Interest rate risk modeling using extended lognormal distribution with variable volatility

It has become common to quantify portfolio risks through risk measures such as Expected Shortfall, and utilize them in risk management. On the other hand, as seen in the discussion of international accounting standard, the importance of mark-to-market basis evaluation on assets and liabilities have come to be progressively recognized. In other to calculate risks deriving from not only assets side but also from liability side in an appropriate way, it is essential to recognize the risk stemming from the volatility of interest rate that is used to discount the future cash flow into present value. The calculation of interest rate risk therefore has significant importance because of the influence on both asset side and liability side. The utilization of historical data in a risk measurement is a challenging problem due to the extremely low interest rate environment of Japan. In this paper, the simulation method through extended lognormal distribution with variable volatility, whose parameters are linked with the levels of interest rates at each future times, is introduced as a solution of these matters, and some results in comparison with conventional methods are shown.