Tesi di LAUREA SPECIALISTICA
TitoloPricing e Risk-Management dei prodotti derivati su tassi di interesse nel quadro Multi-Curve
Data2011-12-20
Autore/iGalante, Flavia
RelatoreSgarra, C.
Full textnon disponibile
AbstractSince the subprime crisis of 2007, massive arbitrages have raised the question of the traditional valuation theory for rate products. It is now widely recognised that a unique rate curve is no longer enough to reproduce the behaviour of the market of interest rates and that it is necessary to consider several curves to estimate forward rates of di erent tenors. In this report, we shall rst present the multi curve model in terms of vanilla option prices and general pricing methods then we shall tackle the question of the construction of several curves. Finally, we shall get into more details for the Kenyon model, a multi curve extension of the one factor Hull-White model that will allow us to have a theoretical framework to price bermudan swaptions thanks to a 2 dimensional PDE and an ADI numerical method. In particular, in Chapter 1 we will detail the multi-curve problematic, giving some examples that gave rise to the problem (the cotations of the forward swap rates Euribor vs Eonia, the FRA rates vs Forward rates and the basis swaps) and describing the market evolution in the pricing of interest rate derivatives. In Chapter 2 we will introduce the bootstrapping procedure to build the yield curves. First we will illustrate the market instruments used for the calibration procedure, then we will show the di erence between the mono-curve and the multi-curves frameworks in the construction procedure, giving numerical examples. In Chapter 3, we shall rst recall the HJM framework, then we shall illustrate the Hull-White 1 and 2 factors models and nally we shall detail the Kenyon framework. We will demonstrate the existence of an analytical formula for the pricing of an European Swaption. In Chapter 4 considering the Kenyon framework, for an interest rate derivative we will write the 2-dimensional PDE associated to the state variables and we will solve numerically the problem thanks to the ADI method to price a Bermudan Swaption.