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Stochastic Jumps
  • Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. The model is quite accurate. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large position gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio high profitable, especially for a large movement in the underlying stock price. , Tim Xiao (2013)
  • Pricing Constant Maturity Credit Default Swaps Under Jump Dynamics , H.Jonsson, W.Schoutens (2008)
  • Smart Expansion and Fast Calibration for Jump Diffusion Programming , E.Benhamou, E.Gobet, M.Miri (2007)
  • Constant Proportion Portfolio Insurance in Presence of Jumps in Asset Prices , R. Cont, P. Tankov (2007)
  • A Multi-factor Jump-Diffusion Model for Commodities , J.Crosby (2006)
  • Hedging Exotic Options in Stochastic Volatility and Jump Diffusion Models , K. Detlefsen (2005)
  • Option Pricing Under a Double Exponential Jump Diffusion Model , S.G. Kou, H. Wang (2004)
  • A Jump-Diffusion Model for Option Pricing , S.G. Kou (2002)
  • Static Hedging of Standard Options , P. Carr, L. Wu (2002)
  • Jump-Diffusion Processes : Volatility Smile Fitting and Numerical Methods for Pricing , L. Andersen, J. Andreasen (1999)

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