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

A teoria de opções propicia um vasto campo de aplicações. No Brasil, a aplicação desta teoria à estabilidade financeira vem se tornando cada vez mais favorável: 1) pela relativa estabilidade da economia, 2) pela determinação do Banco Central do Brasil no sentido de controlar o risco das instituições financeiras e 3) pelo natural desenvolvimento do mercado financeiro brasileiro. Esta tese está dividida em três ensaios e os dois primeiros focaram numa abordagem de poder de previsão. No primeiro, compararam-se volatilidades estimadas por diferentes modelos vis-à-vis a volatilidade realizada e encontrou-se alguma evidência empírica de que as implícitas do modelo de Vasicek-Estendido são informacionalmente superiores às dos outros modelos. No segundo, mostrou-se que é possível utilizar medidas da classe “distância ao default" para atribuir classificação de risco a bancos dentro do setor bancário brasileiro. No terceiro ensaio, analisou-se a nova Lei de Falência usando a teoria de opções e a teoria dos contratos. Conclui-se dos três ensaios que a teoria de opções é uma boa ferramenta para avaliar questões de estabilidade financeira. / The option pricing theory provides a myriad of applications. In Brazil, the application of this theory to financial stability is becoming more and more favourable: 1) for the increasing stability of the economy, 2) for the commitment of the Central Bank of Brazil in controlling the risk of the financial institutions and 3) for the development of the Brazilian financial market. This thesis is divided in three essays and the first two focused on a predictive-power approach. In the first one, volatilities estimated by different models were compared vis-à-vis the realized volatility and we obtained some empirical evidence that the Extended-Vasicek’s implied volatility is informationally superior to the other models’. In the second one, it was argued that it is possible to use measures of the class “distance to default" in order to rank the banks of the Brazilian banking sector in terms of risk. In the third essay, the new Brazilian Bankruptcy Law is analysed by using the option pricing theory and the theory of contracts. The three essays conclude that the option pricing theory is a good tool to evaluate financial stability issues.

Doctor of Philosophy(PhD) / This thesis builds on the real estate lease model of Grenadier which consists of the Black Scholes PDE and an upper reflecting boundary condition. Extending the method of images of Buchen, a new technique was developed to solve this class of problems. Problems that previously required difficult integration can now be solved with algebra and simple integrals. In addition, the compound option in this framework is solved using this new technique. To the best of our knowledge the solution of the compound problem has not been published. An interesting symmetry between this class of problems and the lookback option was also discovered and described in this thesis. The extension of the method of images to include problems with the reflecting boundary condition in the context of real estate leases was presented at the Financial Integrity Research Network Doctoral Tutorials at the University of Technology, Sydney, in 2006. The presentation was awarded the ``FIRN Best Paper Award''. This paper has been submitted to the Journal of Financial Mathematics for publication. The solution to the compound problem in the context of the upward-only market review option is the subject of the next paper.

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

One of the main challenges that investors in the Clean Development Mechanism (CDM) project face is the management of the volatility of the price of Certified Emission Reduction (CERs). Large scale CDM projects require a long-term investment with significant amount of costs, and this type of investment is often irreversible. Project investors should quantitatively assess the CER trigger price that justifies the initiation of a CDM investment. The traditional discounted cash flow valuation is unable to capture the option value associated with uncertain investment, and thus it tends to underestimate the trigger price which initiates the investment. Real options theory explicitly considers the option value of delayed investment and can provide a better measurement of the trigger price. This paper presents a theoretical model of the CDM investment project and derives the CER trigger prices that guide investment decisions by using historical market data. It develops a stochastic dynamic programming model for both the geometric Brownian motion process and the mean-reverting process. An analytical solution for the trigger price is derived for the former process, and the trigger price is numerically estimated for the latter. By considering various parameter values, it analyzes the effects of different market environments on the trigger price.

American options are financial contracts that allow exercise at any time until ex- piration. While the pricing of standard American option contracts has been well researched, with a few exceptions no analytical solutions exist. Valuation of more in- volved American option contracts, which include multiple underlying assets or path- dependent payoff, is still to a high degree an uncharted area. Most numerical methods work badly for such options as their time complexity scales exponentially with the number of dimensions. In this Master’s thesis we study valuation methods based on Monte Carlo sim- ulations. Monte Carlo methods don’t suffer from exponential time complexity, but have been known to be difficult to use for American option pricing due to the forward nature of simulations and the backward nature of American option valuation. The studied methods are: Parametrization of exercise rule, Random Tree, Stochastic Mesh and Regression based method with a dual approach. These methods are evaluated and compared for the standard American put option and for the American maximum call option. Where applicable the values are compared with those from deterministic reference methods. The strengths and weaknesses of each method is discussed. The Regression based method essentially reduces the problem to one of selecting suitable basis functions. This choice is empirically evaluated for the following Amer- ican option contracts; standard put, maximum call, basket call, Asian call and Asian call on a basket. The set of basis functions considered include polynomials in the underlying assets, the payoff, the price of the corresponding European contract as well as certain analytic approximation of the latter. Results from the empirical studies show that the regression based method is the best choice when pricing exotic American options. Furthermore, using available analytical approximations for the corresponding European option values as a basis function seems to improve the performance of the method in most cases.

One of the main challenges that investors in the Clean Development Mechanism (CDM) project face is the management of the volatility of the price of Certified Emission Reduction (CERs). Large scale CDM projects require a long-term investment with significant amount of costs, and this type of investment is often irreversible. Project investors should quantitatively assess the CER trigger price that justifies the initiation of a CDM investment. The traditional discounted cash flow valuation is unable to capture the option value associated with uncertain investment, and thus it tends to underestimate the trigger price which initiates the investment. Real options theory explicitly considers the option value of delayed investment and can provide a better measurement of the trigger price. This paper presents a theoretical model of the CDM investment project and derives the CER trigger prices that guide investment decisions by using historical market data. It develops a stochastic dynamic programming model for both the geometric Brownian motion process and the mean-reverting process. An analytical solution for the trigger price is derived for the former process, and the trigger price is numerically estimated for the latter. By considering various parameter values, it analyzes the effects of different market environments on the trigger price.

Background: In an increasingly globalized environment, corporations perform transactions across borders on a day-to-day basis. As multinational corporations expand their businesses the number of currencies in their operations increases. The consequence of operating with several currencies is the risk associated with currency fluctuations. Sandvik AB is a worldwide corporation where activities are conducted through representation in more than 130 countries. Currency exposures are controlled through risk management where financial derivatives are applied to protect the corporation from potential losses caused by fluctuations. Sandvik AB recently implemented a hedging strategy entitled Layered Basket Option hedging. The strategy is a combination of a layered- and a basket option approach to maximize the effect of the hedge. There is a limited amount of previous research regarding Layered Basket Option hedging and Sandvik AB is the first corporation to actively practice this strategy. Purpose: The purpose is to investigate and provide information about how currency risk most effectively is hedged for the multinational corporation Sandvik AB. Furthermore, we want to evaluate if Sandvik’s recently implemented hedging strategy, Layered Basket Option hedging, is the best-suited strategy for them and if there are any improvements to be made. This thesis will further investigate the importance of currency hedging for multinational corporations, which are dependent on reporting to their stakeholders. Hopefully, this thesis will also facilitate the communication of Sandvik’s currency strategies throughout the organization and make it more comprehensible. Method: Exchange rates on daily basis for the period 2002-2012 were collected from Bank of Canada and Reuters database. The collected data was thereafter used as a basis to perform calculations to determine if Layered Basket Option hedging is the optimal solution for Sandvik AB. Conclusion: The results of this study highlight the benefits from applying a Layered Basket Option hedging strategy and the strategy succeeds to reduce the volatility caused by currency fluctuation. The results indicate that the combination of a layered- and a basket option approach successfully creates a suitable strategy for Sandvik AB. Furthermore, this thesis has recognized that there exists room for improvement by actively allocating currencies according to their weights and correlations to fully exploit the effects from the strategy.

<p>The first essay of my dissertation introduces a new method for eliciting market beliefs about the expected outcomes of a merger negotiation after announcement. During a merger negotiation, the market prices of the firms involved</p><p>reflect beliefs about their values both in the merged and</p><p>standalone states, as well as the likelihood of either outcome.</p><p>These beliefs determine stock price reactions to news of a possible</p><p>merger, but those prices alone do not contain sufficient information</p><p>to identify the latent beliefs that they reflect. I develop a new</p><p>method which, by using additional data in the form of option prices,</p><p>is able to identify these beliefs. This method allows for a clear</p><p>decomposition of a negotiating firm's expected value change into two</p><p>parts: the value of the transaction to the firm, and new information</p><p>about its standalone value. Previous research into estimating</p><p>merger synergies has struggled to obtain an appropriate alternative</p><p>against which to measure the realized outcome. The market's beliefs</p><p>about state-contingent firm values give an estimate of both. Through</p><p>a direct comparison of the estimates of a firm's value in both the</p><p>merged and standalone states, I obtain a strong, practical measure</p><p>of the expected value-creating potential of a merger before its</p><p>consummation.</p><p>The second essay applies the state-contingent payoff estimation method developed previously to addressing questions about the size effect in mergers. A growing body of evidence indicates that large acquisitions destroy value. However, we do not yet know why. Several theories have been advanced, but their effects are difficult to observe in isolation. It has thus been impossible to tell whether negative post-announcement acquirer returns are caused by market expectations of value-destroying acquisitions or revealed bad news about standalone value. This paper resolves this issue by decomposing expectations about merger outcomes into expected value change from completing the acquisition and revision of beliefs about standalone firm value. The data show that deal size is correlated with value destruction, while acquirer size is correlated with release of unfavorable information. Deal size correlates with value destruction, acquirer size with bad news about the firm. Furthermore, the results suggest that overpayment is a prerequisite for large acquisitions. These findings reduce the set of possible theoretical explanations for the size effect.</p> / Dissertation

This thesis is composed of two parts. The first parts deals with a technique for pricing American-style contingent options. The second part details a statistical arbitrage model using statistical process control approaches. We propose a novel simulation approach for pricing American-style contingent claims. We develop an adaptive policy search algorithm for obtaining the optimal policy in exercising an American-style option. The option price is first obtained by estimating the optimal option exercising policy and then evaluating the option with the estimated policy through simulation. Both high-biased and low-biased estimators of the option price are obtained. We show that the proposed algorithm leads to convergence to the true optimal policy with probability one. This policy search algorithm requires little knowledge about the structure of the optimal policy and can be naturally implemented using parallel computing methods. As illustrative examples, computational results on pricing regular American options and American-Asian options are reported and they indicate that our algorithm is faster than certain alternative American option pricing algorithms reported in the literature. Secondly, we investigate arbitrage opportunities arising from continuous monitoring of the price difference of highly correlated assets. By differentiating between two assets, we can separate common macroeconomic factors that influence the asset price movements from an idiosyncratic condition that can be monitored very closely by itself. Since price movements are in line with macroeconomic conditions such as interest rates and economic cycles, we can easily see out of the normal behaviors on the price changes. We apply a statistical process control approach for monitoring time series with the serially correlated data. We use various variance estimators to set up and establish trading strategy thresholds.