Long memory (long-term dependence) of volatility counts as one of the ubiquitous stylized facts of financial data. Inspired by the long memory property, multifractal processes have recently been introduced as a new tool for modeling financial time series. In this paper, we propose a parsimonious version of a bivariate multifractal model and estimate its parameters via both maximum likelihood and simulation based inference approaches. In order to explore its practical performance, we apply the model for computing value-at-risk and expected shortfall statistics for various portfolios and compare the results with those from an alternative bivariate multifractal model proposed by Calvet et al. (2006) and the bivariate CC-GARCH of Bollerslev (1990). As it turns out, the multifractal models provide much more reliable results than CC-GARCH, and our new model compares well with the one of Calvet et al. although it has an even smaller number of parameters.