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An excellent approximation for the m out of n day provision

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  • Liu, Qiang
  • Guo, Shuxin

Abstract

The m out of n day provision (MooN) of convertible bonds is difficult to handle. To approximating the MooN better, this paper proposes an approach named the conditional range probability (CRP). CRP is the simulated probability of the MooN being reached within a price range at a future time, conditional on today’s price of the underlying, and can be incorporated into any conventional derivatives pricing method. For a purposely designed exotic call option with a 20 out of 30 day provision, CRP under finite difference is found to outperform significantly several existing approaches and produce a mean pricing error of 1% over a wide range of initial underlying prices for the exotic call. The result implies that finite difference utilizing CRP will yield excellent approximating prices for convertible bonds.

Suggested Citation

  • Liu, Qiang & Guo, Shuxin, 2020. "An excellent approximation for the m out of n day provision," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    • Handle: RePEc:eee:ecofin:v:54:y:2020:i:c:s1062940820301194
    DOI: 10.1016/j.najef.2020.101222
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    References listed on IDEAS

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    4. Ali Bora Yiǧitbaşioǧlu & Carol Alexander, 2006. "Pricing And Hedging Convertible Bonds: Delayed Calls And Uncertain Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 415-453.
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    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Tian‐Shyr Dai & Chen‐Chiang Fan & Liang‐Chih Liu & Chuan‐Ju Wang & Jr‐Yan Wang, 2022. "A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2103-2134, December.

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    More about this item

    Keywords

    M out of n day provision; Soft call provision; Simulated conditional range probabilities; Consecutive m out of n day provision; 20 out of 30 day provision;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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