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A Barrier Option of American Type

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Abstract.

We obtain closed-form expressions for the prices and optimal hedging strategies of American put-optionsin the presence of an ``up-and-out" barrier , both with and without constraints on the short-selling of stock. The constrained case leads to a stochastic optimization problem of mixed optimal stopping/singular controltype. This is reduced to a variational inequality which is then solved explicitly in two qualitatively separate cases, according to a certain compatibility condition among the market coefficients and the constraint.

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Authors and Affiliations

  1. Departments of Mathematics and Statistics, 619 Math. Bldg., Columbia University, New York, NY 10027, USA ik@math.columbia.edu, USA

    I. Karatzas

  2. Division of Applied Mathematics, 182 George Street, Room 223, Brown University, Box F, Providence, RI 02915, USAhuiwang@cfm.brown.edu , USA

    H. Wang

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  1. I. Karatzas
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  2. H. Wang
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Accepted 18 May 2000. Online publication 13 November 2000.

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Karatzas, I., Wang, H. A Barrier Option of American Type. Appl Math Optim 42, 259–279 (2000). https://doi.org/10.1007/s002450010013

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  • DOI: https://doi.org/10.1007/s002450010013

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