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Comparison results for path-dependent options

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  • Bergenthum Jan

    (Universität Freiburg, Department of Mathematical Stochastics, Freiburg)

  • Rüschendorf Ludger

Abstract

In this paper comparison results of convex type are established for several path-dependent options in some classes of semimartingale models. The options considered are some classes of lookback options, Asian and American options and barrier options. Comparison of the path-dependent options is based on ordering properties of the local characteristics of the underlying processes as well as on suitable propagation of convexity property. These properties allow a stochastic analysis of the basic linking process which establishes a link between the value processes in the underlying models. The linking process gives a unified tool to obtain comparison results for these path-dependent options. This paper extends and unifies several results in the literature.

Suggested Citation

  • Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    • Handle: RePEc:bpj:strimo:v:26:y:2008:i:1:p:53-72:n:5
    DOI: 10.1524/stnd.2008.0912
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    References listed on IDEAS

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    1. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    2. Jonatan Eriksson, 2006. "Monotonicity In The Volatility Of Single-Barrier Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 987-996.
    3. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    4. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    5. Vicky Henderson, 2000. "Price comparison results and super‐replication: An application to passport options," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 16(4), pages 297-310, October.
    6. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    7. Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
    8. X. Zhang, 1997. "Some Intersection Theorems and Minimax Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 195-207, July.
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    Cited by:

    1. Gilles Pag`es & Christian Yeo, 2024. "Convex ordering for stochastic control: the swing contracts case," Papers 2406.07464, arXiv.org, revised Jun 2024.

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