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Price comparison results and super‐replication: An application to passport options

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  • Vicky Henderson

Abstract

In this paper, we provide a new proof of the result that option prices are increasing in volatility when the underlying is a diffusion process. This has been shown to hold for convex payoff, path‐independent options by El Karoui et al. and Hobson amongst others. The advantage of the new proof is that it can be extended to establish monotonicity results for path‐dependent payoffs where the payoff depends on the maximum (or minimum) of the asset price process. The techniques used to prove each of these results are mean comparison theorems of Hajek and coupling of stochastic processes. Using these results, and the connection between passport and look back options, we prove that the price of a passport option is increasing in volatility for general diffusion models for the asset price. It is shown that the seller of a passport option can super‐replicate if the volatility is overestimated, regardless of the strategy followed by the holder. Copyright © 2000 John Wiley & Sons, Ltd.

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  • 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.
    • Handle: RePEc:wly:apsmbi:v:16:y:2000:i:4:p:297-310
    DOI: 10.1002/1526-4025(200010/12)16:43.0.CO;2-M
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    Cited by:

    1. Vicky Henderson & David Hobson, 2001. "Passport options with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 97-118.
    2. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    3. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.

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