Volatility modelling and accurate minimun capital risk requirements : a comparison among several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported

Estimating persistence in the volatility of asset returns with signal plus noise models

This paper examines the degree of persistence in the volatility of financial time series using a Long Memory Stochastic Volatility (LMSV) model. Specifically, it employs a Gaussian semiparametric (or local Whittle) estimator of the memory parameter, based on the frequency domain, proposed by Robinson (1995a), and shown by Arteche (2004) to be consistent and asymptotically normal in the context of signal plus noise models. Daily data on the NASDAQ index are analysed. The results suggest that volatility has a component of longmemory behaviour, the order of integration ranging between 0.3 and 0.5, the series being therefore stationary and mean-reverting.The second-named author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA project at the University of Navarra

Quasi-Maximum Likelihood estimation of Stochastic Volatility models

Publicado además en: Recent developments in Time Series, 2003, vol. 2, ISBN13: 9781840649512, pp. 117-134Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the volatility as an unobserved vatiable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. This article analyses the asymptotic and finite sample properties of a Quasi-Maximum Likelihood (QML) estimator based on the Kalman filter. The relative efficiency of the QML estimator when compared with estimators based on the Generalized Method of Moments is shown to be quite high for parameter values often found in empirical applications. The QML estimator can still be employed when the SV model is generalized to allow for distributions with heavier tails than the normal. SV models are finally fitted to daily observations on the yen/dollar exchange rate.Publicad

Modelling intra-daily volatility by functional data analysis: an empirical application to the spanish stock market

We propose recent functional data analysis techniques to study the intra-daily volatility. In particular, the volatility extraction is based on functional principal components and the volatility prediction on functional AR(1) models. The estimation of the corresponding parameters is carried out using the functional equivalent to OLS. We apply these ideas to the empirical analysis of the IBEX35 returns observed each _ve minutes. We also analyze the performance of the proposed functional AR(1) model to predict the volatility along a given day given the information in previous days for the intra-daily volatility for the firms in the IBEX35 Madrid stocks inde

Bayesian estimation of the gaussian mixture garch model

In this paper, we perform Bayesian inference and prediction for a GARCH model where the innovations are assumed to follow a mixture of two Gaussian distributions. This GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. The method is illustrated using the Swiss Market Index

Real Option Pricing in Mixed-use Development Projects

The application of real options theory to commercial real estate has developed rapidly during the last 15 Years. In particular, several pricing models have been applied to value real options embedded in development projects. In this study we use a case study of a mixed use development scheme and identify the major implied and explicit real options available to the developer. We offer the perspective of a real market application by exploring different binomial models and the associated methods of estimating the crucial parameter of volatility. We include simple binomial lattices, quadranomial lattices and demonstrate the sensitivity of the results to the choice of inputs and method.

Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets