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Câmara, T., and P. Mota. "Simple Moving Average vs Buy and Hold Revisited." (Submitted). Abstract

Nowadays, there are still countless researchers defending the effectiveness of the moving average technical analysis and they are able to present evidences for certain stocks, indexes and/or markets where this technical indicator is extremely useful for defining trading strategies. But the contrary also exists, i.e. a lot of researchers show distrust of this technical indicator and also provide evidences with particular stocks, indexes and/or markets where moving averages based strategies do not work well.
Aiming to understand why is it that with some stocks the moving average is indeed an excellent indicator while with others it is not, in this paper we implement moving average based strategies to buy and/or sell stocks for more than 480 companies from the NASDAQ 100, FTSE 100 and SP 500 indexes and compare the results with the ones obtained when using the buy-and-hold strategy.

Costa, S., M. Faias, P. Júdice, and P. Mota. "Cross-sectional modeling of bank deposits." (Submitted). Abstract

Studying the dynamics of deposits is important for three reasons: first, it serves as an important component of liquidity stress testing; second, it is crucial to asset-liability management exercises and the allocation between liquid and illiquid assets; third, it is the support for a liquidity at risk (LaR) methodology.

Current models are based on AR(1) processes that often underestimate liquidity risk. Thus a bank relying on those models may face failure in an event of crisis. We propose a novel approach for modeling deposits, using panel data and a momentum term.

The model enables the simulation of a variety of deposit trajectories, including episodes of financial distress, showing much higher drawdowns and realistic liquidity at risk estimates, as well as density plots that present a wide range of possible values, corresponding to booms and financial crises.

Therefore, this methodology is more suitable for liquidity management at banks, as well as for conducting liquidity stress tests.

Esquível, M. L., P. Mota, and J. P. Pina. "On a Stochastic Model for a Cooperative Banking Scheme for Microcredit." Theory of Probability and its Applications (In Press). Abstract

We propose and study a simple model for microcredit using two sums, with a random number of terms, of identically distributed random variables, the number of terms being Poisson distributed; the first sum accounts for the payments { the payables{ made to the collective vault by the participants and the second sum, subtracted to the first, accounts for the loans received by the participants, the receivables.
Under a global independence hypothesis we de fine, by mean of moment generating functions, an easily
implementable condition for the sustainability of the collective vault. That is, if, for all the participants and at any time, on average, the sum of the loans is strictly less than the sum of the payments to the collective vault then the probability of the collective vault failing can be made arbitrarily small, provided the loans only start to be accepted after a sufficiently large delay. We present numerical illustrations of collective vaults for exponential and chi-squared distributed random terms. For the practical management of such a collective vault it may be advisable to have loan granting rules that destroy independence of the random terms. We present a first simulation study that shows the effect of such a breaking dependence loan granting rule on maintaining the stability of the collective vault.

Esquível, Manuel L., Pedro P. Mota, and João Tiago Mexia. "On some statistical models with a random number of observations." Journal of Statistical Theory and Practice. 10 (2016): 805-823. AbstractWebsite

We extend some classical statistical inference to the case of a random number of observations with a stabilized distribution: namely, in the normal model, inference for the mean with known and unknown variance and inference for the variance. We describe some useful models for the number of observations obtained by truncation or translation of usual models given by integer-valued random variables: Poisson, binomial, geometric, and negative binomial. We present an efficient random search algorithm for the computation of the quantiles of the relevant statistics, we describe an interval estimation procedure for the extended model, and we propose a parametric bootstrap simulation study to validate the proposed procedure.

Esquível, Manuel L., and Pedro Mota. "On Some Auto-Induced Regime Switching Double-Threshold Glued Diffusions." Journal of Statistical Theory and Practice. 8 (2014): 760-771. AbstractWebsite

Regime switching processes are usually defined with an external random source driving the regime changes. In this article, we define and study a regime switching diffusion considering two thresholds, and regime switching occurring, by a change in the diffusion drift and volatility, whenever the trajectory touches the upper threshold after having crossed, or touched, the lower threshold or touches the lower threshold after having crossed, or touched, the upper threshold. We develop an estimation procedure for the thresholds and for the regime parameters of the diffusions. We show that a generalized Black–Scholes model with the regime switching diffusion as the law of the risky asset is arbitrage free and complete under an additional hypothesis on the diffusion coefficients of the two regime diffusions.

Faias, Marta, Pedro Mota, Alberto Mulenga, and Joaquim P. Pina. "Asymmetry of ARCH effects and natural resources disease or virtue: Mozambique experience." AIP Conference Proceedings. 1738 (2016). AbstractWebsite

We study the exchange rate behavior, mainly as to the presence of asymmetry in the shocks to conditional variance. Particularly, we investigate if the presence of that asymmetric response is specific to a marked behavior of the currency, appreciation/Dutch disease/depreciation, and if it appears masked when taking long non-homogeneous periods. Taking Mozambique Metical bilateral exchange rate against South Africa Rand, a major trading partner, we identify specific movements in defined sub-periods, where the most recent has the Dutch disease under scrutiny. Our results point out that asymmetry emerges especially when the currency is depreciating, while it is masked when considering larger periods that combine differences in currency behavior.

Mota, Pedro, and Manuel L. Esquível. "Pseudo Maximum Likelihood and Moments Estimators for Some Ergodic Diffusions." Contributions to Statistics. Springer International Publishing, 2018. 335-343. Abstract

When (Xt)t≥0 is an ergodic process, the density function of Xt converges to some invariant density as t →∞. We will compute and study some asymptotic properties of pseudo moments estimators obtained from this invariant density, for a specific class of ergodic processes. In this class of processes we can find the Cox-Ingersoll & Ross or Dixit & Pindyck processes, among others. A comparative study of the proposed estimators with the usual estimators obtained from discrete approximations of the likelihood function will be carried out.

Mota, Pedro. "On a Continuous-Time Stock Price Model with Two Mean Reverting Regimes." Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Eds. João Lita da Silva, Frederico Caeiro, Isabel Natário, and Carlos A. Braumann. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. 297-305. Abstract

Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.

Mota, P., and M. L. Esquível. "A double diffusion model." (Submitted). Abstract

In earlier studies we have defined regime switching diffusion processes by considering one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation whose solution defines a continuous time diffusion process. The change in regime occurs whenever the trajectory of the process crosses a threshold, eventually with some delay. In this paper we generalize those results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and for both regimes diffusion's parameters.

Mota, P. "New improvements in old approximations to the Normal CDF." International Journal of Applied Mathematics. 32.1 (2019): 83-89. AbstractWebsite

The list of approximations to the Normal cumulative distribution function is long and, eventually, not fully known due to the large number of published articles in the last decades. In this paper we will present new improvements in some well known approximations, without increasing the complexity of the formulas.

Mota, Pedro, and Manuel L. Esquível. "On a continuous time stock price model with regime switching, delay, and threshold." Quantitative Finance. 14 (2014): 1479-1488. AbstractWebsite

Motivated by the need to describe bear-bull market regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes, threshold and delay, given by a stochastic differential equation. When the difference between the regimes is simply given by a different set of real valued parameters for the drift and diffusion coefficients, with changes between regimes depending only on these parameters, we show that if the delay is known there are consistent estimators for the threshold as long we know how to classify a given observation of the process as belonging to one of the two regimes. When the drift and diffusion coefficients are of geometric Brownian motion type we obtain a model with parameters that can be estimated in a satisfactory way, a model that allows differentiating regimes in some of the NYSE 21 stocks analyzed and also, that gives very satisfactory results when compared to the usual Black–Scholes model for pricing call options.

Mota, Pedro P., and Manuel L. Esquível. "Model selection for stock prices data." Journal of Applied Statistics. 43 (2016): 2977-2987. AbstractWebsite

The geometric Brownian motion (GBM) is very popular in modeling the dynamics of stock prices. However, the constant volatility assumption is questionable and many models with nonconstant volatility have been developed. In the papers [7,12] the authors introduce a regime switching process where in each regime the process is driven by GBM and the change in regime is defined by the crossing of a threshold. In this paper we used Akaike's and Bayesian information criteria to show that the GBM with regimes provides a better fit than the GBM. We also perform a forecasting comparison of the models for two selected companies.

Mota, Pedro. "Normality assumption for the Log-return of the stock prices." Discussiones Mathematicae - Probability and Statistics. 32 (2012): 47-58. AbstractWebsite

The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified in the real world, that is, for a large number of company stock prices we will test the normality assumption for the log-return of their prices. We will apply the KolmogorovSmirnov [10, 5], the Shapiro-Wilks [17, 16] and the Anderson-Darling [1, 2] tests for normality to a wide number of company prices from companies quoted in the Nasdaq composite index.

Mulenga, A., M. Faias, P. Mota, and J. P. Pina. "What happens when the stock markets are closed?" Electronic Journal of Applied Statistical Analysis. 12.2 (2019): 405-415. AbstractWebsite

The normality of the log-return of stock prices is often assumed by the market players in order to use some useful results, as for instance, the Black-Scholes formula for pricing European options. However, several studies regarding different indexes have shown that the normality assumption of the returns usually fails.
In this paper we analyse the normality assumption for intra-day and inter-day log-returns, comparing opening prices and/or closing prices for a large number of companies quoted in the Nasdaq Composite index. We use the Pearson's Chi-Square, Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilks and Jarque-Bera goodness-of-fit tests to study the normality assumption.
We find that the failure rate in the normality assumption for the log-return of stock prices is not the same for intra-day and inter-day prices, is somewhat test dependent and strongly dependent on some extreme price observations.
To the best of our knowledge, this is the first study on the normality assumption for the log-return of stock prices dealing simultaneously with a large number of companies and normality tests, and at the same time considering various scenarios of intra-day, inter-day prices and data trimming.

Mulenga, A., M. Faias, P. Mota, and J. P. Pina. "Exchange rate volatility: An asymmetric tale from Mozambique." (Submitted). Abstract

This paper inspects how risk is affected by news sign and size within - depreciation, appreciation, stability - distinct exchange rate trends, and by volatility model choice, taking on various asymmetric Generalized Autoregressive Conditional Heteroskedasticity models to daily Mozambique New Metical against South Africa Rand, MZN/ZAR, exchange rate over January 2010 - December 2014. Our results show that risk measurement
and asymmetry of shocks to volatility depend on exchange rate trend, being that estimating the full sample conceals the actual behavior, and model choice, specifically the degree of nonlinearity and persistence. In particular, we find that when positive/negative news type matches the sign of the exchange rate trend, risk increases by more. Interestingly, this means that in times of appreciation the good news turns out to be bad,
likely because they raise the fear of overvaluation, under monitoring in natural resource producers and exporting countries. The findings contribute to the growing concern on nonlinear economic policy design, exchange rate targeting and surely international trade and investment decisions, where an incorrect assessment exchange rate risk and asymmetry may lead to mispricing of assets, namely options, and eventual underestimation of
measures, as Value at Risk, relevant for Basel agreement.

Ramos, Luís P., Pedro Mota, and João T. Mexia. "Sample Partitioning Estimation for Ergodic Diffusions." Communications in Statistics - Simulation and Computation. 44 (2015): 105-117. AbstractWebsite

In this article, we present a new technique to obtain estimators for parameters of ergodic processes. When a diffusion is ergodic its transition density converges to the invariant density Durett (1996). This convergence enabled us to introduce a sample partitioning technique that gives, in each subsample, observations that can be treated as independent and identically distributed. Within this framework, is possible the construction of estimators like maximum likelihood estimators or others.