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Agricultural loans issued to farmers in Virginia from the years 1980-1985 are examined to determine the factors which significantly predict repayment ability. Through a review of literature, extension meetings, conferences and informal conversation with agricultural lenders in the state, a list of financial variables and operation characteristics is compiled and analyzed. Results of the analysis are considered in terms of their immediate and potential assistance to lenders in making loan decisions. Using data from various commercial banks, Production Credit Associations and Farmers Home Administrations throughout Virginia, a model is developed to determine repayment ability of a borrower. Results indicate that several factors are significant in determining this process. Financial ratios such as percent equity, current debt, cash flow I and cash expense-cash receipt are important in determining if a borrower will repay his loan as scheduled. A number of operation characteristics were also found significant. These include: the number of creditors of the borrower, the amount of diversification of the operation and the amount of non-farm income. The results of the study should prove to be a significant aid to lenders and implies need for further research in the loan repayment area. / M.S.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised hyperbolic processes was studied. This approach was motivated by empirical evidence proving that models driven by a Brownian motion have several shortcomings, such as inability to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy processes and the change of measure techniques necessary for simplification and derivation of pricing formulae were also investigated. For robustness in numerical valuation, several transform methods were investigated and compared in terms of speed and accuracy. The models were calibrated to liquid South African data (ATM) interest rate caps using two methods of optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods. Two numerical valuation approaches had been implemented in this study, the COS method and the fractional fast Fourier transform (FrFT), and were compared to the existing methods in the context. Our numerical results showed that these two methods are quite efficient and very competitive. We have chose the COS method for calibration due to its rapidly speed and we have suggested a suitable approach for truncating the integration range to address the problems it has with short-maturity options. Our calibration results provided a nearly perfect fit, such that it was difficult to decide which model has a better fit to the current market state. Finally, all the implementations were done in MATLAB and the codes included in appendices. / AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer. Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde uitgloeimetode en die sekans-Levenberg–Marquardt-metode. Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.

Thesis (MSc)--Stellenbosch University, 2015 / AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in verband met die prysbepaling van vanielje-en eksotiese opsies, en vergelyk die prestasie van verskeie Lévy modelle. ’n Nuwe metode om modelrisiko te meet word ook voorgestel (hoofstuk 6). Ons kalibreer eers verskeie Lévy modelle aan die log-opbrengs van die S&P500 indeks. Statistiese toetse en grafieke voorstellings toon albei aan dat suiwer sprongmodelle (VG, NIG en CGMY) die verdeling van die opbrengs beter beskryf as die Black-Scholes model. Daarna kalibreer ons hierdie vier modelle aan S&P500 indeks opsie data en ook aan "CGMY-wˆ ereld" data (’n gesimuleerde wÃłreld wat beskryf word deur die CGMY-model) met behulp van die wortel van gemiddelde kwadraat fout. Die CGMY model vaar beter as die VG, NIG en Black-Scholes modelle. Ons waarneem ook ’n effense verskil tussen die nuwe parameters van CGMY model en sy wisselende parameters, ten spyte van die feit dat CGMY model gekalibreer is aan die "CGMYwêreld" data. Versperrings-en terugblik opsies word daarna geprys, deur gebruik te maak van die gekalibreerde parameters vir ons modelle. Hierdie pryse word dan vergelyk met die "ware" pryse (bereken met die ware parameters van die "CGMY-wêreld), en ’n beduidende verskil tussen die modelpryse en die "ware" pryse word waargeneem. Ons eindig met ’n poging om hierdie modelrisiko te kwantiseer / ENGLISH ABSTRACT : The growing interest in calibration and model risk is a fairly recent development in financial mathematics. This thesis focussing on these issues, particularly in relation to the pricing of vanilla and exotic options, and compare the performance of various Lévy models. A new method to measure model risk is also proposed (Chapter 6). We calibrate only several Lévy models to the log-return of S&P500 index data. Statistical tests and graphs representations both show that pure jump models (VG, NIG and CGMY) the distribution of the proceeds better described as the Black-Scholes model. Then we calibrate these four models to the S&P500 index option data and also to "CGMY-world" data (a simulated world described by the CGMY model) using the root mean square error. Which CGMY model outperform VG, NIG and Black-Scholes models. We observe also a slight difference between the new parameters of CGMY model and its varying parameters, despite the fact that CGMY model is calibrated to the "CGMY-world" data. Barriers and lookback options are then priced, making use of the calibrated parameters for our models. These prices are then compared with the "real" prices (calculated with the true parameters of the "CGMY world), and a significant difference between the model prices and the "real" rates are observed. We end with an attempt to quantization this model risk.

Standard finance theory portrays investors as rational utility maximisers. Persisting market anomalies and observed investor practice, however, have led to widespread recognition that the fundamental axioms of rationality are often violated. In response to the limitations inherent in standard theory, the Behavioural Finance approach relaxes the rationality assumption and takes account of psychological influences on individuals’ decision-making processes. Adopting the behavioural approach, this thesis, which includes two empirical studies, examines why, and to what extent, investors depart from rational or optimal investment practices. The thesis examines the effect of Myopic Loss Aversion (MLA) suggested by Benartzi and Thaler (1995) as a response to the Equity Premium Puzzle highlighted by Mehra and Prescott (1985). While previous studies are almost exclusively based on experiments in a laboratory setting, this approach provides more compelling empirical evidence by investigating the effects of MLA on real individual investors’ portfolio allocations through the use of the Dutch National Bank Household Survey. For the first time, the concept of MLA is identified through the interaction of two separate effects, firstly, individuals’ myopia, reflected in portfolio evaluation and rebalancing frequencies, and secondly, loss aversion. The thesis finds that individuals who are less affected by MLA invest more in risky financial assets. Further, individuals who are less myopic increase their share of risky assets invested in their financial portfolios over time, although this is unrelated to their loss aversion. These findings support the prediction of MLA theory that short investment horizons and high loss aversion lead to a significantly lower share of risky investments. In summary, the high equity premium can be explained by the notion of MLA. If individuals evaluate their investment performance over the long-term, they perceive much smaller risks relative to stockholding returns; consequently, they will be prepared to accept smaller equity premiums. The findings suggest possible interventions by policy makers and investment advisors to encourage individuals to remain in the stock market, such as providing long-term investment instruments, or restricting evaluation frequency to the annual reporting of investment performance. In response to the stockholding puzzle (Haliassos and Bertaut, 1995), this thesis also investigates individuals’ stock market returns expectations and their varying levels of risk aversion. Previous studies find that individuals’ heterogeneous stock market expectations determine variations in their stockholdings. The thesis accounts for the effect of risk aversion on stock market expectations, as well as on stockholding decisions. Additionally, the causality issue as between individuals’ expectations and stockholding status is controlled. The thesis finds that more risk averse individuals hold lower stock market expectations, and that the stock market return expectations of more risk averse individuals affect their stock market participation decisions negatively. The portfolio allocation decisions of individuals who already hold stocks are only affected by their expectations, with risk aversion being no longer significant. The thesis argues that persistent risk aversion effects cause individuals to hold pessimistic views of stock market returns, thus contributing to the enduring stockholding puzzle. The thesis reinforces existing perceptions that individuals in the real world may not make fully rational decisions due to their judgments which are based on heuristics and affected by cognitive biases. Individual investors often fail to maximise their utility given their preferences and constraints. Consequently, this thesis draws attention to the possible role of institutions, policy makers, and financial advisory bodies in providing effective interventions and guidelines to improve individuals’ financial decisions.

A thesis presented to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of Witwatersrand in fulfilment of the requirements for the degree of Master of Commerce (M.Com) in Business Finance, January 2017 / Diversification has remained a central tenet in investment theory over multiple decades due to its demonstrated value as a risk mitigation technique. Increasing the number assets in a portfolio, where the magnitude of correlation is relatively slim, increases the amount of diversification while also encountering increased costs in the form of transaction costs, taxes and the like. Thus, it is imperative to solve for the optimal point of diversification to ensure an investor does not encounter unnecessary costs. This study aims to solve for the point of optimal diversification in an equity portfolio, focusing on the South African environment. This is achieved by employing a framework using both the traditional simulation method as well as more advanced mathematical techniques, namely: genetic programming and particle swarm optimisation. Marked improvements are realised in this study with regards to the methodology and results through the application of advanced mathematical approaches in addition to removing the restriction of equal weightings being applied to each share in the portfolio. The results revealed that an optimal portfolio can be constructed using up to only 15 shares. Secondly, the genetic programming approach demonstrated increased strength compared to the traditional simulation and particle swarm optimisation approaches, obtaining a greater level of diversification with fewer shares. Finally, although the aim of the study is focused on modelling the relationship between the number of shares in a portfolio and the achievable diversification benefits, it is also established that the portfolios indicated as being optimally diversified achieved market beating returns. / XL2018

Fads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of stochastic calculus and optimization to obtain analogous results to those obtained in the purely continuous market. We approximate optimal portfolios and utilities using the instantaneous centralized and quasi-centralized moments of the stocks percentage returns. We also link the random portfolios of the investors, under asymmetric information to the purely deterministic optimal portfolio, under symmetric information. / by Winston S. Buckley. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Bibliography: leaves 268-272.

In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we prove the strong convergence of the exchange rate approximations and the convergence of Monte Carlo estimators for a number of vanilla and exotic options. Then, we calibrate the model to market data and discuss its fitness for pricing FX options. Next, due to the relatively slow convergence of the Monte Carlo method in the number of simulations, we examine a variance reduction technique obtained by mixing Monte Carlo and finite difference methods via conditioning. We consider a purely stochastic version of the model and price vanilla and exotic options by simulating the paths of the volatility and the short rates, and then evaluating the "inner" Black-Scholes-type expectation by means of a partial differential equation. We prove the convergence of numerical approximations and carry out a theoretical variance reduction analysis. Finally, we illustrate the efficiency of the method through a detailed quantitative assessment.

General diffusion processes (GDP), or Ito's processes, are potential candidates for the modeling of asset prices, interest rates and other financial quantities to cope with empirical evidence. This thesis considers the applications of general diffusions in finance and potential extensions. In particular, we focus on financial problems involving (optimal) stopping times. A typical example is the valuation of American options. We investigate the use of Laplace-Carson transform (LCT) in valuing American options, and discuss its strengthen and weaknesses. Homotopy analysis from topology is then introduced to derive closed-form American option pricing formulas under GDP. Another example is taken from optimal dividend policies with bankruptcy procedures, which is closely related to excursion time and occupation time of a general diffusion. With the aid of Fourier transform, we further extend the analysis to the case of multi-dimensional GDP by considering the currency option pricing with mean reversion and multi-scale stochastic volatility. / Zhao, Jing. / Adviser: Hoi-Ying Wong. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 97-105). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

An important application of term structure models is to measure the difference between the evolutions of two yield curves starting from the same initial point. Such a geometric problem can be tackled by use of the notion of information geometry after the mapping of yield curves to density functions on a Hilbert space. We prove that a pair of yield curves with large initial Bhattacharyya spherical distance would diverge from each other with a significant probability. / Finally, we implement the proposed model with initial data in the US swap market for 15 Feb, 2007. To test our model improvements over the traditional models, we also run the simulation with the Hull-White model and compare these two no-arbitrage models in various major characteristics. It shows that the proposed model forms a bridge linking interest rates and discount bonds, namely, given the initial term structure density and the volatility structure, we are able to reconstruct the short rate process and the bond price process. Our term structure density model is thus a unification of traditional models each having its own advantage. / Following the initial study of Brody and Hughston on applying information geometry to interest rate modeling, we propose a novel term structure model and investigate its application in the US swap market. Different from the traditional term structure models that impose assumptions on either bonds or rates, the newly proposed model is characterized by the evolution of a density function which is obtained from the derivative of the discount function with respect to the time left till maturity. We prove that such a density function can be interpreted as interest return on the discount bond. / The introduction of the term structure density turns the problem of yield curve dynamics into a problem of the evolution of a density distribution. There are at least three steps to model the dynamics of the density function: calibrate the initial term structure density, specify the market risk premium, and choose a proper volatility structure. First, we introduce two initial calibration methods, one by maximizing the Tsallis entropy and the other by the notion of superstatistics. By use of either method, we deduce a power-law distribution for the initial term structure density function. The entropy index q in this function, which is a well-known physics quantity, now finds its financial interpretation as the measure of departure of the current term structure from flatness on a continuously compounded basis. Our empirical experiments in the US swap market fully demonstrate this observation. Next, given the calibrated initial density, we develop the term structure dynamics in the risk-neutral world and prove that the market risk premium is immaterial. To deduce a concise martingale representation for the bond pricing formula, we choose a density volatility that possesses zero mean. Finally, as an illustration of the importance of volatility structure, the HJM volatilities are redesigned for interest rate positivity under the framework of the current model. / Yang, Yiping. / Adviser: Kwong Chung Ping. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 187-192). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.