The accurate computation of statistical quantities from sampled data is of paramount importance in the analysis of economic and financial time series. The Epps effect is an empirically observed phenomenon where the sample correlation between the logarithmic returns of two stock prices decreases as the sampling frequency of data increases. The full explanation of this phenomenon is currently an open problem and several potential contributing factors are reported in the scientific literature. However, asynchronous sampling times in the stock prices is one of the key components originating the Epps effect. This article investigates in a quantitative way how asynchronous price data contribute to the Epps effect by modeling stock prices as correlated geometric Brownian motions and considering trading times as Poisson point processes. Under these assumptions we show that the Epps effect can be considered as a statistical artifact producing a bias on the sample correlation of the logarithmic returns. We also provide an analytic expression describing this bias. This expression can be used to compensate the bias on the sample correlation in order to obtain an unbiased estimate.