Negative Libor rates in the swap market model
نویسندگان
چکیده
We apply Stroock and Varadhan’s Support Theorem to show that there is a positive probability that within the Swap Market Model the implied Libor rates become negative in finite time.
منابع مشابه
Trivariate support of flat-volatility forward Libor rates
This paper investigates the multivariate support of forward Libor rates in the one-factor, constant volatilities Libor market model. The comparatively simple bivariate case was solved in Jamshidian [2] in connection to the recent finding by Davis and MataixPastor [1] of positive probability of negative Libor rates in the swap market model. The approach here builds on [2] but becomes really effe...
متن کاملLibor Market Model with Stochastic Volatility
In this paper we extend the standard LIBOR market model to accommodate the pronounced phenomenon of implied volatility smiles/skews. We adopt a multiplicative stochastic factor to the volatility functions of all relevant forward rates. The stochastic factor follows a square-root diffusion process, and it can be correlated to the forward rates. For any swap rate, we derive an approximate process...
متن کاملPricing CMS spreads in the Libor market model
We present two approximation methods for pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The rst method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study d...
متن کاملLibor and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis
In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both one-factor and two-fa...
متن کاملA Libor Market Model with Default Risk
In this paper a new credit risk model for credit derivatives is presented. The model is based upon the ‘Libor market’ modelling framework for default-free interest rates. We model effective default-free forward rates and effective forward credit spreads as lognormal diffusion processes, and recovery is modelled as a fraction of the par value of the defaulted claim. The newly introduced survival...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Finance and Stochastics
دوره 11 شماره
صفحات -
تاریخ انتشار 2007