Annuity pricing is essential to insurance companies for their financial liabilities. Therefore, one of the purposes of companies is to adjust the annuity prices using a forecasting model that fits their historical data best. However, historical data may have outliers influencing the model. Extraordinary events such as a weak health system, an outbreak of war, and pandemics like Spanish flu or, more recently, Covid-19 may cause outliers resulting in misevaluation of mortality rates. These outliers should be taken into account to preserve the life insurance industry's financial strength and liability. In this study, we aim to find if there is an impact of mortality outliers in annuity pricing. We analyze the annuity price fluctuations among different countries using two models: Lee-Carter model and Outlier-Adjusted Lee-Carter model. Since the effect of possible outliers in the mortality data may vary according to race, geographic location, economic welfare, and demographic structures, we choose five countries for comparison. Russia and Bulgaria as emerging countries, Canada, Japan, and United Kingdom, as developed countries with high longevity risk, are considered. Moreover, we show the annuity pricing on a simulated diverse portfolio created for the prices of four types of life annuities for a more comprehensive assessment. The results of this study prove the use of outlier-adjusted models for specific countries.