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The modified sequential hedging strategy: Hedger’s loss distribution

  • Stochastic Systems, Queueing Systems
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Abstract

We study the distribution of hedging costs for the seller of an American call option who uses the modified sequential hedging strategy. Buying and selling of the underlying asset is done when the underlying asset’s price intersects a band that includes the exercise price. We obtain analytic expressions for conditional and unconditional distribution functions of the hedger’s costs. The conditional distribution is found for a known number of intersections of the band by the underlying asset’s course trajectory. We propose an algorithm for estimating the quantile of the cost distribution (VaR criterion) that uses the quantile values for the hedger’s conditional cost distribution.

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References

  1. Seidenverg, E., A Case of Confused Identity, Finan. Anal. J., 1988, vol. 44, no. 4, pp. 63–67.

    Article  Google Scholar 

  2. Carr, P., The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value, Rev. Finan. Studies, 1990, vol. 3, no. 3, pp. 469–492.

    Article  Google Scholar 

  3. Burenin, A.N., F’yuchersnye, forvardnye i optsionnye rynki (Future, Forward, and Option Markets), Moscow: Trivola, 1995.

    Google Scholar 

  4. Burenin, A.N., Rynki proizvodnykh finansovykh instrumentov (Markets of Financial Derivatives), Moscow: Infra-M, 1996.

    Google Scholar 

  5. Guberniev, V.A. and Kibzun, A.I., Stop-Loss Start-Gain Strategy: Analysis and Improvement, Autom. Remote Control, 1999, vol. 60, no. 1, part 2, pp. 92–101.

    MATH  MathSciNet  Google Scholar 

  6. Kibzun, A.I. and Sobol’, V.R., A Modernization of the Sequential Hedging Strategy for an Option Position, Proc. Inst. Math. Mekh., Ural Branch of RAS, 2013, vol. 19, no. 2, pp. 179–192.

    MathSciNet  Google Scholar 

  7. Rockafellar, R.T. and Uryasev, S., Conditional Value-at-Risk for General Loss Distributions, J. Bank. Finance, 2002, vol. 26, no. 7, pp. 1443–1471.

    Article  Google Scholar 

  8. Borisov, I.S. and Nikitina, N.N., Distribution of the Number of Intersections of a Band by Trajectories of Elementary Random Walks and Wiener Process with Shift, Teor. Veroyat. Primen., 2011, vol. 56, no. 1, pp. 152–158.

    Article  MathSciNet  Google Scholar 

  9. Formalev, V.F. and Reviznikov, D.L., Chislennye metody (Numerical Methods), Moscow: Fizmatlit, 2004.

    Google Scholar 

  10. Artzner, P., Coherent Measures of Risk, Math. Finance, 1999, vol. 9, no. 3, pp. 203–228.

    Article  MATH  MathSciNet  Google Scholar 

  11. Semakov, S.L., Vybrosy sluchainykh protsessov. Prilozheniya v aviatsii (Outliers of Random Processes. Applications in Aviation), Moscow: Nauka, 2005.

    Google Scholar 

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Moscow, Russia

    A. I. Kibzun & V. R. Sobol’

Authors
  1. A. I. Kibzun
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  2. V. R. Sobol’
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Correspondence to A. I. Kibzun.

Additional information

Original Russian Text © A.I. Kibzun, V.R. Sobol’, 2015, published in Avtomatika i Telemekhanika, 2015, No. 11, pp. 34–50.

This paper was recommended for publication by A.V. Nazin, a member of the Editorial Board

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Kibzun, A.I., Sobol’, V.R. The modified sequential hedging strategy: Hedger’s loss distribution. Autom Remote Control 76, 1931–1944 (2015). https://doi.org/10.1134/S000511791511003X

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  • DOI: https://doi.org/10.1134/S000511791511003X

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