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On the Relation between Linearity-Generating Processes and Linear-Rational Models

Author

Listed:
  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute)

  • Martin Larsson

    (ETH Zurich - Department of Mathematics)

  • Anders B. Trolle

    (Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute)

Abstract

We review the notion of a linearity-generating (LG) process introduced by Gabaix (2009) and relate LG processes to linear-rational (LR) models studied in Filipovic, Larsson, and Trolle (2014). We show that every LG process can be represented as an LR model of the same dimension. More importantly, we identify those (m 1)-dimensional LG processes that can be represented as m-dimensional LR models. We show that these are the only LG processes that are stationary and mean-reverting after exponential scaling. We highlight the ease with which LR models can be specified and be made consistent with nonnegative interest rates. We also show that LR models fit naturally into the state price density factorization due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009).

Suggested Citation

  • Damir Filipović & Martin Larsson & Anders B. Trolle, 2016. "On the Relation between Linearity-Generating Processes and Linear-Rational Models," Swiss Finance Institute Research Paper Series 16-23, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1623
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    File URL: http://ssrn.com/abstract=2753484
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    Cited by:

    1. Likuan Qin & Vadim Linetsky, 2018. "Long-term factorization in Heath–Jarrow–Morton models," Finance and Stochastics, Springer, vol. 22(3), pages 621-641, July.

    More about this item

    Keywords

    Linearity-Generating Process; Linear-Rational Model; Long-Term Risk; State Price Density;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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