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Abstract: The crisis that affected financial markets in the last years leaded marketpractitioners to revise well known basic concepts like the ones of discountfactors and forward rates. A single yield curve is not sufficient any longer todescribe the market of interest rate products. On the other hand, usingdifferent yield curves at the same time requires a reformulation of most of thebasic assumptions made in interest rate models. In this paper we discuss marketevidences that led to the introduction of a series of different yield curves.We then define a HJM framework based on a multi-curve approach, presenting alsoa bootstrapping algorithm used to fit these different yield curves to marketprices of plain-vanilla contracts such as basic Interest Rate Swaps IRS andForward Rate Agreements FRA. We then show how our approach can be used inpractice when pricing other interest rate products, such as forward startingIRS, plain-vanilla European Swaptions, Constant Maturity Swaps CMS and CMSspread options, with the final goal to investigate whether the market isactually using a multi-curve approach or not. We finally present some numericalexamples for a simple formulation of the framework which embeds by constructionthe multi-curve structure; once the model is calibrated to market prices ofplain-vanilla options, it can be used via a Monte Carlo simulation to pricemore complicated exotic options.

Autor: Andrea Pallavicini, Marco Tarenghi


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