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SABR Model
  • Advanced Analytics for the SABR Model In this paper, we present advanced analytical formulas for SABR model option pricing. The first technical result consists of a new exact formula for the zero correlation case. This closed form is a simple 2D integration of elementary functions, particularly attractive for numerical implementation. The second result is an effective approximation of the general correlation case. We use a map to the zero correlation case having a nice behavior on strike edges. The map formulas are easily implemented and do not contain any numerical integration. These formulas are important in volatility surface construction and CMS products replication because they provide correct behavior for far strikes and reduced approximation error. The latter is also helpful for dynamic SABR models. , A.Antonov, M.Spector (2012)
  • Series Expansion of the SABR Joint Density 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 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)
  • Asymptotic Implied Volatility at the Second Order with Application to the SABR Model We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model. , L.Paulot (2009)
  • LIBOR market model with SABR style stochastic volatility , P.Hagan, A.Lesniewski (2008)
  • Local Time for the SABR Model: Connection with the Complex Black Scholes and Application to CMS and Spread Options , E.Benhamou, O.Croissant (2008)
  • A Stochastic Volatility Alternative to SABR , L.C.G.Rogers, L.A.M.Veraart (2008)
  • Effective Parameters for Stochastic Volatility Models , Z.Wang (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)
  • Fine-tune your smile: Correction to Hagan et al , J.Obloj (2007)
  • No-Arbitrage Dynamics for a Tractable SABR Term Structure Libor Model , M.Morini, F.Mercurio (2007)
  • The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model , Y.Osajima (2007)
  • A Note on the SABR Model , M.Morini, F.Mercurio (2006)
  • Managing Smile Risk , P.S.Hagan, D.Kumar, A.Lesniewski, D.E.Woodwar (2004)





















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