Infinitely many securities and the fundamental theorem of asset pricing

Several authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets

Infinitely many securities and the fundamental theorem of asset pricing

Several authors have pointed out the possible absence of martingale measures for static arbitrage-free markets with an infinite number of available securities. This paper addresses this caveat by drawing on projective systems of probability measures. Firstly, it is shown that there are two distinct sorts of models whose treatment is necessarily different. Secondly, and more important, we analyze those situations for which one can provide a projective system of ó .additive measures whose projective limit may be interpreted as a risk-neutral probability. Hence, the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.

Regime switching models of hedge fund returns

We estimate and compare the forecasting performance of several dynamic models of returns of different hedge fund strategies. The conditional mean of return is an ARMA process while its conditional volatility is modeled according to the GARCH specification. In order to take into account the high level of risk of these strategies, we also consider a Markov switching structure of the parameters in both equations to capture jumps. Finally, the one-step-ahead out-of-sample forecast performance of different models is compared.Markov switching ARMA-GARCH, forecasting performance

Market imperfections, discount factors and stochastic dominance: an empirical analysis with oil-linked derivatives

Oil-linked derivatives are becoming very important in Modern Investment Theory. Accordingly, the analysis of Pricing Techniques and Portfolio Choice Problems involving these securities is a major topic for both managers and researchers. We focus on both the No-Arbitrage Approach and Stochastic Discount Factor (SDF) based methods in order to study oil-linked derivatives available at The New York Mercantile Exchange, Inc, one of the world's largest markets in energy and precious metals. First, we generalize some theoretical properties of the SDF in order to capture the effects induced by the bid-ask spread when analyzing dominated/efficient portfolios. Secondly, we apply our findings and empirically analyze the existence of dominated assets and portfolios in the oil derivatives market. Our results reveal the systematic presence of dominated prices, which should be taken into account by traders when composing their portfolios. Additionally, the test yields pricing and portfolio choice methods as well as new strategies that may allow brokers to outperform their service for their clients. It is worth to point out that the conclusions of the test have two important characteristics: On the one hand, they are very precise since we draw on perfectly synchronized bid/ask prices, as provided by Reuters. On the other hand, they are robust in the sense that they do not depend on any assumption about the underlying asset price dynamics. Finally, despite the empirical test focuses on oil derivatives, the methodology is general enough to apply to a broad range of markets

MARKET IMPERFECTIONS, DISCOUNT FACTORS AND STOCHASTIC DOMINANCE: AN EMPIRICAL ANALYSIS WITH OIL-LINKED DERIVATIVES

Oil-linked derivatives are becoming very important in Modern Investment Theory. Accordingly, the analysis of Pricing Techniques and Portfolio Choice Problems involving these securities is a major topic for both managers and researchers. We focus on both the No-Arbitrage Approach and Stochastic Discount Factor (SDF) based methods in order to study oil-linked derivatives available at The New York Mercantile Exchange, Inc, one of the world's largest markets in energy and precious metals. First, we generalize some theoretical properties of the SDF in order to capture the effects induced by the bid-ask spread when analyzing dominated/efficient portfolios. Secondly, we apply our findings and empirically analyze the existence of dominated assets and portfolios in the oil derivatives market. Our results reveal the systematic presence of dominated prices, which should be taken into account by traders when composing their portfolios. Additionally, the test yields pricing and portfolio choice methods as well as new strategies that may allow brokers to outperform their service for their clients. It is worth to point out that the conclusions of the test have two important characteristics: On the one hand, they are very precise since we draw on perfectly synchronized bid/ask prices, as provided by Reuters. On the other hand, they are robust in the sense that they do not depend on any assumption about the underlying asset price dynamics. Finally, despite the empirical test focuses on oil derivatives, the methodology is general enough to apply to a broad range of markets.

Infinitely many securities and the fundamental theorem of asset pricing

Several authors have pointed out the possible absence of martingale measures for static arbitrage free markets with an infinite number of available securities. Accordingly, the literature constructs martingale measures by generalizing the concept of arbitrage (free lunch, free lunch with bounded risk, etc.) or introducing the theory of large financial markets. This paper does not modify the definition of arbitrage and addresses the caveat by drawing on projective systems of probability measures. Thus we analyze those situations for which one can provide a projective system of σ−additive measures whose projective limit may be interpreted as a risk-neutral probability of an arbitrage free market. Hence the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets.Partially funded by the Spanish Ministry of Science and Education (ref: BEC2003 − 09067 − C04 − 03) and Comunidad Autónoma de Madrid (ref: s − 0505/tic/000230).Publicad

Teorema fundamental de valoración de activos : extensiones teóricas y aplicaciones empíricas

En la literatura financiera varios autores, entre otros, Harrison y Kreps (1979), Dalang et al. (1990), Schachermayer (1992), Delbaen y Schachermayer (1998), Jacod y Shiryaev (1998) o Pham y Tuozi (1999) han demostrado diferentes versiones del tal llamado ”Teorema Fundamental de Valoraci´on de Activos” (de aquí en adelante TFVA). En el caso de mercados sin fricciones con un número finito de activos y en el tiempo discreto finito, este teorema simplemente establece la equivalencia entre la ausencia de arbitraje y la existencia de medidas de martingalas equivalentes. La ausencia de arbitraje en estos casos implica el cumplimiento de la ”Ley de Precio Único” y lleva a la existencia de Factores de Descuento Estocástico (FDE) que proporcionan las reglas de valoración y carteras óptimas en términos de media-varianza (véase por ejemplo, Chamberlain y Rothschild 1983, Hansen y Jagannathan, 1997). Sin embargo, si el conjunto de activos es infinito, o el conjunto de fechas de negociación es infinito, o bien si existen fricciones (costes de transacción, horquillas de precios bid-ask, restricciones de compra/venta de determinados activos, etc.) en el mercado, una versión simple del TFVA no se puede probar ya que la ausencia de arbitraje no es suficiente para construir las probabilidades neutrales al riesgo bajo las que el proceso de precios sea una martingala. Back y Pliska (1991) y Schachermayer (1992) han presentado simples contraejemplos para demostrar la ausencia de medidas de martingalas equivalentes en mercados libres de arbitraje en el caso de tiempo infinito e infinitos activos, respectivamente. Para poder solucionar este problema y caracterizar la existencia de medidas de martingalas equivalentes, varios autores han utilizado un concepto mucho más débil que el concepto de arbitraje, llamado ”free-lunch” (comida gratuita) e introducido por Clark (1993). Desde entonces el “free lunch” ha sido la clave en las futuras extensiones del TFVA. Sin embargo, la ausencia de arbitraje es un concepto mucho más intuitivo y de más fácil comprobación empírica que la ausencia del ”free-lunch’. Merece la pena también recordar que los clásicos modelos de valoración (por ejemplo, el modelo binomial, el modelo de Black- Scholes, etc.) suelen tratar con el concepto de arbitraje. Sería interesante, entonces, estudiar la posibilidad de extender el TFVA bajo un supuesto simple e intuitivo como la ausencia de arbitraje en los casos mencionados arriba. Lo que se refiere a los mercados con imperfecciones, estos han sido tratados, por ejemplo, por Garman and Ohlson (1981), He and Modest (1995), Luttmer (1996), Prisman (1986, 1997), Bizid and Jouini (2005). En particular, Jouini y Kallal (1995) han demostrado la equivalencia entre la ausencia del ”free-lunch” y la existencia de un proceso de precios que se encuentra entre los procesos de precios bid y ask que cumple la propiedad de martingala con respecto a una medida de probabilidad. Sin embargo, la ausencia de arbitraje en un mercado con fricciones no implica, en general, el cumplimiento de la Ley de Precio Único o la existencia de FDE. Luttmer (1996) trata con una clase de pagos teóricos (pero no necesariamente alcanzables) tales que la esperanza de pago distorsionado de un activo (es decir, pago del activo multiplicado por esta clase de pagos teóricos) tiene que estar entre la horquilla inicial de los precios bid/ask. En He and Modest (1995) para funciones de utilidad típicas en las inversiones óptimas solo se adquieren (venden) algunos activos cuyo precio bid (ask) se obtiene como la esperanza de su pago distorsionado final. A pesar de los resultados anteriores, no existe ninguna extensión de la noción de FDE al caso de mercados imperfectos, es decir, un resultado independiente de la función de utilidad que garantice la existencia de un pago alcanzable que minimice la varianza de los retornos y que simultáneamente proporcione las reglas de valoración para calcular los precios bid y ask. Teniendo en cuenta los problemas que acabamos de mencionar, nos proponemos en esta Tesis estudiar el TFVA y sus posibles extensiones utilizando el concepto de arbitraje. Los resultados de la Tesis tanto teóricos como empíricos nos permiten contribuir de forma significativa a la investigación en la moderna Teoría Financiera y resolver varios problemas identificados en la literatura