The paper investigates the methods of quantitative analysis of hidden statistical relationships of the financial indicators of companies under conditions of high investment risk. A new semi-parametric method for estimating tail dependence indicators using BB1 and BB7 dependence structures is proposed. For a dataset containing the cost indicators of leading Russian companies, computer experiments were carried out, as a result of which it was shown that the proposed method has a higher stability and accuracy in comparison with other considered methods. Practical application of the proposed risk management method would allow financial companies to assess investment risks adequately in the face of extreme events.