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Splitting and matrix exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps

Author

Listed:
  • Andrey Itkin

    (School of Engineering, New York University)

Abstract

This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard finite-difference methods. For the jump part, we transform the jump integral into a pseudo-differential operator and construct its second order approximation on a grid which supersets the grid used for the diffusion part. The proposed schemes are unconditionally stable in time and preserve positivity of the solution which is computed either via a matrix exponential, or via its Páde approximation. Various numerical experiments are provided to justify these results.

Suggested Citation

  • Andrey Itkin, 2014. "Splitting and matrix exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps," Algorithmic Finance, IOS Press, vol. 3(3-4), pages 233-250.
    • Handle: RePEc:ris:iosalg:0033
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    Cited by:

    1. is not listed on IDEAS
    2. Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513, arXiv.org, revised Nov 2014.
    3. Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.

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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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