Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Modelling world investment markets using threshold conditional correlation models

In this paper we propose a parsimonious regime-switching approach to model the correlations between assets, the threshold conditional correlation (TCC) model. This method allows the dynamics of the correlations to change from one state (or regime) to another as a function of observable transition variables. Our model is similar in spirit to Silvennoinen and Teräsvirta (2009) and Pelletier (2006) but with the appealing feature that it does not suffer from the course of dimensionality. In particular, estimation of the parameters of the TCC involves a simple grid search procedure. In addition, it is easy to guarantee a positive definite correlation matrix because the TCC estimator is given by the sample correlation matrix, which is positive definite by construction. The methodology is illustrated by evaluating the behaviour of international equities, govenrment bonds and major exchange rates, first separately and then jointly. We also test and allow for different parts in the correlation matrix to be governed by different transition variables. For this, we estimate a multi-threshold TCC specification. Further, we evaluate the economic performance of the TCC model against a constant conditional correlation (CCC) estimator using a Diebold-Mariano type test. We conclude that threshold correlation modelling gives rise to a significant reduction in portfolio´s variance.

Communication, Coordination, and Efficiency in Evolutionary One-population Models

We analyze the role of commitment in pre-play communication for ensuring efficient evolutionarily stable outcomes in coordination games. All players are a priori identical as they are drawn from the same population. In games where efficient outcomes can be reached by players coordinating on the same action we find commitment to be necessary to enforce efficiency. In games where efficienct outcomes only result from play of different actions, communication without commitment is most effective although efficiency can no longer be guaranteed. Only when there are many messages then inefficient outcomes are negligible as their basins of attraction become very small.

Back to square one: Identification issues in DSGE models

We investigate identifiability issues in DSGE models and their consequences for parameter estimation and model evaluation when the objective function measures the distance between estimated and model impulse responses. We show that observational equivalence, partial and weak identification problems are widespread, that they lead to biased estimates, unreliable t-statistics and may induce investigators to select false models. We examine whether different objective functions affect identification and study how small samples interact with parameters and shock identification. We provide diagnostics and tests to detect identification failures and apply them to a state-of-the-art model.

Communication, coordination and efficiency in evolutionary one-population models

We analyze the role of commitment in pre-play communication for ensuringefficient evolutionarily stable outcomes in coordination games. All players are a priori identical as they are drawn from the same population. In games where efficient outcomes can be reached by players coordinating on the same action we find commitment to be necessary to enforce efficiency. In games where efficienct outcomes only result from play of different actions, communication without commitment is most effective although efficiency can no longer be guaranteed. Only when there are many messages then inefficient outcomes are negligible as their basins of attraction become very small.

Exchange rate predictability

The main goal of this article is to provide an answer to the question: "Does anything forecast exchange rates, and if so, which variables?". It is well known thatexchange rate fluctuations are very difficult to predict using economic models, andthat a random walk forecasts exchange rates better than any economic model (theMeese and Rogoff puzzle). However, the recent literature has identified a series of fundamentals/methodologies that claim to have resolved the puzzle. This article providesa critical review of the recent literature on exchange rate forecasting and illustratesthe new methodologies and fundamentals that have been recently proposed in an up-to-date, thorough empirical analysis. Overall, our analysis of the literature and thedata suggests that the answer to the question: "Are exchange rates predictable?" is,"It depends" -on the choice of predictor, forecast horizon, sample period, model, andforecast evaluation method. Predictability is most apparent when one or more of thefollowing hold: the predictors are Taylor rule or net foreign assets, the model is linear, and a small number of parameters are estimated. The toughest benchmark is therandom walk without drift.

Another Look at the Null of Stationary Real Exchange Rates: Panel Data with Structural Breaks and Cross-section Dependence

This paper re-examines the null of stationary of real exchange rate for a panel of seventeen OECD developed countries during the post-Bretton Woods era. Our analysis simultaneously considers both the presence of cross-section dependence and multiple structural breaks that have not received much attention in previous panel methods of long-run PPP. Empirical results indicate that there is little evidence in favor of PPP hypothesis when the analysis does not account for structural breaks. This conclusion is reversed when structural breaks are considered in computation of the panel statistics. We also compute point estimates of half-life separately for idiosyncratic and common factor components and find that it is always below one year.

Current Account imbalances, thriftiness and the real exchange rate in a growing economy

This paper analyses the theoretical relevance of the dynamical aspects of growth on the discussion about the observed positive correlation between per capita real income and real exchange rates. With this purpose, we develop a simple exogenous growth model where the internal, external and intertemporal equilibrium conditions of a typical macroeconomic model are imposed; this last one through the inclusion of a balanced growth path for the foreign assets accumulation. The main result under this consideration is that the relationship defended by the Balassa-Samuelson hypothesis is no more so straightforward. In our particular approach, the mentioned bilateral relationship depends on a parameter measuring thriftiness in the economy. Therefore, the probability of ending up with a positive relationship between growth and real exchange rates -as the classical economic theory predicts- will be higher when the economy is able to maintain a minimum saving ratio. Moreover, given that our model considers a simple Keynesian consumption function, some explosive paths can also be possible.

The structural approach of a natrex model on equilibrium exchange rates

Following a general macroeconomic approach, this paper sets a closed micro-founded structural model to determine the long run real exchange rate of a developed economy. In particular, the analysis follows the structure of a Natrex model. The main contribution of this research paper is the development of a solid theoretical framework that analyse in depth the basis of the real exchange rate and the details of the equilibrium dynamics after any shock influencing the steady state. In our case, the intertemporal factors derived from the stock-flow relationship will be particularly determinant. The main results of the paper can be summarised as follows. In first place, a complete well-integrated structural model for long-run real exchange rate determination is developed from first principles. Moreover, within the concrete dynamics of the model, it is found that some convergence restrictions will be necessary. On one hand, for the medium run convergence the sensitivity of the trade balance to changes in real exchange rate should be higher that the correspondent one to the investment decisions. On the other hand, and regarding long-run convergence, it is also necessary both that there exists a negative relationship between investment and capital stock accumulation and that the global saving of the economy depends positively on net foreign debt accumulation. In addition, there are also interesting conclusions about the effects that certain shocks over the exogenous variables of the model have on real exchange rates.

Search and bargaining in large markets with homogeneous traders

We study pair-wise decentralized trade in dynamic markets with homogeneous, non-atomic, buyers and sellers that wish to exchange one unit. Pairs of traders are randomly matched and bargaining a price under rules that offer the freedom to quit the match at any time. Market equilbria, prices and trades over time, are characterized. The asymptotic behavior of prices and trades as frictions (search costs and impatience) vanish, and the conditions for (non) convergence to walrasian prices are explored. As a side product of independent interest, we present a self-contained theory of non-cooperative bargaining with two-sided, time-varying, outside options.

On the choice of an exchange rate regime: target zones revisited

From the classical gold standard up to the current ERM2 arrangement of the European Union, target zones have been a widely used exchange regime in contemporary history. This paper presents a benchmark model that rationalizes the choice of target zones over the rest of regimes: the fixed rate, the free float and the managed float. It is shown that the monetary authority may gain efficiency by reducing volatility of both the exchange rate and the interest rate at the same time. Furthermore, the model is consistent with some known stylized facts in the empirical literature that previous models were not able to produce, namely, the positive relation between the exchange rate and the interest rate differential, the degree of non-linearity of the function linking the exchage rate to fundamentals and the shape of the exchange rate stochastic distribution.

Real equilibrium exchange rates. A panel data approach for advanced and emerging economies.

Based on an behavioral equilibrium exchange rate model, this paper examines the determinants of the real effective exchange rate and evaluates the degree of misalignment of a group of currencies since 1980. Within a panel cointegration setting, we estimate the relationship between exchange rate and a set of economic fundamentals, such as traded-nontraded productivity differentials and the stock of foreign assets. Having ascertained the variables are integrated and cointegrated, the long-run equilibrium value of the fundamentals are estimated and used to derive equilibrium exchange rates and misalignments. Although there is statistical homogeneity, some structural differences were found to exist between advanced and emerging economies.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Market effects of foreign exchange coordinated intervention

In this article we develop a theoretical microstructure model of coordinated central bank intervention based on asymmetric information. We study the economic implications of coordination on some measures of market quality and show that the model predicts higher volatility and more significant exchange rate changes when central banks coordinate compared to when they intervene unilaterally. Both these predictions are in line with empirical evidence. Keywords: coordinated foreign exchange intervention, market microstructure. JEL Classification: D82, E58, F31, G14

Models de simulació per coordinar serveis d'emergència

El projecte exposat té com a propòsit definir i implementar un model de simulació basat en la coordinació i assignació dels serveis d’emergència en accidents de trànsit. La definició del model s’ha realitzat amb l’ús de les Xarxes de Petri Acolorides i la implementació amb el software Rockwell Arena 7.0. El modelatge de la primera simulació ens mostra un model teòric basat en cues mentre que el segon, mostra un model més complet i real gràcies a la connexió mitjançant la plataforma Corba a una base de dades amb informació geogràfica de les flotes i de les rutes. Com a resultat de l’estudi i amb l’ajuda de GoogleEarth, podem realitzar simulacions gràfiques per veure els accidents generats, les flotes dels serveis i el moviment dels vehicles des de les bases fins als accidents.