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Efficient Option Pricing with Transaction Costs

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  • Michael Monoyios

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  • Alberto Montagnoli
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    Abstract

    A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor's basic portfolio selection problem, without the insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete time Markov chain approximation to a continuous time singular stochastic optimal control problem. A general de nition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed.

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    Bibliographic Info

    Paper provided by Economics and Finance Section, School of Social Sciences, Brunel University in its series Economics and Finance Discussion Papers with number 02-22.

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    Length: 23 pages
    Date of creation: Jul 2002
    Date of revision:
    Handle: RePEc:bru:bruedp:02-22

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    Postal: Brunel University, Uxbridge, Middlesex UB8 3PH, UK

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