Ren, You. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 48-51). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Option Pricing Theory --- p.1 / Chapter 1.2 --- American Option Pricing --- p.3 / Chapter 1.3 --- Numerical Approximation of American Option Price --- p.8 / Chapter 1.4 --- Statistical Issues --- p.12 / Chapter 1.4.1 --- Empirical Calibration --- p.13 / Chapter 2 --- Mixed Effects Model for American Option Prices --- p.16 / Chapter 2.1 --- Model --- p.16 / Chapter 2.2 --- Model Selection --- p.19 / Chapter 2.3 --- Empirical Bayes Prediction --- p.21 / Chapter 3 --- Simulation and Empirical Data --- p.22 / Chapter 3.1 --- Simulation --- p.22 / Chapter 3.1.1 --- Simulation of Stock Price Path and a Set of Options --- p.22 / Chapter 3.1.2 --- Training Mixed Effects Model --- p.27 / Chapter 3.1.3 --- Performance Measure and Prediction Result --- p.30 / Chapter 3.2 --- An Application to P&G American Options --- p.36 / Chapter 3.2.1 --- The Empirical Data and Setup --- p.36 / Chapter 3.2.2 --- Training Mixed Effects Option Pricing Model --- p.37 / Chapter 3.2.3 --- Performance Analysis --- p.41 / Chapter 4 --- Conclusion and Discussion --- p.46 / Bibliography --- p.48

Tang, Sze Ki = 計算美式賣權的最優提早履約邊界及期權金 / 鄧思麒. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 96-102). / Abstracts in English and Chinese. / Tang, Sze Ki = Ji suan Mei shi mai quan de zui you ti zao lu yue bian jie ji qi quan jin / Deng Siqi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Black-Scholes Option Pricing Model --- p.1 / Chapter 1.1.1 --- Geometric Brownian Motion --- p.1 / Chapter 1.1.2 --- The Black-Scholes Equation --- p.3 / Chapter 1.1.3 --- The European Put Option --- p.5 / Chapter 1.1.4 --- The American Put Option --- p.7 / Chapter 1.1.5 --- Perpetual American Option --- p.9 / Chapter 1.2 --- Literature Review --- p.9 / Chapter 1.2.1 --- Direct Numerical Method --- p.10 / Chapter 1.2.2 --- Analytical Approximation --- p.11 / Chapter 1.2.3 --- Analytical Representation --- p.12 / Chapter 1.2.4 --- Mean-Reverting Lognormal Process --- p.13 / Chapter 1.2.5 --- Constant Elasticity of Variance Process --- p.15 / Chapter 1.2.6 --- Model Parameters with Time Dependence --- p.17 / Chapter 1.3 --- Overview --- p.18 / Chapter 2 --- Mean-Reverting Lognormal Model --- p.21 / Chapter 2.1 --- Moving Barrier Rebate Options under GBM --- p.21 / Chapter 2.2 --- Simulating American Puts under GBM --- p.25 / Chapter 2.3 --- Special Case: Time Independent Parameters --- p.26 / Chapter 2.3.1 --- Reduction to Ingersoll's Approximations --- p.26 / Chapter 2.3.2 --- Perpetual American Put Option --- p.28 / Chapter 2.4 --- Moving Barrier Rebate Options under MRL Process --- p.29 / Chapter 2.4.1 --- Reduction to Black-Scholes Model --- p.30 / Chapter 2.5 --- Simulating the American Put under MRL Process --- p.32 / Chapter 3 --- Constant Elasticity of Variance Model --- p.34 / Chapter 3.1 --- Transformations --- p.35 / Chapter 3.2 --- Homogeneous Solution on a Semi-Infinite Domain --- p.37 / Chapter 3.3 --- Particular Solution on a Semi-Infinite Domain --- p.38 / Chapter 3.4 --- Moving Barrier Options with Rebates --- p.39 / Chapter 3.5 --- Simulating the American Options --- p.40 / Chapter 3.6 --- Implication from the Special Case L = 0 --- p.41 / Chapter 4 --- Optimization for the Approximation --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- The Optimization Scheme --- p.44 / Chapter 4.2.1 --- Illustrative Examples --- p.44 / Chapter 4.3 --- Discussion --- p.45 / Chapter 4.3.1 --- Upper Bound of the Exact Early Exercise Price --- p.45 / Chapter 4.3.2 --- Tightest Lower Bound of the American Put Option Price --- p.48 / Chapter 4.3.3 --- Ingersoll's Early Exercise Decision Rule --- p.51 / Chapter 4.3.4 --- Connection between Ingersoll's Rule and Samuelson's Smooth Paste Condition --- p.51 / Chapter 4.3.5 --- Computation Efficiency --- p.52 / Chapter 4.4 --- Robustness Analysis --- p.53 / Chapter 4.4.1 --- MRL Model --- p.53 / Chapter 4.4.2 --- CEV Model --- p.55 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Multi-stage Approximation Scheme --- p.59 / Chapter 5.1 --- Introduction --- p.59 / Chapter 5.2 --- Multistage Approximation Scheme for American Put Options --- p.60 / Chapter 5.3 --- Black-Scholes GBM Model --- p.61 / Chapter 5.3.1 --- "Stage 1: Time interval [0, t1]" --- p.61 / Chapter 5.3.2 --- "Stage 2: Time interval [t1, T]" --- p.62 / Chapter 5.4 --- Mean Reverting Lognormal Model --- p.63 / Chapter 5.4.1 --- "Stage 1: Time interval [0, t1]" --- p.63 / Chapter 5.4.2 --- "Stage 2: Time interval [t1, T]" --- p.64 / Chapter 5.5 --- Constant Elasticity of Variance Model --- p.66 / Chapter 5.5.1 --- "Stage 1: Time interval [0, t1]" --- p.66 / Chapter 5.5.2 --- "Stage 2: Time interval [t1, T]" --- p.67 / Chapter 5.6 --- Duration of Time Intervals --- p.69 / Chapter 5.7 --- Discussion --- p.72 / Chapter 5.7.1 --- Upper Bounds for the Optimal Early Exercise Prices --- p.73 / Chapter 5.7.2 --- Error Analysis --- p.74 / Chapter 5.8 --- Conclusion --- p.77 / Chapter 6 --- Numerical Analysis --- p.79 / Chapter 6.1 --- Sensitivity Analysis of American Put Options in MRL Model --- p.79 / Chapter 6.1.1 --- Volatility --- p.79 / Chapter 6.1.2 --- Risk-free Interest Rate and Dividend Yield --- p.80 / Chapter 6.1.3 --- Speed of Mean Reversion --- p.81 / Chapter 6.1.4 --- Mean Underlying Asset Price --- p.83 / Chapter 6.2 --- Sensitivity Analysis of American Put Options in CEV Model --- p.85 / Chapter 6.2.1 --- Elasticity Factor --- p.87 / Chapter 6.3 --- American Options with time-dependent Volatility --- p.87 / Chapter 6.3.1 --- MRL American Options --- p.89 / Chapter 6.3.2 --- CEV American Options --- p.90 / Chapter 6.3.3 --- Discussion --- p.91 / Chapter 7 --- Conclusion --- p.94 / Bibliography --- p.96 / Chapter A --- Derivation of The Duhamel Superposition Integral --- p.101 / Chapter A.1 --- Time Independent Inhomogeneous Boundary Value Problem --- p.101 / Chapter A.2 --- Time Dependent Inhomogeneous Boundary Value Problem --- p.102

The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.

This paper studies the influence on the Japanese stock (cash and futures) markets of the Nikkei put warrants which were traded in Toronto and New York from February 1989 to April 1993. Implied changes in the Japanese prices based on the previous days’ North American warrant prices are compared to the actual price changes. Special attention is placed on the period from January 1990 to August 1992 when the Japanese stock market had a major decline.

Thesis (M.B.A.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 59).

This paper studies the influence on the Japanese stock (cash and futures) markets of the Nikkei put warrants which were traded in Toronto and New York from February 1989 to April 1993. Implied changes in the Japanese prices based on the previous days’ North American warrant prices are compared to the actual price changes. Special attention is placed on the period from January 1990 to August 1992 when the Japanese stock market had a major decline. / Business, Sauder School of / Graduate

Opbrengskoerse van vasterentedraende effekte verander as gevolg van veranderings in vraag en aanbod op die kapitaalmark. Die veranderinge in opbrengskoerse bei'nvloed die pryse van vasterentedraende effekte, asook van die opsies op hierdie effekte en stel beleggers in hierdie instrumente bloot aan beleggingsrisiko. Hierdie studie ondersoek die uitwerking van veranderings in die opbrengskoerse op die pryse van vasterentedraende eff ekte en opsies indien geen verskansing teen beleggingsrisiko toegepas word nie. Verder word verskillende verskansingstegnieke vergelyk ten einde te bepaal welke tegniek beleggingsrisiko die mees doeltreffendste kan beperk. Die studie toon aan dat dit wenslik is om beleggings en vasterentedraende effekte en opsies teen beleggingsrisiko te verskans. Empiriese toetse is op verskeie tegnieke gedoen om te bepaal watter verskansingstegnieke beleggingsrisiko die doeltreffendste kan beperk. Die gevolgtrekking is dat beleggingsrisiko inderdaad doeltreffend beperk kan word. Vir elke posisie in vasterentedraende en opsies is 'n spesifieke verskansingstegniek gei'dentifiseer om sodanige posisie doeltreffend in terme van winsgewendheid te verskans. / Yield on fixed interest bearing securities change as a result of changes in the supply and demand in the capital market. These changes in the yield influence the prices of fixed interest securities, as well as options on fixed interest securities and expose .investors in these instruments to investment risk. This study investigates the effect of changes in yield on the prices of fixed interest securities and options if no hedging against investment risk is instituted. Different techniques are compared to establish which technique will restrict investment risk effectively. This study shows that it is desirable to hedge investments in fixed interest securities and options against investment risk. Empirical tests were conducted on a variety of techniques to establish which technique would restrict investment risk effectively. The conclusion is that investment risk can be limited. A specific technique has been identified for each position in fixed interest securities and options that can hedge such a position effectively against investment risk in terms of profitability. / Business Management / MCOM (Bedryfsekonomie)

Thesis (MBA)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: The following study project was written by the author in the scope of his MBA Program at the University of Stellenbosch. While the number of articles and books that deal with the theory of real options is extremely large, the use of real options as a valuation tool is not widely accepted in practice. The reason for this obvious discrepancy is the fact that these papers and the models developed therein are highly mathematical and require a thorough knowledge of statistical methods. There are few papers or books that explain the fundamental ideas and basic techniques in such a way that general managers are likely to be convinced that real options valuation is an interesting and valuable tool. The purpose of this study project is to fill this gap, to bring the theory of real options closer to a wider range of people and to make it comprehensible for people who have not studied mathematics or finance. To achieve this aim the study project consists of four parts. Recalling the well-known concept of financial options, the first part explains in detail the basic idea of real options theory. The second part deals with the different existing models that are used to determine the value of real options. However, the focus lies on the comprehensibility of these models and not on the pure mathematical side. In the third and main part of this thesis the different variables that are needed for evaluating real options are discussed and methods to determine realistic values of these variables are explained. Some recommendations will be made as to what one ought to focus on in determining the variables. A valuation with "real" data is discussed in the fourth part. / AFRIKAANSE OPSOMMING: Die werkstuk is in die loop van die outeur se MBA-kursus aan die Universiteit van Stellenbosch voltooi. Die aantal bronne en artikels wat betrekking het op die teorie is eindeloos, terwyl die werklike opsies nog nie wyd aanvaar word in die praktyk nie. Die rede vir die ooglopende verskil is die feit dat die artikels wat betrekking het op die teorie en modelle hoogs wiskundig is en 'n deeglike kennis van statistiek vereis. Daar is tans 'n tekort aan artikels en boeke wat die fundamentele idees en basiese tegnieke van reële opsies verduidelik/oordra op so 'n manier dat dit deur algemene bestuurders gebruik kan word. Die doel van die werkstuk is om hierdie probleem te oorkom deur reële opsie valuasies aan 'n wyer gehoor bekend te stel wat nie 'n wiskundige of finansiele agtergrond beskik nie. Om bogenoemde doelwit te bereik, word die werkstuk in vier dele opgedeel. Die eerste deel verduidelik die basiese beginsel van reële opsie teorie in groot detail. Die tweede deeI dek die verskillende modelle wat tans gebruik word om reële opsies te waardeer. Die fokus Iê egter op die verstaanbaarheid van die modelle en nie noodwendig die wiskundige onder bou nie. In die derde en kerndeel van die verhandeling word die verskillende metodes om reële opsies te waardeer, bespreek, asook die maniere om realistiese waardes volgens verskillende metodes te vind. 'n Waardasie met werklike data word in die finale deel aangebied.

published_or_final_version / Real Estate and Construction / Master / Master of Science in Real Estate and Construction

published_or_final_version / Business Administration / Master / Master of Business Administration