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Extensions of the Libor Market Model
  • Analytical Formulas for Pricing CMS Products in the LIBOR Market Model with the Stochastic Volatility In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for model calibration to the market, including European swaptions and CMS products. The first technical achievement of this work is related to the optimal calculation of the measure change. For single-rate CMS products, we have used the standard linear regression of the measure change, with optimally calculated coefficients. For the CMS spread options, where the linear procedure does not work, we propose a new effective extit{non-linear} measure change technique. The fit quality of the new results is confirmed numerically using Monte Carlo simulations. The second technical advance of the article is a theoretical derivation of the generalized spread option price via two-dimensional Laplace transform presented in a closed form in terms of the complex Gamma-functions. , A.Antonov, M.Arneguy (2009)
  • Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Discounting and Forwarding Yield Curves In this paper we revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using different yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors (e.g. Euribor 3 months, 6 months,.etc.). Within such double-curve-single-currency framework, adopted by the market after the liquidity crisis started in summer 2007, standard single-curve no arbitrage relations are no longer valid and can be formally recovered through the introduction of a basis adjustment. Numerical results show that the resulting basis adjustment curves may display an oscillating micro-term structure that may induce appreciable effects on the price of interest rate instruments. Recurring to the foreign-currency analogy we also derive no arbitrage double-curve market-like formulas for basic plain vanilla interest rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These expressions include a quanto adjustment typical of cross-currency derivatives, naturally originated by the change between the numeraires associated to the two yield curves, that carries on a volatility and correlation dependence. Numerical scenarios confirm that such correction can be non-negligible, thus making unadjusted double-curve prices, in principle, not arbitrage free. , M.Bianchetti (2009)
  • Post Credit Crunch Interest Rates: Formulas and Market Models , F. Mercurio (2009)
  • BOOTSTRAPPING THE ILLIQUIDITY The large basis spreads observed on the interest rate mar- ket since the liquidity crisis of summer 2007 imply that di?erent 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 multi- ple 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 e?ects and is ro- bust 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. , E. Gobet (2008)
  • LIBOR market model with SABR style stochastic volatility , P.Hagan, A.Lesniewski (2008)
  • Libor Market Model with Local Volatility , M.P.A.Henrard (2007)
  • An Extended Libor Market Model With Nested Stochastic Volatility Dynamics , J.Zhu (2007)
  • Unifying the Bgm and Sabr Models: a Short Ride in Hyperbolic Geometry , P.Henry-Labordere (2007)
  • A Time-Homogeous, SABR-Consistent Extension of the LMM: Calibration And Numerical Results , R.Rebonato (2007)
  • No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model , M.Morini, F.Mercurio (2007)
  • A Note on the SABR Model , M.Morini, F.Mercurio (2006)
  • LIBOR Market Model with Stochastic Volatility , L.Wu, F.Zhang (2006)
  • LIBOR Market Model with Stochastic Volatility , S.Svoboda (2005)
  • Capturing the Skew in Interest Rate Derivatives : A Shifted Lognormal LIBOR Model with Uncertain Parameters , E. Errais, G. Mauri, F. Mercurio (2004)
  • Cap and swaption approximations in Libor market models with jumps , P.Glasserman, N.Merener (2003)
  • A Stochastic Volatility Model for Bermuda Swaptions and Callable CMS Swaps , C.Albanese, M.Trovato (2003)
  • A Stochastic Volatility Forward Libor Model With a Term Structure Of Volatility Smiles , V.Pitebarg (2003)
  • LIBOR Market Model with Stochastic Volatility , D.Gatarek (2003)
  • A stochastic-volatility, displaced-diffusion extension of the LIBOR Market Model , M.Joshi, R.Rebonato (2002)
  • Yield Curve Modelling with Skews and Stochastic Volatility , L.Andersen, J.Andreasen (2002)
  • Extended Libor Market Models with Stochastic Volatility , L.Andersen, R.Brotherton-Ratcliffe (2001)
  • Volatility Skews and Extensions of the Libor Market Model , L.Andersen, J.Andreasen (1998)

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