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Robust hedging of double touch barrier options


Reference:

Cox, A. M. G. and Obloj, J., 2011. Robust hedging of double touch barrier options. SIAM Journal on Financial Mathematics, 2 (1), pp. 141-182.

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    Official URL:

    http://dx.doi.org/10.1137/090777487

    Abstract

    We consider robust pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the initial prices of call options with the same maturity and all strikes are known. In such circumstances, we are able to give upper and lower bounds on the arbitrage-free prices of the relevant options and show that these bounds are tight. Moreover, pathwise inequalities are derived, which provide the trading strategies with which we are able to realize any potential arbitrages. These super- and subhedging strategies have a simple quasi-static structure, their associated hedging error is bounded below, and in practice they carry low transaction costs. We show that, depending on the risk aversion of the investor, they can outperform significantly the standard delta/vega-hedging in presence of market frictions and/or model misspecification. We make use of embeddings techniques; in particular, we develop two new solutions to the (optimal) Skorokhod embedding problem.

    Details

    Item Type Articles
    CreatorsCox, A. M. G.and Obloj, J.
    DOI10.1137/090777487
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementRobustDoubleTouchSIAMFinal.pdf: ©SIAM Journal on Financial Mathematics
    RefereedYes
    StatusPublished
    ID Code25602

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