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Weak time-derivatives and no-arbitrage pricing

Author

Listed:
  • Massimo Marinacci

    (Università Bocconi)

  • Federico Severino

    (Università della Svizzera Italiana (USI)
    Università Bocconi)

Abstract

We prove a risk-neutral pricing formula for a large class of semimartingale processes through a novel notion of weak time-differentiability that permits to differentiate adapted processes. In particular, the weak time-derivative isolates drifts of semimartingales and is null for martingales. Weak time-differentiability enables us to characterize no-arbitrage prices as solutions of differential equations, where interest rates play a key role. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (Econometrica 77:177–234, 2009) by employing weak time-derivatives.

Suggested Citation

  • Massimo Marinacci & Federico Severino, 2018. "Weak time-derivatives and no-arbitrage pricing," Finance and Stochastics, Springer, vol. 22(4), pages 1007-1036, October.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:4:d:10.1007_s00780-018-0371-9
    DOI: 10.1007/s00780-018-0371-9
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    References listed on IDEAS

    as
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    7. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    No-arbitrage pricing; Weak time-derivative; Martingale component; Special semimartingales; Stochastic interest rates;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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