Modeling financial time series through second-order stochastic differential equations

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Modeling financial time series through second order stochastic differential equations João NicolauTo cite this version: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Keywords: di¤usion processes, second order stochastic di¤erential equations. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT AbstractIn this paper we motivate the use of second order stochastic di¤erential equations in economics and …nance. We provide an empirical illustration and discuss a parametric second order stochastic di¤erential equation for stock prices and exchange rates.Postal address: ISEG,

Bias Correction Estimation for a Continuous‐Time Asset Return Model with Jumps

“…It is also shown the quadratic form with positive coefficient for volatility estimator with a minimum at 0.07 in Figure , which coincides with the economic phenomenon of ‘volatility smile’. The shapes of estimated curves for these unknown coefficients coincide with those in Nicolau ().…”

“…Through the Augmented Dickey-Fuller test statistic in Table XII, we can easily observe that the null hypothesis of non-stationarity is accepted for the logarithm of stock index log Y t at the 5% significance level, but is rejected of 'volatility smile'. The shapes of estimated curves for these unknown coefficients coincide with those in Nicolau (2008). However there is an interesting phenomenon discovered in the volatility line of return series: this line is asymmetric not like the symmetric one in Nicolau (2008) and the volatility has different rates to positive return and negative return.…”

“…However there is an interesting phenomenon discovered in the volatility line of return series: this line is asymmetric not like the symmetric one in Nicolau () and the volatility has different rates to positive return and negative return. The finding coincides with the conclusion in most empirical analysis that asymmetric features are depicted for volatility with respect to positive perturbations (good news) and negative perturbations (bad news).…”

“…Johannes (2004) provided the statistical and economic roles of jumps in continuous-time interest rate models. However, the current observations in empirical finance usually behave as the cumulation of all past perturbations such as stock prices by means of asset returns (see Nicolau, 2008). Furthermore, in the research field involved with model (1.1), although the scholars focused on the price of the asset, most of them did not consider the returns of the asset.…”

Estimation for a Second-Order Jump Diffusion Model from Discrete Observations: Application to Stock Market Returns

“…As pointed out by Nicolau [1,5], model (1) is especially useful in empirical finance. First, the model accommodates nonstationary integrated stochastic process that can be made stationary by differencing.…”