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  • Calibrating the SABR Model to Noisy FX Data We consider the problem of fitting the SABR model to an FX volatility smile. It is demonstrated that the model parameter β cannot be determined from a log-log plot of σATM against F. It is also shown that, in an FX setting, the SABR model has a single state variable. A new method is proposed for fitting the SABR model to observed quotes. In contrast to the fitting techniques proposed in the literature, the new method allows all the SABR parameters to be retrieved and does not require prior beliefs about the market. The effect of noise on the new fitting technique is also investigated. , Hilary (2018)  
  • Joining the SABR and Libor models together Fabio Mercurio and Massimo Morini propose a Libor market model consistent with SABR dynamics and develop approximations that allow for the use of the SABR formula with modified inputs. They verify that the approximations are acceptably precise, imply good fitting of market data and produce regular Libor rate parameters. They finally show that the correct assessment of the no-arbitrage volatility drift leads to a more sensible pricing of derivatives not included in the calibration set. , Mercurio, Morini (2009)  
  • Extensions to the Gaussian copula: random recovery and random factor loadings This paper presents two new models of portfolio default loss that extend the standard Gaussian copula model yet preserve tractability and com- putational efficiency. In one extension, we randomize recovery rates, explicitly allowing for the empirically well-established effect of inverse correlation between recovery rates and default frequencies. In another extension, we build into the model random systematic factor loadings, effectively allowing default correlations to be higher in bear markets than in bull markets. In both extensions, special cases of the models are shown to be as tractable as the Gaussian copula model and to allow efficient calibration to market credit spreads. We demonstrate that the models – even in their simplest versions – can generate highly significant pricing effects such as fat tails and a correlation “skew” in synthetic CDO tranche prices. When properly calibrated, the skew effect of random recovery is quite minor, but the extension with random factor loadings can produce correlation skews similar to the steep skews observed in the market. We briefly discuss two alternative skew models, one based on the Marshall- Olkin copula, the other on a spread-dependent correlation specification for the Gaussian copula. , L. Andersen, J. Sidenius (2005)  

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