The Price-Rate Duality: Theory of the Basis Spreads

Abstract

After the Subprime Crisis of 2007, basis spreads quoted for swaps and cross currency swaps rose. Until that moment, these spreads could be considered negligible from a pricing point of view and, as a consequence of this, valuation systems did not include these spreads as relevant variables. However, for as long as the size of these spreads did not return to the previous level, their impact in pricing had to be considered. The most standard model consists in the substitution of the interest rate curve by several rate curves depending on: either the tenors in order to estimate their forwards (for pricing basis swaps), or the currency chosen as local currency in order to estimate discount factors (for pricing cross currency swaps). The model proposed in this paper postulates the existence of a Price-Rate duality in the swap market in order to get a deeper understanding of this phenomenon. Furthermore, this model establishes a new way of reducing the number of curves that the multi-curve model needs.