This paper introduces a multivariate stochastic variance model for financial time series, which extends the univariate GARCH model by modeling variance as an unobserved stochastic process. The model is based on the idea that volatility can be represented as a stochastic process, allowing for more flexible and interpretable modeling of volatility dynamics. The paper discusses the statistical treatment of the model, its estimation using a quasi-maximum likelihood method, and its application to real data. It also explores how the model can capture common movements in volatility across multiple series, and how it can be generalized to handle heavy-tailed distributions. The model is applied to daily exchange rate data, showing its ability to capture common volatility patterns and provide insights into the underlying factors driving volatility in different currencies. The paper concludes that the multivariate stochastic variance model is a useful and flexible tool for modeling financial time series, particularly in capturing common volatility movements and providing insights into the structure of volatility in financial markets.This paper introduces a multivariate stochastic variance model for financial time series, which extends the univariate GARCH model by modeling variance as an unobserved stochastic process. The model is based on the idea that volatility can be represented as a stochastic process, allowing for more flexible and interpretable modeling of volatility dynamics. The paper discusses the statistical treatment of the model, its estimation using a quasi-maximum likelihood method, and its application to real data. It also explores how the model can capture common movements in volatility across multiple series, and how it can be generalized to handle heavy-tailed distributions. The model is applied to daily exchange rate data, showing its ability to capture common volatility patterns and provide insights into the underlying factors driving volatility in different currencies. The paper concludes that the multivariate stochastic variance model is a useful and flexible tool for modeling financial time series, particularly in capturing common volatility movements and providing insights into the structure of volatility in financial markets.