A basic overview of mathematical finance and pricing theory is given. The Black-Scholes model and the LIBOR Market Model are explained, and their assumptionsare discussed and tested on historical data. The normality of log-returns of stocksand forward rates is tested for different time periods, and is found to be varyinggreatly over time. The models are calibrated using the Exponentially WeightedMoving Average (EWMA) method and implemented to perform a backtest againsthistorical data of two risk measures, Value at Risk and Expected Shortfall. Thebacktesting is done on five portfolios of varying risk, in the European and Norwegianmarkets. Three unleveraged portfolios consisting of bonds and stocks in differentproportions, and two leveraged portfolios consisting of stocks and interest rate capsrespectively are considered.The performance of the risk measures is found to be not satisfactory for all portfolios, but performance is better for riskier portfolios and assets. Variation ofperformance over different time periods is found. The periods of worst performanceare those of turbulent market conditions, notably in late 2008. These periods arefound to loosely correspond to the time periods in which log-returns of equity andforward rates are least normal.A sensitivity analysis of performances to the weighting parameter in the EWMAis done. The sensitivity is found to be substantial for all portfolios except for theportfolios holding stocks in the Norwegian market.