Dans la mesure où les environnements économiques et financiers sont régis par de nombreux aléas, la prise de décision en matière d'investissement immobilier s'avère de plus en plus complexe.Le premier chapitre commence par présenter les méthodes traditionnelles d'évaluation des choix d'investissement dans le secteur immobilier. La notion d'option réelle est ensuite introduite au travers du lien entre les options réelles et les options financières. Le deuxième chapitre s'intéresse à différents cas de recours aux options réelles dans le secteur immobilier en faisant systématiquement référence à la littérature qui leur est consacrée. Le troisième chapitre présente des analyses de mesure de la performance et de dynamique des rendements et de volatilité sur les marchés européens et américains. / As the economic and financial environments are governed by many uncertainties, decision-making on real estate investments is becoming increasingly complex.The first chapter begins by presenting the traditional methods to value real estate investments. The concept of real options is then introduced through the link between real options and financial options. The second chapter focuses on different use cases of real options in the real estate industry by referring to the literature devoted to them. The third chapter presents a performance measurement analysis and a study of the dynamics of returns and volatility in European and American markets.

實證證據顯示商品價格有均值回歸和跳躍的特性。由於一些商品期權收益涉及歷史商品價格的算術平均，因此我們求出算術亞式期權在均值回歸跳躍擴散過程下的分析解。比分析解是對資產價格最終值和實際平均值的聯合特徽函數進行快速傅立葉變換獲得。我們通過數值模擬研究來檢驗此建議方法的準確度和計算效率。 / Empirical evidence indicates that commodity prices are mean reverting and exhibit jumps. As some commodity option payoff involves the arithmetic average of historical commodity prices, we derive an analytical solution to arithmetic Asian options under a mean reverting jump diffusion process. The analytical solution is implemented with the fast Fourier transform based on the joint characteristic function of the terminal asset price and the realized average value. We also examine the accuracy and computational efficiency of the proposed method through numerical studies. / Detailed summary in vernacular field only. / Chung, Shing Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 40-42). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Model with constant parameters --- p.5 / Chapter 2.1 --- Model specification --- p.6 / Chapter 2.2 --- Joint characteristic function --- p.8 / Chapter 3 --- Model with time-dependent parameters --- p.12 / Chapter 3.1 --- Model specification --- p.13 / Chapter 3.2 --- Joint characteristic function --- p.13 / Chapter 4 --- Fast Fourier transform on Asian option prices --- p.18 / Chapter 5 --- Numerical results --- p.20 / Chapter 5.1 --- Comparison of the analytical solution and Monte Carlo simulation . --- p.20 / Chapter 5.2 --- Price sensitivity and model parameters --- p.26 / Chapter 5.3 --- Price sensitivity and payoff structure --- p.26 / Chapter 6 --- Conclusion --- p.33 / Chapter A --- Normally distributed jump size --- p.34 / Bibliography --- p.40

The main contribution of this thesis is to examine binary options within the British payoff mechanism introduced by Peskir and Samee. This includes British cash-or-nothing put, British asset-or-nothing put, British binary call and American barrier binary options. We assume the geometric Brownian motion model and reduce the optimal stopping problems to free-boundary problems under the Markovian nature of the underlying process. With the help of the local time-space formula on curves, we derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterised as the unique solution to a non-linear integral equation. We begin by investigating the binary options of American-type which are also called `one-touch' binary options. Then we move on to examine the British binary options. Chapter~2 reviews the existing work on all different types of the binary options and sets the background for the British binary options. We price and analyse the American-type (one-touch) binary options using the risk-neutral probability method. In Chapters~3 ~4 and ~5, we present the British binary options where the holder enjoys the early exercise feature of American binary options whereupon his payoff is the `best prediction' of the European binary options payoff under the hypothesis that the true drift equals a contract drift. Based on the observed price movements, if the option holder finds that the true drift of the stock price is unfavourable then he can substitute it with the contract drift and minimise his losses. The key to the British binary option is the protection feature as not only can the option holder exercise at unfavourable stock price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive high returns. Chapters~3 and~4 focus on the British binary put options and Chapter~5 on call options. We also analyse the financial meaning of the British binary options and show that with the contract drift properly selected the British binary options become very attractive alternatives to the classic European/American options. Chapter~6 extends the binary options into barrier binary options and discusses the application of the optimal structure without a smooth-fit condition in the option pricing. We first review the existing work for the knock-in options and present the main results from the literature. Then we examine the method in \cite{dai2004knock} in the application to the knock-in binary options. For the American knock-out binary options, the smooth-fit property does not hold when we apply the local time-space formula on curves. We transfer the expectation of the local time term into a computational form under the basic properties of Brownian motion. Using standard arguments based on Markov processes, we analyse the properties of the value function.

<p>This thesis conserns stock options. The writers major task has been to analyse and to show under which circumstanses, according to swedish law, options are considered to be stock options.</p>

This thesis conserns stock options. The writers major task has been to analyse and to show under which circumstanses, according to swedish law, options are considered to be stock options.

An Asian option is a path-dependent option whose payoff depends on the average of the underlying asset price over a certain time interval. It can be European or American. The time interval can be the entire interval of the option's life from the initiation to the expiration, or beginning from some time later than the initiation until the option's expiration. The average can be arithmetic or geometric. This paper derives a closed-form solution for the valuation of European Geometric average fixed strike Asian call option and a closed-form solution for the valuation of a forward-starting Asian call option with arithmetic average floating strike. The valuation formula is obtained by relying upon a slight linear approximation. And the valuation formula of Asian call option with arithmetic average floating strike we have derived is different from that of L. Bouaziz, E. Briys and M. Crouhy (1994). We believe that our argument here is correct, and theirs is wrong.

This paper applies a real option approach to analyze the optimal decisions of mergers, stock offers, and cash offers. We use the two-stage approach to investigate the optimal decisions of mergers and acquisitions. At the first stage, the merger company has to choose the target company to obtain the largest synergy, which comes from the increasing return to scale, improved performance, acquired R&D, and increased market power. At the second stage, the main work is to determine the takeover threshold (timing), exchange rate of stocks or bid premium under the three forms of mergers and acquisitions. We find that the increasing return to scale, improved performance, and increased market power will lower takeover threshold and speed up merger activity. Finally, the forms of mergers and acquisitions will affect the timing and the returns of the acquirer and acquiree. Cash offers will happen even later than mergers and stock offers. This thesis also constructs a model to study the multi-firms¡¦ merger strategies and derives the multi-firms¡¦ synergy value, timing and terms of merges. In addition, we study the effect of firms¡¦ competitive intensity, market power, fixed cost, and demand shocks on the decisions of merges. We find that the increased competitive intensity, increased market power, higher fixed cost, and lower demand shocks will enhance the motives of merges and accelerate merger activities.

The first option has been publicly traded for more than 30 years. With the progress of time, despite the European option is still the exchange-traded option. But evolved through the years, the European option has not meet people's needs, so exotic option was born. Similarly, the pricing model, from the traditional closed-form solution (under the Black-Scholes assumption), now commonly used binomial trees, finite difference, or by using the Monte Carlo simulation. The main impact of the following factors: the first, with the complexity of the option contract - from single asset to multi-assets, from the plain vanilla option to the path-dependent option, it is more difficult to find the closed-form solution of the option. Second, with the development of personal computers, making numerical computing is no longer a difficult task. It is precisely these two front reason, there will be the birth of this article. Himalaya option is also an exotic options. With the multi-assets and path dependent features, we want to find a closed-form solution is very difficult. Under multi-assets situation, the binomial tree and finite difference will be time-consuming calculation. Therefore, this paper is using Monte Carlo simulation of reasons. In this paper, we use Monte Carlo simulation to pricing Himalaya option, which includes several variance reduction techniques used to reduce sample variance. Finally, when pricing completed, we try to do a simple study to option hedging.

Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type. / In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit. / The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.