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on Market Microstructure |
| By: | Benjamin Jourdain (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique - INRIA - Ecole Nationale des Ponts et Chaussées); Mohamed Sbai (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique - INRIA - Ecole Nationale des Ponts et Chaussées) |
| Abstract: | In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô's formula, we get rid, in the asset price dynamics, of the stochastic integral with respect to the Brownian motion driving this SDE. Taking advantage of this structure, we propose - a scheme, based on the Milstein discretization of this SDE, with order one of weak trajectorial convergence for the asset price, - a scheme, based on the Ninomiya-Victoir discretization of this SDE, with order two of weak convergence for the asset price. We also propose a specific scheme with improved convergence properties when the volatility of the asset price is driven by an Orstein-Uhlenbeck process. We confirm the theoretical rates of convergence by numerical experiments and show that our schemes are well adapted to the multilevel Monte Carlo method introduced by Giles [2008a,b]. |
| Keywords: | discretization schemes, stochastic volatility models, weak trajectorial convergence, multilevel Monte Carlo |
| Date: | 2009–08–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00409861_v1&r=mst |
| By: | Chia-Lin Chang (Department of Applied Economics, National Chung Hsing University); Michael McAleer (Econometric Institute, Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo); Roengchai Tansuchat (Faculty of Economics, Maejo University and Faculty of Economics, Chiang Mai University) |
| Abstract: | This paper estimates univariate and multivariate conditional volatility and conditional correlation models of spot, forward and futures returns from three major benchmarks of international crude oil markets, namely Brent, WTI and Dubai, to aid in risk diversification. Conditional correlations are estimated using the CCC model of Bollerslev (1990), VARMAGARCH model of Ling and McAleer (2003), VARMA-AGARCH model of McAleer et al. (2009), and DCC model of Engle (2002). The paper also presents the ARCH and GARCH effects for returns and shows the presence of significant interdependences in the conditional volatilities across returns for each market. The estimates of volatility spillovers and asymmetric effects for negative and positive shocks on conditional variance suggest that VARMA-GARCH is superior to the VARMA-AGARCH model. In addition, the DCC model gives statistically significant estimates for the returns in each market, which shows that constant conditional correlations do not hold in practice. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2009cf640&r=mst |