foundation for the derivation of the Black Scholes differential equation, and various Black Scholes formulas are thus obtained. Then, the model is modified to cater for dividend paying stock and for the pricing of options on futures. Multi-period binomial model is very flexible even for the valuation of options that do not have a closed form analytical formula. We consider the pricing of vanilla options both on non dividend and dividend paying stocks. Then show that the model converges to the Black-Scholes value as we increase the number of steps. We discuss the Finite difference methods quite extensively with a focus on the Implicit and Crank-Nicolson methods, and apply these numerical techniques to the pricing of vanilla options. Finally, we compare the convergence of the multi-period binomial model, the Implicit and Crank Nicolson methods to the analytical Black Scholes price of the option. We conclude with the pricing of exotic options with special emphasis on path dependent options. Monte Carlo simulation technique is applied as this method is very versatile in cases where there is no closed form analytical formula. The method is slow and time consuming but very flexible even for multi dimensional problems.

No abstract available.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014. / The period between 2008 and 2009 was an interesting and dramatic time for financial markets. This period marked the beginning of the financial tsunami that would plague global markets for many years to come. This economic meltdown had massive effects on many everyday issues such as house prices, interest rates and inflation. Investment banks were also affected with numerous investment banks either defaulting or being taken over by the U.S. Federal Reserve to avoid default. This group of investment banks include names such as Lehman Brothers, Bear Sterns, Fannie Mae, Freddy Mac and many more. The myth of “too big to fail” was tested and failed because of the number of banks that were allowed to default during the crisis. Many things have changed because of the crisis. One area in finance that has changed is the pricing of financial derivatives. The realisation that huge investment banks can default has dried up the liquidity in capital markets. Therefore banks cannot borrow a shortfall of cash at a risk-free rate anymore but rather at a significant spread over the risk-free rate. The risk-free rate is a core concept of derivative pricing. If investment banks cannot borrow and lend at the risk-free rate then the Black-Sholes-Merton theory laid down in the 1970’s may not be applicable post the credit crisis. The aim of this dissertation is to review the framework of Piterbarg, Burgard and Kjaer to price a general derivative post the credit crisis. This review includes a variety of numerical methods to implement the framework.

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.

Lai, Kwok Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 64-66). / Abstracts in English and Chinese. / Abstract --- p.i / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.9 / Chapter 3 --- Preliminary Analysis of Data --- p.17 / Chapter 3.1 --- Data --- p.17 / Chapter 3.2 --- Preliminary Analysis of Unspanned Stochastic Volatility --- p.20 / Chapter 4 --- A Jump-Diffusion Model for Federal Funds Target Rate --- p.23 / Chapter 4.1 --- Model Specification --- p.23 / Chapter 4.2 --- Estimation Result --- p.31 / Chapter 5 --- Pricing and Hedging Performance of Interest Rate Derivatives --- p.34 / Chapter 5.1 --- Pricing Performance of Interest Rate Cap --- p.34 / Chapter 5.2 --- Hedging Performance of Interest Rate Caplet --- p.38 / Chapter 5.3 --- Hedging Performance of Interest Rate Straddle --- p.42 / Chapter 6 --- Conclusion --- p.49 / Figures --- p.51 / Tables --- p.55 / Bibliography --- p.64

Thesis (M.C.A.)--Victoria University of Wellington, 2009. / Includes bibliographical references.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy