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Additive logistic processes in option pricing

Author

Listed:
  • Peter Carr

    (NYU Tandon School of Engineering)

  • Lorenzo Torricelli

    (University of Parma)

Abstract

In option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, it is possible to reverse this paradigm: starting from an arbitrage-free option valuation formula, one could derive a family of risk-neutral probabilities and a corresponding risk-neutral underlying asset process. In this paper, we start from two simple arbitrage-free valuation equations, inspired by the log-sum-exponential function and an ℓ p $\ell ^{p}$ vector norm. Such expressions lead respectively to logistic and Dagum (or “log-skew-logistic”) risk-neutral distributions for the underlying security price. We proceed to exhibit supporting martingale processes of additive type for underlying securities having as time marginals two such distributions. By construction, these processes produce closed-form valuation equations which are even simpler than those of the Bachelier and Samuelson–Black–Scholes models. Additive logistic processes provide parsimonious and simple option pricing models capturing various important stylised facts at the minimum price of a single market observable input.

Suggested Citation

  • Peter Carr & Lorenzo Torricelli, 2021. "Additive logistic processes in option pricing," Finance and Stochastics, Springer, vol. 25(4), pages 689-724, October.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:4:d:10.1007_s00780-021-00461-8
    DOI: 10.1007/s00780-021-00461-8
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    References listed on IDEAS

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    Cited by:

    1. Michele Azzone & Roberto Baviera, 2023. "Is (independent) subordination relevant in option pricing?," Papers 2307.08628, arXiv.org, revised Oct 2023.
    2. Michele Azzone & Roberto Baviera, 2023. "A fast Monte Carlo scheme for additive processes and option pricing," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    3. Zheng Cao, 2024. "Stochastic Calculus for Option Pricing with Convex Duality, Logistic Model, and Numerical Examination," Papers 2408.05672, arXiv.org.
    4. Michele Azzone & Roberto Baviera, 2021. "A fast Monte Carlo scheme for additive processes and option pricing," Papers 2112.08291, arXiv.org, revised Jul 2023.
    5. Jimin Lin & Guixin Liu, 2024. "Neural Term Structure of Additive Process for Option Pricing," Papers 2408.01642, arXiv.org, revised Oct 2024.

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    More about this item

    Keywords

    Logistic distribution; Additive processes; Derivative pricing; Dagum distribution; Generalised z $z$ -distributions;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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