Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

TL;DR

This paper develops a comprehensive framework for pricing and hedging interest rate derivatives using multiple yield curves, incorporating forward basis and quanto adjustments, with numerical analysis showing significant effects on prices.

Contribution

It introduces a generalized no-arbitrage formula for double-curve interest rate derivatives, accounting for forward basis and cross-currency adjustments, extending standard models.

Findings

Forward basis curves exhibit rich micro-term structures affecting prices.

Quanto adjustments depend on volatility and correlation, impacting arbitrage considerations.

Unadjusted prices may violate no-arbitrage conditions due to basis and adjustment effects.

Abstract

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations are no longer valid, and can be recovered by taking properly into account the forward basis bootstrapped from market basis swaps. Numerical results show that the resulting forward basis curves may display a richer micro-term structure that may induce appreciable effects on the price of interest rate instruments. By recurring to the foreign-currency analogy we also derive generalised no-arbitrage double-curve market-like formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of cross-currency derivatives, naturally originated by the change between the numeraires associated to the two yield curves, that carries on a volatility and correlation dependence. Numerical scenarios confirm that such correction can be non negligible, thus making unadjusted double-curve prices, in principle, not arbitrage free. Both the forward basis and the quanto adjustment find a natural financial explanation in terms of counterparty risk.