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Linear‐Quadratic Jump‐Diffusion Modeling

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  • Peng Cheng
  • Olivier Scaillet

Abstract

We aim at accommodating the existing affine jump‐diffusion and quadratic models under the same roof, namely the linear‐quadratic jump‐diffusion (LQJD) class. We give a complete characterization of the dynamics of this class by stating explicitly the structural constraints, as well as the admissibility conditions. This allows us to carry out a specification analysis for the three‐factor LQJD models. We compute the standard transform of the state vector relevant to asset pricing up to a system of ordinary differential equations. We show that the LQJD class can be embedded into the affine class using an augmented state vector. This establishes a one‐to‐one equivalence relationship between both classes in terms of transform analysis.

Suggested Citation

  • Peng Cheng & Olivier Scaillet, 2007. "Linear‐Quadratic Jump‐Diffusion Modeling," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 575-598, October.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:4:p:575-598
    DOI: 10.1111/j.1467-9965.2007.00316.x
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    4. Li Chen & Damir Filipović & H. Vincent Poor, 2004. "Quadratic Term Structure Models For Risk‐Free And Defaultable Rates," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 515-536, October.
    5. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, University Library of Munich, Germany.
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