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Density estimation through quasi-analytic Monte-Carlo simulation: Options arbitrage with transactions costs

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  • N. Chidambaran

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    Abstract

    Discretely rebalanced options arbitrage strategies in the presence of transaction costs have path dependent returns that are difficult to model analytically. I instead use a quasi-analytic procedure that combines the computational efficiency of analytical solutions with the flexibility of simulations. The central feature is the estimation of the distribution of returns of the arbitrage strategy by mapping simulated returns percentiles and the input parameter set. Using the estimated density, I evaluate the tradeoff between transaction costs and risk exposure under generalized transaction costs structures that includes bid-ask spread and brokerage commission. I show that the optimal strategy depends on transaction costs, volatility, and option moneyness. Strategies such as rebalancing when the hedge ratio changes by 0.25, balances transaction costs and risk exposure, and can be optimal. Copyright Springer Science+Business Media, LLC 2007

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    File URL: http://hdl.handle.net/10.1007/s11156-006-0005-8
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    Bibliographic Info

    Article provided by Springer in its journal Review of Quantitative Finance and Accounting.

    Volume (Year): 28 (2007)
    Issue (Month): 1 (January)
    Pages: 101-122

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    Handle: RePEc:kap:rqfnac:v:28:y:2007:i:1:p:101-122

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    Web page: http://springerlink.metapress.com/link.asp?id=102990

    Related research

    Keywords: Rebalancing; Discrete; Frequency; Options arbitrage; Density estimation; Transactions cost;

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    1. Russell P. Robins & Barry Schachter, 1994. "An Analysis of the Risk in Discretely Rebalanced Option Hedges and Delta-Based Techniques," Management Science, INFORMS, vol. 40(6), pages 798-808, June.
    2. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March.
    4. Figlewski, Stephen, 1989. " Options Arbitrage in Imperfect Markets," Journal of Finance, American Finance Association, vol. 44(5), pages 1289-1311, December.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
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