Assume that we have one single liability cash flow of 248.91 at time 23. The annual interest rate is 15%.
The asset portfolio is constructed using two cash flows: $A at time 2, and $B at time t. The value of A, B, and t are calculated such that the asset portfolio has the chosen present value, modified duration, and convexity.
Move the sliders and find the conditions for assets volatility and convexity such that the net present value is positive for all interest rate.
The plot on the left shows the present value of assets and liability separately. The plot on the right shows the net present value, with the shaded area representing the region where the NPV is negative.