Libor Market Model in Premia* BERMUDAN PRICER, STOCHASTIC VOLATILITY AND MALLIAVIN CALCULUS

T he aim of Premia is to provide with numerical algorithms applied to the pricing of derivative products with the relevant mathematical details. Up to Premia 6 all the focus was on equity derivative products. All known numerical methods, from partial differential equations methods to Monte Carlo methods were applied to equity derivative pricing and/or calibration. Therefore it was rather natural to start the implementation of the models devoted to other derivatives markets. The interest rate derivatives market appears to be the next challenging step. Since the seminal work of Vasicek [26] on the pricing of a bond in a stochastic interest rates framework a large number of works dealing with the pricing of interest rate derivatives were proposed by academies. The fi rst extensions of this model made in the early eighties mainly specifi ed different dynamics for the short rate thus following the modeling strategy proposed by Vasicek. The focus was on bond pricing and the pricing of a call/put on a bond and option on a coupon bearing bond which were the most important derivatives in the eighties. One of the main diffi culty with this approach was the lack of consistency with the initial term structure of interest rates. As pointed out by Cox, Ingersoll and Ross [10] this problem could be overcome by letting the parameters to be time dependent. Nevertheless this solution proved to be unsatisfactory in certain case. It leads Heath, Jarrow and Morton [14] to reformulate the modeling of interest rates by taking as state variables not only the short rate but all the (instantaneous) forward rate curve thus building a framework which is consistent with the initial term structure by construction.