Texas is the leading U.S. producer of cotton, and the U.S. is the largest international market supplier of cotton. Risks and uncertainties plague Texas cotton producers with unpredictable weather, insects, diseases, and price variability. Risk management studies have examined the risk reducing capabilities of alternative management strategies, but few have looked at the interaction of using several strategies in different combinations. The research in this study focuses on managing risk faced by cotton farmers in Texas using irrigation, put options, and yield insurance. The primary objective was to analyze the interactions of irrigation, put options, and yield insurance as risk management strategies on the economic viability of a 1,000 acre cotton farm in the Lower Rio Grande Valley (LRGV) of Texas. The secondary objective was to determine the best combination of these strategies for decision makers with alternative preferences for risk aversion. Stochastic values for yields and prices were used in simulating a whole-farm financial statement for a 1000 acre furrow irrigated cotton farm in the LRGV with three types of risk management strategies. Net returns were simulated using a multivariate empirical distribution for 16 risk management scenarios. The scenarios were ranked across a range of risk aversion levels using stochastic efficiency with respect to a function. Analyses for risk averse decision makers showed that multiple irrigations are preferred, and that yield insurance is strongly preferred at lower irrigation levels. The benefits to purchasing put options increase with yields, so they are more beneficial when higher yields are expected from applying more irrigation applications.

Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.

Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.

Philosophiae Doctor - PhD / Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided. / South Africa

Over 22 billion derivative contracts were traded on different stock exchanges globally during the year 2010 of which almost 50% were futures while the remaining 50% were options. An overall 25% increase in such contracts was registered as compared to those traded in the year 2009 (International Options Market Association (IOMA) Report, 2011).Investors often use a wide array of trading tools, market indicators and market trading strategies to get the best possible returns for the money that was invested. The main objective of this paper is to focus on the use of market sentiment indicators, specifically the Put-Call Ratio (PCR) as a predictor of returns for an investor.The Put-Call Ratio is defined as a ratio of the trading volume of put options to call options. It is called a sentiment indicator because it measures the “feelings” of option traders. Additionally, it has longed been viewed as an indicator of investors’ sentiment in the market (Put-Call Ratio, 2012) and is possibly the most favoured description of market psychology (James, 2011). / Dissertation (MBA)--University of Pretoria, 2012. / Gordon Institute of Business Science (GIBS) / unrestricted

Philosophiae Doctor - PhD / Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston's volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.

論文摘要 Reiner（1992）說明投資人對他國投資股票時，除了關心外國股價風險外，也關切匯率變動的風險，所以他提出了匯率連動選擇權，來規避匯率風險。另外，對於規避股價風險方面，Bouaziz, Briys and Crouhy（1994；以下簡稱BBC（1994））為了防止商品受人為操縱或其他原因而產生不合理的股價風險，提出遠期生效亞洲選擇權。以及Gray及Whaley（1999）提出了重設型賣權，它不但具有一般賣權的基本特徵，也能使投資人於購買股票時，同時買進一個重設型賣權。它不但可規避股價下跌的風險，在股價上升時，因賣權的重設使得保險的底值（Floor）向上提昇而鎖住股價上漲的資本利得。 本論文分別結合上述兩種選擇權的特徵（規避匯率風險與股價風險）而設計出兩種新金融商品，分別是：「匯率連動遠期生效亞洲選擇權」與「匯率連動重設型賣權」。它們的優點為：（1）可提供投資人同時對外國股價風險及匯率風險進行避險。（2）同時，評價模型的簡單化（類似Black-Scholes模型）以及避險操作的簡易性，使發行券商（或銀行）可獲得風險控管，因此可降低避險損失，提昇利潤。