Two curves, one price

The financial crisis has multiplied the yield curves used to price plain vanilla interest rate derivatives, making classic single-curve no-arbitrage relations and pricing formulas no longer valid. Marco Bianchetti shows that no-arbitrage can be recovered by taking into account the basis adjustment bootstrapped from market basis swaps, and that generalised no-arbitrage double-curve pricing formulas can be derived for vanillas by using the foreign currency analogy, including a quanto-like adjustment typical of cross-currency derivatives. Both the basis and the quanto adjustments find a simple financial interpretation in terms of counterparty risk

The credit crunch that began in the second half of 2007 has triggered, among many consequences, the explosion of the basis spreads quoted on the market between single-currency interest rate instruments (swaps in particular) characterised by different underlying rate tenors (Xibor three-month and Xibor six-month, etc, where Xibor denotes a generic interbank offered rate). In figure 1, we show a snapshot of the market quotations as of February 16, 2009 for the six basis swap term structures