Posts Tagged ‘stochastic


Paper: Volatilidad explosiva

Explosive Volatility: A Model of Financial Contagion

This paper proposes a model of financial contagion that accounts for explosive, mutually exciting shocks to market volatility. We fit the model using country-level data during the European sovereign debt crisis, which has its roots in the period 2008–2010, and was continuing to affect global markets as of October, 2011. Our analysis shows that existing volatility models are unable to explain two key stylized features of global markets during presumptive contagion periods: shocks to aggregate market volatility can be sudden and explosive, and they are associated with specific directional biases in the cross-section of country-level returns. Our model repairs this deficit by assuming that the random shocks to volatility are heavy-tailed and correlated cross-sectionally, both with each other and with returns.
We find evidence for significant contagion effects during the major EU crisis periods of May 2010 and August 2011, where contagion is defined as excess correlation in the residuals from a factor model incorporating global and regional market risk factors. Some of this excess correlation can be explained by quantifying the impact of shocks to aggregate volatility in the cross-section of expected returns—but only, it turns out, if one is extremely careful in accounting for the explosive nature of these shocks. We show that global markets have time-varying cross-sectional sensitivities to these shocks, and that high sensitivities strongly predict periods of financial crisis. Moreover, the pattern of temporal changes in correlation structure between volatility and returns is readily interpretable in terms of the major events of the periods in question.

Link al Paper


Paper: Pricing y Modelo estructural de Credito

Stochastic evolution equations in portfolio credit modelling


We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a stochastic partial differential equation and we establish existence and uniqueness for thesolution taking values in a suitable function space. The loss function of the portfolio is then a function of the evolution of this density at the default boundary. We develop numerical methods for pricing and calibration of the model to credit indices and consider its performance pre and post credit crunch.

Link al Paper


Paper: Ruido de Microestructura

Modeling microstructure noise with mutually exciting point processes


We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2(for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process withthe positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increment sin microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales.More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

Link al Paper


Paper Predicción y Ratios

Do Decomposed Financial Ratios Predict Stock Returns and Fundamentals Better?

We investigate the prediction of excess returns and fundamentals by financial ratios – dividend-price ratio, earnings-price ratio, and book-to-market ratio – by decomposing financial ratios into a cyclical component and a stochastic trend component. We find both components predict excess returns and fundamentals. The cyclical components predict increases in future stock returns, while the stochastic trend components predict declines in future stock returns, in particular, in long horizons. This helps explain previous findings that financial ratios in the absence of decomposition find weak predictive power in short horizons and some predictive power in long horizons. We also find both components predict fundamentals, consistent with present value models.

Link al Paper

Fun & Finance


Fun & Finance Rollover

"It is hard to be finite upon an infinite subject, and all subjects are infinite." Herman Melville

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