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A probabilistic analysis of the trading the line strategy

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  • V. Abramov
  • M. K. Khan
  • R. A. Khan

Abstract

We provide analytic models for which the appropriate statistics of the trading the line strategy, Nh, can be derived in closed form. In particular, we provide closed-form expressions concerning the average duration of the open position, E(Nh), the variance of the open duration, Var(Nh), the average of the stopped log price, E(SNh), the variance of the stopped log price, Var(SNh), the correlation, Corr(Nh, SNh), and the Laplace transform, E(e-sNh). These results are obtained, in discrete time settings, for binomial and other price scenarios. Furthermore, when analytic results are not possible, such as the case of a normal distribution for log returns, we show by simulation that our general conclusions still hold. Using these statistics we point out some of the subtle features of the trailing stops strategy.

Suggested Citation

  • V. Abramov & M. K. Khan & R. A. Khan, 2008. "A probabilistic analysis of the trading the line strategy," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 499-512.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:5:p:499-512
    DOI: 10.1080/14697680701489427
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    References listed on IDEAS

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    1. Khan, Rasul A., 1979. "Some first passage problems related to cusum procedures," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 207-215, November.
    2. Donald L. Iglehart & Mark L. Stone, 1983. "Regenerative Simulation for Estimating Extreme Values," Operations Research, INFORMS, vol. 31(6), pages 1145-1166, December.
    3. Peter W. Glynn & Donald L. Iglehart, 1995. "Trading Securities Using Trailing Stops," Management Science, INFORMS, vol. 41(6), pages 1096-1106, June.
    4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Bochuan Dai & Ben R. Marshall & Nhut H. Nguyen & Nuttawat Visaltanachoti, 2021. "Risk reduction using trailing stop‐loss rules," International Review of Finance, International Review of Finance Ltd., vol. 21(4), pages 1334-1352, December.

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