The accuracy of risk assessment inherent in the financial sector is of great importance in modern realities. Gross volumes of operations today are such that even seemingly insignificant increase in the accuracy of calculations, for example, of reserves of funds, the insured share of assets, insurance premiums, etc. can bring a noticeable profit for the owner, seller or buyer of volatility. The algebraic risk theory created in the last two decades offers effective computational methods for assessing the risks of financial instruments and their portfolios, which are characterized by increased accuracy. The computational experiments presented in the work demonstrate the promise of the proposed risk assessment methods against the background of the results obtained using the Monte Carlo method even when the latter utilizes huge computational resources.