Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

Confronto tra sistemi trend following e mean reversion

Si descrivono strategie di trading trend following e strategie mean reversion applicate a vari strumenti finanziari

Mean reversion in the short horizon returns of UK portfolios

This paper will show that short horizon stock returns for UK portfolios are more predictable than suggested by sample autocorrelation co-efficients. Four capitalisation based portfolios are constructed for the period 1976–1991. It is shown that the first order autocorrelation coefficient of monthly returns can explain no more than 10% of the variation in monthly portfolio returns. Monthly autocorrelation coefficients assume that each weekly return of the previous month contains the same amount of information. However, this will not be the case if short horizon returns contain predictable components which dissipate rapidly. In this case, the return of the most recent week would say a lot more about the future monthly portfolio return than other weeks. This suggests that when predicting future monthly portfolio returns more weight should be given to the most recent weeks of the previous month, because, the most recent weekly returns provide the most information about the subsequent months' performance. We construct a model which exploits the mean reverting characteristics of monthly portfolio returns. Using this model we forecast future monthly portfolio returns. When compared to forecasts that utilise the autocorrelation statistic the model which exploits the mean reverting characteristics of monthlyportfolio returns can forecast future returns better than the autocorrelation statistic, both in and out of sample.

On the robustness of short-term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.

DISPOSITION EFFECT AMONG BRAZILIAN EQUITY FUND MANAGERS

The disposition effect predicts that investors tend to sell winning stocks too soon and ride losing stocks too long. Despite the wide range of research evidence about this issue, the reasons that lead investors to act this way are still subject to much controversy between rational and behavioral explanations. In this article, the main goal was to test two competing behavioral motivations to justify the disposition effect: prospect theory and mean reversion bias. To achieve it, an analysis of monthly transactions for a sample of 51 Brazilian equity funds from 2002 to 2008 was conducted and regression models with qualitative dependent variables were estimated in order to set the probability of a manager to realize a capital gain or loss as a function of the stock return. The results brought evidence that prospect theory seems to guide the decision-making process of the managers, but the hypothesis that the disposition effect is due to mean reversion bias could not be confirmed.

Brownian bridge and other path-dependent Gaussian processes vectorial simulation

The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein-Ulenbeck mean reversion process.

Predicting market movement with Artificial Neural Networks

This paper presents an application of an Artificial Neural Network (ANN) to the prediction of stock market direction in the US. Using a multilayer perceptron neural network and a backpropagation algorithm for the training process, the model aims at learning the hidden patterns in the daily movement of the S&P500 to correctly identify if the market will be in a Trend Following or Mean Reversion behavior. The ANN is able to produce a successful investment strategy which outperforms the buy and hold strategy, but presents instability in its overall results which compromises its practical application in real life investment decisions.

Leverage instability and persistence: Evidence from the United States and Europe

We find that leverage behavior both in level and time-series variation is very similar between the United States and Europe throughout the 1990-2013 period. Leverage regimes are simultaneously unstable and persistent for both regions. We define instability as the extent to which firms largely deviate from their long-term leverage mean, while persistence as the extent to which today’s leverage influences its future levels. We then show that this simultaneous evidence imply a mean-reversion behavior of leverage and discuss some of its implications for future research on this field.

Valuing an offshore exploration project through real options analysis

This thesis applied real options analysis to the valuation of an offshore oil exploration project, taking into consideration the several options typically faced by the management team of these projects. The real options process is developed under technical and price uncertainties, where it is considered that the mean reversion stochastic process is more adequate to describe the movement of oil price throught time. The valuation is realized to two case scenarios, being the first a simplified approach to develop the intuition of the used concepts, and the later a more complete cases that is resolved using both the binomial and trinomial processes to describe oil price movement. Real options methodology demonstrated to be capable of assessing and valuing the projects options, and of overcoming common capital budgeting methodologies flexibility limitation. The added value of the application of real options is evident, but so is the method's increased complexity, which adversely influence its widespread implementation.

Stock market volatility and learning

Introducing bounded rationality in a standard consumption-based asset pricing model with time separable preferences strongly improves empirical performance. Learning causes momentum and mean reversion of returns and thereby excess volatility, persistence of price-dividend ratios, long-horizon return predictability and a risk premium, as in the habit model of Campbell and Cochrane (1999), but for lower risk aversion. This is obtained, even though our learning scheme introduces just one free parameter and we only consider learning schemes that imply small deviations from full rationality. The findings are robust to the learning rule used and other model features. What is key is that agents forecast future stock prices using past information on prices.

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.

Transitory Economic Shocks and Civil Conflict

I examine whether civil conflict is triggered by transitory negative economic shocks. My approach follows Miguel, Satyanath, and Sergenti (2004) in using rainfall as an exogenous source of economic shocks in Sub-Saharan African countries. The main difference is that my empirical specifications take into account that rainfall shocks are transitory. Failure to do so may, for example, lead to the conclusion that civil conflict is more likely to break out following negative rainfall shocks when conflict is most probable following years with exceptionally high rainfall levels.

On the impact of leverage constraints on asset prices and trading volume

Researchers have used stylized facts on asset prices and trading volumein stock markets (in particular, the mean reversion of asset returnsand the correlations between trading volume, price changes and pricelevels) to support theories where agents are not rational expected utilitymaximizers. This paper shows that this empirical evidence is in factconsistent with a standard infite horizon perfect information expectedutility economy where some agents face leverage constraints similar tothose found in todays financial markets. In addition, and in sharpcontrast to the theories above, we explain some qualitative differencesthat are observed in the price-volume relation on stock and on futuresmarkets. We consider a continuous-time economy where agents maximize theintegral of their discounted utility from consumption under both budgetand leverage con-straints. Building on the work by Vila and Zariphopoulou(1997), we find a closed form solution, up to a negative constant, for theequilibrium prices and demands in the region of the state space where theconstraint is non-binding. We show that, at the equilibrium, stock holdingsvolatility as well as its ratio to stock price volatility are increasingfunctions of the stock price and interpret this finding in terms of theprice-volume relation.