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.

Mathematical modeling and analysis of the interaction of populations of bacteria and bacteriophages within chicken intestine

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Stochastic optimal bid to electricity markets with environmental risk constraints

There are many factors that influence the day-ahead market bidding strategies of a generation company (GenCo) in the current energy market framework. Environmental policy issues have become more and more important for fossil-fuelled power plants and they have to be considered in their management, giving rise to emission limitations. This work allows to investigate the influence of both the allowances and emission reduction plan, and the incorporation of the derivatives medium-term commitments in the optimal generation bidding strategy to the day-ahead electricity market. Two different technologies have been considered: the coal thermal units, high-emission technology, and the combined cycle gas turbine units, low-emission technology. The Iberian Electricity Market and the Spanish National Emissions and Allocation Plans are the framework to deal with the environmental issues in the day-ahead market bidding strategies. To address emission limitations, some of the standard risk management methodologies developed for financial markets, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), have been extended. This study offers to electricity generation utilities a mathematical model to determinate the individual optimal generation bid to the wholesale electricity market, for each one of their generation units that maximizes the long-run profits of the utility abiding by the Iberian Electricity Market rules, the environmental restrictions set by the EU Emission Trading Scheme, as well as the restrictions set by the Spanish National Emissions Reduction Plan. The economic implications for a GenCo of including the environmental restrictions of these National Plans are analyzed and the most remarkable results will be presented.

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.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Behavioral aspects of investment fund's markets: are good managers lucky or skilled?

It is generally accepted that financial markets are efficient in the long run a lthough there may be some deviations in the short run. It is also accepted that a good portfolio manager is the one who beats the market persistently along time, this type of manager could not exist if markets were perfectly efficient According to this in a pure efficient market we should find that managers know that they can not beat the market so they would undertake only pure passive management strategies. Assuming a certain degree of inefficiency in the short run, a market may show some managers who tr y to beat the market by undertaking active strategies. From Fama’s efficient markets theory we can state that these active managers may beat the market occasionally although they will not be able to enhance significantly their performance in the long run. On the other hand, in an inefficient market it would be expected to find a higher level of activity related with the higher probability of beating the market. In this paper we follow two objectives: first, we set a basis to analyse the level of efficiency in an asset invest- ment funds market by measuring performance, strategies activity and it’s persistence for a certain group of funds during the period of study. Second, we analyse individual performance persistence in order to determine the existence of skilled managers. The CAPM model is taken as theoretical background and the use of the Sharpe’s ratio as a suitable performance measure in a limited information environment leads to a group performance measurement proposal. The empiri- cal study takes quarterly data from 1999-2007 period, for the whole population of the Spanish asset investment funds market, provided by the CNMV (Comisión Nacional del Mercado de Valores). This period of study has been chosen to ensure a wide enough range of efficient market observation so it would allow us to set a proper basis to compare with the following period. As a result we develop a model that allows us to measure efficiency in a given asset mutual funds market, based on the level of strategy’s activity undertaken by managers. We also observe persistence in individual performance for a certain group of funds

Continuum formalism for modeling growing networks with deletion of nodes

We present a continuum formalism for modeling growing random networks under addition and deletion of nodes based on a differential mass balance equation. As examples of its applicability, we obtain new results on the degree distribution for growing networks with a uniform attachment and deletion of nodes, and complete some recent results on growing networks with preferential attachment and uniform removal

Direct and indirect subsidies in markets with system goods in the presence of externalities. Preliminary version

This paper derives a model of markets with system goods and two technological standards. An established standard incurs lower unit production costs but causes a negative externality. The paper derives the conditions for policy intervention and compares the effect of direct and indirect cost-reducing subsidies in two markets with system goods in the presence of externalities. If consumers are committed to the technology by purchasing one of the components, direct subsidies are preferable. For a medium-low cost difference between technological standards and a low externality cost it is optimal to provide a direct subsidy only to the first technology adopter. As the higher the externality cost raises, the more technology adopters should be provided with direct subsidies. This effect is robust in all extensions. In the absence of consumers commitment to a technological standard indirect and direct subsidies are both desirable. In this case, the subsidy to the first adopter is lower then the subsidy to the second adopter. Moreover, for the low cost difference between technological standards and low externality cost the fi rst fi rm chooses a superior standard without policy intervention. Finally, a perfect compatibility between components based on different technological standards enhances an advantage of indirect subsidies for medium-high externality cost and cost difference between technological standards. Journal of Economic Literature Classi fication Numbers: C72, D21, D40, H23, L13, L22, L51, O25, O33, O38. Keywords: Technological standards; complementary products; externalities; cost-reducing subsidies; compatibility.

Contagion or Interdependence in the recent Global Financial Crisis? An application to the stock markets using unconditional cross-market correlations

We consider stock market contagion as a significant increase in cross-market linkages after a shock to one country or group of countries. Under this definition we study if contagion occurred from the U.S. Financial Crisis to the rest of the major stock markets in the world by using the adjusted (unconditional) correlation coefficient approach (Forbes and Rigobon, 2002) which consists of testing if average crossmarket correlations increase significantly during the relevant period of turmoil. We would not reject the null hypothesis of interdependence in favour of contagion if the increase in correlation only suggests a continuation of high linkages in all state of the world. Moreover, if contagion occurs, this would justify the intervention of the IMF and the suddenly portfolio restructuring during the period under study.

Genetic and genomic analysis modeling of germline c-MYC overexpression and cancer susceptibility

Background: Germline genetic variation is associated with the differential expression of many human genes. The phenotypic effects of this type of variation may be important when considering susceptibility to common genetic diseases. Three regions at 8q24 have recently been identified to independently confer risk of prostate cancer. Variation at 8q24 has also recently been associated with risk of breast and colorectal cancer. However, none of the risk variants map at or relatively close to known genes, with c-MYC mapping a few hundred kilobases distally. Results: This study identifies cis-regulators of germline c-MYC expression in immortalized lymphocytes of HapMap individuals. Quantitative analysis of c-MYC expression in normal prostate tissues suggests an association between overexpression and variants in Region 1 of prostate cancer risk. Somatic c-MYC overexpression correlates with prostate cancer progression and more aggressive tumor forms, which was also a pathological variable associated with Region 1. Expression profiling analysis and modeling of transcriptional regulatory networks predicts a functional association between MYC and the prostate tumor suppressor KLF6. Analysis of MYC/Myc-driven cell transformation and tumorigenesis substantiates a model in which MYC overexpression promotes transformation by down-regulating KLF6. In this model, a feedback loop through E-cadherin down-regulation causes further transactivation of c-MYC.Conclusion: This study proposes that variation at putative 8q24 cis-regulator(s) of transcription can significantly alter germline c-MYC expression levels and, thus, contribute to prostate cancer susceptibility by down-regulating the prostate tumor suppressor KLF6 gene.

Silver space-time trellis-coded modulation

Silver Code (SilC) was originally discovered in [1–4] for 2×2 multiple-input multiple-output (MIMO) transmission. It has non-vanishing minimum determinant 1/7, slightly lower than Golden code, but is fast-decodable, i.e., it allows reduced-complexity maximum likelihood decoding [5–7]. In this paper, we present a multidimensional trellis-coded modulation scheme for MIMO systems [11] based on set partitioning of the Silver Code, named Silver Space-Time Trellis Coded Modulation (SST-TCM). This lattice set partitioning is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding, while the branch metrics are computed by using a sphere-decoding algorithm. It is shown that the proposed SST-TCM performs very closely to the Golden Space-Time Trellis Coded Modulation (GST-TCM) scheme, yetwith a much reduced decoding complexity thanks to its fast-decoding property.

Student modeling based on fuzzy inference mechanisms

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for each student, suggesting the competences the student is more prepared to study. We use fuzzy set theory for dealing with uncertainty. The marks of the assessment tests are transformed into linguistic terms and used for assigning values to linguistic variables. For each competence, the level of difficulty and the level of knowing its prerequisites are calculated based on the assessment marks. Using these linguistic variables and approximate reasoning (fuzzy IF-THEN rules), a crisp category is assigned to each competence regarding its level of recommendation.

Sovereign Risk, Anonymous Markets, and the Effects of Globalization

The goal of this paper is to study the e¤ects of globalization on the workings of financial markets. We adopt a "technological" view of globalization, which consists of an exogenous reduction in the cost of shipping goods across di¤erent regions of the world. We model financial markets where agents anonymously trade securities issued by every other agent in the world. In the absence of frictions, we show how globalization creates trade opportunities among residents of different regions of the world, thereby raising welfare. In the presence of sovereign risk, however, there emerge two crucial interactions between trade among residents within a region and trade among residents of di¤erent regions. First, the more residents within a region trade with each other, the more they can trade with residents of other regions. Second, the possibility of trade with residents of other regions sometimes leads a government to not enforce payments by its residents, destroying trade opportunities among residents within the region. The net effect on welfare of this process of creation and destruction of trade opportunities is ambiguous. We argue that there are no policies governments can take to avoid the negative effects of globalization on trade among domestic residents. In a dynamic extension, we analyze how our results are a¤ected by reputational considerations.

New Trends in Public Facility Location Modeling

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.

Equilibrium asset prices and savings of heterogeneous agents in the presence of incomplete markets and portfolio constraints

We study the quantitative properties of a dynamic general equilibrium model in which agents face both idiosyncratic and aggregate income risk, state-dependent borrowing constraints that bind in some but not all periods and markets are incomplete. Optimal individual consumption-savings plans and equilibrium asset prices are computed under various assumptions about income uncertainty. Then we investigate whether our general equilibrium model with incomplete markets replicates two empirical observations: the high correlation between individual consumption and individual income, and the equity premium puzzle. We find that, when the driving processes are calibrated according to the data from wage income in different sectors of the US economy, the results move in the direction of explaining these observations, but the model falls short of explaining the observed correlations quantitatively. If the incomes of agents are assumed independent of each other, the observations can be explained quantitatively.