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SABR Model
  • Series Expansion of the SABR Joint Density models Under the SABR stochastic volatility model, pricing and hedging contracts that are sensitive to forward smile risk (e.g., forward starting options, barrier options) require the joint transition density. In this paper, we address this problem by providing closed-form representations, asymptotically, of the joint transition density. Specifically, we construct an expansion of the joint density through a hierarchy of parabolic equations after applying total volatility-of-volatility scaling and a near-Gaussian coordinate transformation. We then established an existence result to characterize the truncation error and provide explicit joint density formulas for the first three orders. Our approach inherits the same spirit of a small total volatility-of-volatility assumption as in in the original SABR analysis. Our results for the joint transition density serve as a basis for managing forward smile risk. Through numerical experiments, we illustrate the accuracy of our expansion in terms of joint density, marginal density, probability mass and implied volatilities for European call options , Q.Wu (2010)
  • Fitting the Smile, Smart Parameters for SABR and Heston models In this paper we revisit the problem of calibrating stochastic volatility models. By finding smart initial parameters, we improve robustness of Levenberg-Marquardt. Applying this technique to the SABR and Heston models reduces calibration time by more than 90% compared to global optimization techniques such as Simplex or Differential Evolution. , P.Gauthier, P.H.Y, Rivaille (2009)
  • LIBOR market model with SABR style stochastic volatility models , P.Hagan, A.Lesniewski (2008)
  • Local Time for the SABR Model: Connection with the Complex Black Scholes and Application to CMS and Spread Options models , E.Benhamou, O.Croissant (2008)
  • A Stochastic Volatility Alternative to SABR models , L.C.G.Rogers, L.A.M.Veraart (2008)
  • Effective Parameters for Stochastic Volatility Models models , Z.Wang (2007)
  • Unifying the Bgm and Sabr Models: a Short Ride in Hyperbolic Geometry models , P.Henry-Labordere (2007)
  • A Time-Homogeous, SABR-Consistent Extension of the LMM: Calibration And Numerical Results models , R.Rebonato (2007)
  • Fine-tune your smile: Correction to Hagan et al models , J.Obloj (2007)
  • No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model models , M.Morini, F.Mercurio (2007)
  • The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model models , Y.Osajima (2007)
  • A Note on the SABR Model models , M.Morini, F.Mercurio (2006)
  • Managing Smile Risk models , P.S.Hagan, D.Kumar, A.Lesniewski, D.E.Woodwar (2004)





















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