Yield Reversals and the Yin-Yang Trap: A Note on Time Valuation and Interest Rate Swaps

The time value function for a vanilla interest rate swap is derived in this note. For monotonic and stationary yield curves, value is zero at the end points and either wholly negative or wholly positive over the life of the swap. But reversals in the term structure of interest rates from inverted to normal produce a swing between positive and negative values and result in an apparently alarming loss of value in an exposed swap. This rationalises recent profitability loss in unmatched swaps books.