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Monotonicity In The Volatility Of Single-Barrier Option Prices

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  • JONATAN ERIKSSON

    (Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden)

Abstract

We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the following cases:• If the risk-free rate of return dominates the dividend rate, then it holds for up-and-out options if the contract function is zero at the barrier and for down-and-in options in general.• If the risk-free rate of return is dominated by the dividend rate, then it holds for down-and-out options if the contract function is zero at the barrier and for up-and-in options in general.We apply our results to show that a hedger who misspecifies the volatility using a time-and-level dependent volatility will super-replicate any claim satisfying the above conditions if the misspecified volatility dominates the true (possibly stochastic) volatility almost surely.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:06:n:s0219024906003822
    DOI: 10.1142/S0219024906003822
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    Cited by:

    1. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.

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