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Using Model-Independent Lower Bounds To Improve Pricing Of Asian Style Options In Lã‰Vy Markets

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  • Deelstra, Griselda
  • Rayée, Grégory
  • Vanduffel, Steven
  • Yao, Jing

Abstract

Albrecher et al. (Albrecher, H., Mayer Ph., Schoutens, W. (2008) General lower bounds for arithmetic Asian option prices. Applied Mathematical Finance, 15, 123–149) have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

Suggested Citation

  • Deelstra, Griselda & Rayée, Grégory & Vanduffel, Steven & Yao, Jing, 2014. "Using Model-Independent Lower Bounds To Improve Pricing Of Asian Style Options In Lã‰Vy Markets," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 237-276, May.
    • Handle: RePEc:cup:astinb:v:44:y:2014:i:02:p:237-276_00
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    Cited by:

    1. Florian Stebegg, 2014. "Model-Independent Pricing of Asian Options via Optimal Martingale Transport," Papers 1412.1429, arXiv.org.
    2. Zhou, Ming & Dhaene, Jan & Yao, Jing, 2018. "An approximation method for risk aggregations and capital allocation rules based on additive risk factor models," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 92-100.

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