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Articles
  • OpenAccess
  • A Note on the Kou’s Continuity Correction Formula  [AFM 2015]
  • DOI: 10.4236/jss.2015.311005   PP.28 - 34
  • Author(s)
  • Ting Liu, Chang Feng, Yanqiong Lu, Bei Yao
  • ABSTRACT
  • This article introduces a hyper-exponential jump diffusion process based on the continuity correction for discrete barrier options under the standard B-S model, using measure transformation and stopping time theory to prove the correction, thus broadening the conditions of the continuity correction of Kou.

  • KEYWORDS
  • B-S Model, Discrete Barrier Options, Hyper-Exponential Jump Diffusion, Continuity Correction Formula
  • References
  • [1]
    Kou, S.G. (2003) First Passage Times of a Jump Diffusion Process. Advances in Applied Probability, 35, 504-531.
    http://dx.doi.org/10.1239/aap/1051201658
    [2]
    Kou, S. (1997) A Continuity Correction for Discrete Barrier Options. Mathematical Finance, 7, 325-348.
    http://dx.doi.org/10.1111/1467-9965.00035
    [3]
    Broadie, M., Glasserman, P. and Kou, S.G. (1999) Connecting Discrete and Continuous Path-Dependent Options. Finance Stochastic, 3, 55-82.
    http://dx.doi.org/10.1007/s007800050052
    [4]
    Kou, S.G. (2003) On Pricing of Discrete Barrier Options. Statistic Sinica, 13, 955-964.
    [5]
    Jun, D. (2013) Continuity Correction for Discrete Barrier Options with Two Barriers. Journal of Computational and Applied Mathematics, 237, 520-528.
    http://dx.doi.org/10.1016/j.cam.2012.06.021
    [6]
    Fuh, C.D., Luo, S.F. and Yen, J.F. (2013) Pricing Discrete Path-Dependent Options under a Double Exponential Jump- Diffusion Model. Journal of Banking & Finance, 37, 2702-2713.
    http://dx.doi.org/10.1016/j.jbankfin.2013.03.023
    [7]
    Kou, S.G. (2002) A Jump-Diffusion Model for Option Pricing. Management Science, 48, 1086-1101.
    http://dx.doi.org/10.1287/mnsc.48.8.1086.166
    [8]
    Cai, N. (2009) On First Passage Times of a Hyper-Exponential Jump Diffusion Process. Operations Research Letters, 37, 127-134.
    http://dx.doi.org/10.1016/j.orl.2009.01.002
    [9]
    Thakoor, N., Tangman, D.Y. and Bhuruth, M. (2014) Efficient and High Accuracy Pricing of Barrier Options under the CEV Diffusion. Journal of Computational and Applied Mathematics, 259, 182-193.
    http://dx.doi.org/10.1016/j.cam.2013.05.009
    [10]
    Zhang, C.H. (1988) A Nonlinear Renewal Theory. Annals of Probability, 6, 93-824.
    http://dx.doi.org/10.1214/aop/1176991788

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