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Additive subordination and its applications in finance

Author

Listed:
  • Jing Li

    (CITIC Securities)

  • Lingfei Li

    (The Chinese University of Hong Kong)

  • Rafael Mendoza-Arriaga

    (The University of Texas at Austin)

Abstract

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner’s subordination that has proved to be extremely useful in financial modeling. Probabilistically, Bochner’s subordination corresponds to a stochastic time change with respect to an independent Lévy subordinator, while in additive subordination, the Lévy subordinator is replaced by an additive one. We generalize the classical Phillips theorem for Bochner’s subordination to the additive subordination case, based on which we provide Markov and semimartingale characterizations for a rich class of jump-diffusions and pure jump processes obtained from diffusions through additive subordination, and obtain spectral decomposition for them. To illustrate the usefulness of additive subordination, we develop an analytically tractable cross-commodity model for spread option valuation that is able to calibrate the implied volatility surface of each commodity. Moreover, our model can generate implied correlation patterns that are consistent with market observations and economic intuitions.

Suggested Citation

  • Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:3:d:10.1007_s00780-016-0300-8
    DOI: 10.1007/s00780-016-0300-8
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tong, Zhigang & Liu, Allen, 2022. "Pricing variance swaps under subordinated Jacobi stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    2. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    3. Weiwei Guo & Lingfei Li, 2019. "Parametric inference for discretely observed subordinate diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 77-110, April.
    4. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    5. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.
    6. Michele Azzone & Roberto Baviera, 2021. "A fast Monte Carlo scheme for additive processes and option pricing," Papers 2112.08291, arXiv.org, revised Jul 2023.
    7. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    8. Tong, Zhigang & Liu, Allen, 2021. "A censored Ornstein–Uhlenbeck process for rainfall modeling and derivatives pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    9. Michele Azzone & Roberto Baviera, 2019. "Additive normal tempered stable processes for equity derivatives and power law scaling," Papers 1909.07139, arXiv.org, revised Jan 2022.
    10. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, December.

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    More about this item

    Keywords

    Bochner’s subordination; Additive subordination; Time-inhomogeneous Markov processes; Spread options;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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