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Abstract:
We introduce a new calibration methodology that allows perfect fitting of the displaced diffusion LIBOR market model to caplets and co-terminal swaptions, whilst avoiding global optimizations. The approach works by regarding a forward rate as a difference of swap-rates and then bootstrapping through rates one by one.

market model, calibration, Bermudan swaptions

Abstract:
The large basis spreads observed on the interest rate market since the liquidity crisis of summer 2007 imply that different yield curves are required for market coherent estimation of forward rates with different tenors (e.g. Euribor 3 months, Euribor 6 months, etc.).

In this paper we review the methodology for bootstrapping multiple interest rate yield curves, each homogeneous in the underlying rate tenor, from non-homogeneous plain vanilla instruments quoted on the market, such as Deposits, Forward Rate Agreements, Futures, Swaps, and Basis Swaps.

The approach includes turn of year effects and is robust to deliver smooth yield curves and to ensure non-negative rates also in highly stressed market situations, characterized by crazy roller coaster shapes of the market quotations.

The concrete EUR market case is analyzed in detail, using the open source QuantLib implementation of the proposed algorithms.

Liquidity crisis, credit crunch, interest rates, yield curve, forward curve, discount curve, bootstrapping, pricing, hedging, interest rate derivatives, Deposit, FRA, Futures, Swap, Basis Swap, turn of year, spline, QuantLib