We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial applications. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities will always exist. No-arbitrage bounds are derived in closed form for a given covariance matrix using the least possible number of scenarios. Empirical examples illustrate the practical potential of knowing these bounds. (authors' abstract)

Total valuation adjustment (XVA) is a new technique which takes multiple material financial factors into consideration when pricing derivatives. This paper explores how funding costs and counterparty credit risk affect pricing the American option based on no-arbitrage analysis. We review previous studies of European option pricing with different funding costs. The conclusions help to compute the no- arbitrage price of the American option in the model with different borrowing and lending rates. Another model with counterparty credit risk is set up, and this pricing approach is referred to as credit valuation adjustment (CVA). A defaultable bond issued by the counterparty is used to hedge the loss from the option's default. We incorporate these two models to assess the XVA of an American option. The collateral, which protects the option investors from default, is considered in our benchmark model. To illustrate our results, numerical experiments are designed to demonstrate the relationship between XVA and parameters, which include the funding rates, bond's rate of return, and number of periods.

We compare two popular scenario tree generation methods in the context of financial optimization: Moment matching and scenario reduction. Using a simple problem with a known analytic solution, we find that moment matching - accompanied by a check to ensure absence of arbitrage opportunities - replicates this solution precisely. On the other hand, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions to the approximate optimization problem represented by the reduced tree are biased and highly variable. These results hold for correlated and uncorrelated asset returns, as well as for normal and non-normal returns. (authors' abstract)

An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges, and also study a continuous-time limit in which premium is paid at a certain rate per unit time. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Models of the term structure of interest rates play a central role in the modern theory of pricing bonds and other interest rate claims. Term structure models based on the principle of no-arbitrage, especially those of the Heath-Jarrow-Morton (1992) class, have become very popular recently, both with academics and practitioners. Surprisingly however, although the implied volatility function plays a crucial role in these no-arbitrage term structure models, there is little systematic evidence to guide optimal model specification within this broad class. We study the implied volatility in the Heath-Jarrow-Morton framework using Eurodollar futures options data. We estimate a daily time series of forward rates within the HJM framework such that, by construction, the predicted futures prices from our model exactly match the observed futures prices. Next, we estimate a daily time series of volatility parameters such that the sum of squared errors between futures options prices predicted by the model and observed futures options prices is minimized. We use the six different volatility specifications suggested by Amin and Morton (1994) within the HJM class of models to price interest rate claims. Since the volatilities are the only unobservables, we use these models to infer the volatilities from the market prices of Eurodollar futures options over the 1987-1998 periods. The minimized sum of squared errors in the option prices is used as the measure of accuracy of each specific model. Each model differs from the others in its ability to match the market option prices and the time required for the computation. We compare the performances of the six volatility specifications in the accuracy-versus-computation time tradeoff. We document the systematic biases between the model and market prices as a function of option type, maturity, and moneyness. We also examine alternative numerical implementations of HJM models using the six volatility specifications. In particular, we analyze the impact on accuracy and computation time of using different numbers of time-steps. We also examine the effect of using time-steps of varying lengths within the same estimation procedure, and of ordering the time-steps in different ways. / Ph. D.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of interest rates that determines the joint dynamics of the term structure and the macroeconomic fundamentals under no-arbitrage approach. There has been a long search during the past decades of trying to study the relationship between the term structure of interest rates and the economy, to the extent that much of recent research has combined elements of finance, monetary economics, and the macroeconomics to analyse the term structure. The central interest of the thesis is based on two important notions. Firstly, it is picking up from the important work of Ang and Piazzesi (2003) model who suggested a joint macro- finance strategy in a discrete time affine setting, by also imposing the classical Taylor (1993) rule to determine the association between yields and macroeconomic variables through monetary policy. There is a strong intuition from the Taylor rule literature that suggests that such macroeconomic variables as in inflation and real activity should matter for the interest rate, which is the monetary policy instrument. Since from this important framework, no-arbitrage macro-finance approach to the term structure of interest rates has become an active field of cross-disciplinary research between financial economics and macroeconomics. Secondly, the importance of forecasting the yield curve using the variations on the Nelson and Siegel (1987) exponential components framework to capture the dynamics of the entire yield curve into three dimensional parameters evolving dynamically. Nelson-Siegel approach is a convenient and parsimonious approximation method which has been trusted to work best for fitting and forecasting the yield curve. The work that has caught quite much of interest under this framework is the generalized arbitrage-free Nelson-Siegel macro- nance term structure model with macroeconomic fundamentals, (Li et al. (2012)), that characterises the joint dynamic interaction between yields and the macroeconomy and the dynamic relationship between bond risk-premia and the economy. According to Li et al. (2012), risk-premia is found to be closely linked to macroeconomic activities and its variations can be analysed. The approach improves the estimation and the challenges on identication of risk parameters that has been faced in recent macro-finance literature. / AFRIKAANSE OPSOMMING: Hierdie werk ontleed die makro- nansiese modelle van die term struktuur van rentekoers pryse wat die gesamentlike dinamika bepaal van die term struktuur en die makroekonomiese fundamentele faktore in 'n geen arbitrage wêreld. Daar was 'n lang gesoek in afgelope dekades gewees wat probeer om die verhouding tussen die term struktuur van rentekoerse en die ekonomie te bestudeer, tot die gevolg dat baie onlangse navorsing elemente van nansies, monetêre ekonomie en die makroekonomie gekombineer het om die term struktuur te analiseer. Die sentrale belang van hierdie proefskrif is gebaseer op twee belangrike begrippe. Eerstens, dit tel op by die belangrike werk van die Ang and Piazzesi (2003) model wat 'n gesamentlike makro- nansiering strategie voorstel in 'n diskrete tyd a ene ligging, deur ook die klassieke Taylor (1993) reël om assosiasie te bepaal tussen opbrengste en makroekonomiese veranderlikes deur middel van monetêre beleid te imposeer. Daar is 'n sterk aanvoeling van die Taylor reël literatuur wat daarop dui dat sodanige makroekonomiese veranderlikes soos in asie en die werklike aktiwiteit moet saak maak vir die rentekoers, wat die monetêre beleid instrument is. Sedert hierdie belangrike raamwerk, het geen-arbitrage makro- nansies benadering tot term struktuur van rentekoerse 'n aktiewe gebied van kruis-dissiplinêre navorsing tussen nansiële ekonomie en makroekonomie geword. Tweedens, die belangrikheid van voorspelling van opbrengskromme met behulp van variasies op die Nelson and Siegel (1987) eksponensiële komponente raamwerk om dinamika van die hele opbrengskromme te vang in drie dimensionele parameters wat dinamies ontwikkel. Die Nelson-Siegel benadering is 'n gerie ike en spaarsamige benaderingsmetode wat reeds vertrou word om die beste pas te bewerkstellig en voorspelling van die opbrengskromme. Die werk wat nogal baie belangstelling ontvang het onder hierdie raamwerk is die algemene arbitrage-vrye Nelson-Siegel makro- nansiele term struktuur model met makroekonomiese grondbeginsels, (Li et al. (2012)), wat kenmerkend van die gesamentlike dinamiese interaksie tussen die opbrengs en die makroekonomie en die dinamiese verhouding tussen band risiko-premies en die ekonomie is. Volgens Li et al. (2012), word risiko-premies bevind om nou gekoppel te wees aan makroekonomiese aktiwiteite en wat se variasies ontleed kan word. Die benadering verbeter die skatting en die uitdagings van identi- sering van risiko parameters wat teegekom is in die afgelope makro- nansiese literatuur.

Cette thèse traite des problèmes associes à la théorie de grossissement de filtration. Elle est divisée en deux parties. La première partie est consacrée aux temps aléatoires. On étudie les propriétés des différentes classes de temps aléatoires du point de vue du grossissement de filtration. La deuxième partie concerne l'étude de stabilité de condition d'arbitrage sur le grossissement de filtration. On se concentre sur la condition No Unbounded Profit with Bounded Risk. Dans un premier temps, on étudie l'absence d'arbitrage dans le cas de grossissement progressif avec un temps aléatoire. Puis on regarde le grossissement initial avec une variable aléatoire qui vérifie l'hypothèse de Jacod.

The Nelson-Siegel framework published by Diebold and Li a decade ago created an important benchmark and originated several works in the literature of forecasting term structure of interest rates. For instance, the Arbitrage-Free Nelson-Siegel framework improved predictive performance by imposing no-arbitrage conditions to the Nelson-Siegel framework. However, these frameworks were built on the top of a parametric curve model that may lead to poor fitting for sensible term structure shapes affecting forecast results. We propose DCOBS with no-arbitrage restrictions to forecast the term structure. It is built on the top of the nonparametric constrained smoothing Bsplines yield curve model. This curve model has shown to be an optimum solution between financial integrity and respect to yield curve shapes. Even though this curve model may provide more volatile forward curves than parametric models, they are still more accurate than those from Nelson-Siegel frameworks. A software was developed with a complete implementation of yield curve fitting techniques discussed in this paper. DCOBS has been evaluated for ten years of brazilian government bond data and it has shown good consistence with stylized facts of yield curves. The results of DCOBS are promising, specially in short-term forecast, and has shown greater stability and lower root mean square errors than Arbitrage-Free Nelson-Siegel. / O framework Nelson-Siegel publicado por Diebold e Li uma década atrás criou um importante benchmark e originou diversos trabalhos na literatura de previsão de estrutura a termo de taxas de juros. Por exemplo, o framework Nelson-Siegel Livre de Arbitragem melhorou a performance preditiva impondo condições de não-arbitragem ao framework Nelson-Siegel. No entanto, estes frameworks foram construídos em cima do modelo de curvas paramétricas. Em casos mais sensíveis de formas de curvas, este modelo tem um desempenho muito ruim, afetando o resultado da previsão. Nós propomos o DCOBS com restrições de não-arbitragem para prever a estrutura a termo. Ele é construído em cima do modelo de curva não-paramétrico com B-Splines restritas e suavizadas. Este modelo demonstrou ser uma solução ótima entre integridade financeira e respeito às formas de curvas de juros. Embora este modelo de curva possa resultar em curvas forwards mais voláteis que os modelos paramétricos, ele é ainda mais acurado que aqueles do framework Nelson-Siegel. Um software foi desenvolvido com uma implementação completa das técnicas de ajustes de curvas de juros discutidas nesta dissertação. DCOBS foi avaliado utilizando dez anos de dados de títulos públicos do governo brasileiro e demonstrou boa consistência com os fatos estilizados das curvas de juros. Os resultados do DCOBS são promissores, especialmente na previsão de curto prazo, e demonstrou maior estabilidade e menor erro quadrático médio que o modelo Nelson-Siegel Livre de Arbitragem.

The Nelson-Siegel framework published by Diebold and Li a decade ago created an important benchmark and originated several works in the literature of forecasting term structure of interest rates. For instance, the Arbitrage-Free Nelson-Siegel framework improved predictive performance by imposing no-arbitrage conditions to the Nelson-Siegel framework. However, these frameworks were built on the top of a parametric curve model that may lead to poor fitting for sensible term structure shapes affecting forecast results. We propose DCOBS with no-arbitrage restrictions to forecast the term structure. It is built on the top of the nonparametric constrained smoothing Bsplines yield curve model. This curve model has shown to be an optimum solution between financial integrity and respect to yield curve shapes. Even though this curve model may provide more volatile forward curves than parametric models, they are still more accurate than those from Nelson-Siegel frameworks. A software was developed with a complete implementation of yield curve fitting techniques discussed in this paper. DCOBS has been evaluated for ten years of brazilian government bond data and it has shown good consistence with stylized facts of yield curves. The results of DCOBS are promising, specially in short-term forecast, and has shown greater stability and lower root mean square errors than Arbitrage-Free Nelson-Siegel. / O framework Nelson-Siegel publicado por Diebold e Li uma década atrás criou um importante benchmark e originou diversos trabalhos na literatura de previsão de estrutura a termo de taxas de juros. Por exemplo, o framework Nelson-Siegel Livre de Arbitragem melhorou a performance preditiva impondo condições de não-arbitragem ao framework Nelson-Siegel. No entanto, estes frameworks foram construídos em cima do modelo de curvas paramétricas. Em casos mais sensíveis de formas de curvas, este modelo tem um desempenho muito ruim, afetando o resultado da previsão. Nós propomos o DCOBS com restrições de não-arbitragem para prever a estrutura a termo. Ele é construído em cima do modelo de curva não-paramétrico com B-Splines restritas e suavizadas. Este modelo demonstrou ser uma solução ótima entre integridade financeira e respeito às formas de curvas de juros. Embora este modelo de curva possa resultar em curvas forwards mais voláteis que os modelos paramétricos, ele é ainda mais acurado que aqueles do framework Nelson-Siegel. Um software foi desenvolvido com uma implementação completa das técnicas de ajustes de curvas de juros discutidas nesta dissertação. DCOBS foi avaliado utilizando dez anos de dados de títulos públicos do governo brasileiro e demonstrou boa consistência com os fatos estilizados das curvas de juros. Os resultados do DCOBS são promissores, especialmente na previsão de curto prazo, e demonstrou maior estabilidade e menor erro quadrático médio que o modelo Nelson-Siegel Livre de Arbitragem.

本篇論文建立一般化（與 Bond et al. (1994)比較）兩部門內生性成長模型，其中實質資本與人力資本之生產技術是固定規模報酬。利用傳統靜態國貿理論２Ｘ２模型的特性及結合跨期無套利條件，我們証明出在下列三種情形下(i) 0<α<1 (ii)α=1 (iii) α=0，均衡成長是馬鞍均衡穩定，要素密集度之大小不會影響這項推論。最後，我們仔細研究動態調整的過程並且討論時間偏好及支出比改變的長期效果。 / In this paper, we develop a "more" (compared with Bond et al. (1994)) general two-sector endogenous growth model with constant-return-to-scale production technologies governing the evolution of physical and human capital. 　　By utilizing the properties of traditional static 2x2 inter- national trade model and combining an intertemporal no-arbitrage condition which links the capital gain on human capital to the difference between the rentals on capital and wage rate, we prove that the balanced growth equilibrium is saddle-path stable in three cases (i) 0<α<1 (ii)α=1 (iii) α=0 regardless of the factor intensity ranking. 　　Finally, we provide a detail characterization of transitional dynamics and discuss the long-run effects of changes in time pre-ference and the expenditure share,α.