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Joint distribution of Brownian motion and its maximum, with a generalization to correlated BM and applications to barrier options

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  • Chuang, Chin-Shan

Abstract

Consider Brownian motion Bt and its maximum Mt = max0 [less-than-or-equals, slant] s [less-than-or-equals, slant] t Bs. We derive the joint distribution of (Ms, Bt) for all s and make a generalization to correlated BM. These distributions are applied to price barrier options.

Suggested Citation

  • Chuang, Chin-Shan, 1996. "Joint distribution of Brownian motion and its maximum, with a generalization to correlated BM and applications to barrier options," Statistics & Probability Letters, Elsevier, vol. 28(1), pages 81-90, June.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:1:p:81-90
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    References listed on IDEAS

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    1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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    2. Julien Azzaz & Stéphane Loisel & Pierre-E. Thérond, 2015. "Some characteristics of an equity security next-year impairment," Review of Quantitative Finance and Accounting, Springer, vol. 45(1), pages 111-135, July.
    3. repec:hal:wpaper:hal-00820929 is not listed on IDEAS
    4. Rahul R. Marathe & Sarah M. Ryan, 2009. "Capacity expansion under a service‐level constraint for uncertain demand with lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 250-263, April.
    5. Manfred Marvin Marchione & Enzo Orsingher, 2022. "Hitting Distribution of a Correlated Planar Brownian Motion in a Disk," Mathematics, MDPI, vol. 10(4), pages 1-12, February.

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