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American continuous-installment options of barrier type

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Abstract

This paper analyzes and values an American barrier option with continuous payment plan written on a dividend paying asset under the classical Black-Scholes model. The integral representation of the initial premium along with the delta hedge parameter for an American continuous-installment down-and-out call option are obtained by using the decomposition technique. This offers a system of nonlinear integral equations for determining the optimal exercise and stopping boundaries, which can be utilized to approximate the option price and delta hedge parameter. The implementation is based on discretizing the quadrature formula in the system of equations and using the Newton-Raphson method to compute the two optimal boundaries at each time points. Numerical results are provided to illustrate the computational accuracy and the effects on the initial premium and optimal boundaries with respect to barrier.

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Authors and Affiliations

  1. School of Mathematics, Guangxi Normal University, Guilin, 541004, China

    Guohe Deng

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  1. Guohe Deng
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Correspondence to Guohe Deng.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 40675023 and Guangxi Natural Science Foundation under Grant No. 0991091.

This paper was recommended for publication by Editor WANG Shouyang.

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Deng, G. American continuous-installment options of barrier type. J Syst Sci Complex 27, 928–949 (2014). https://doi.org/10.1007/s11424-013-0310-y

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  • DOI: https://doi.org/10.1007/s11424-013-0310-y

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