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A Poisson-Gaussian model to price European options on the extremum of several risky assets within the HJM framework

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Abstract

This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The stochastic interest rate is assumed to follow an extended multi-factor HJM model with jumps. The authors provide explicitly the closed-form solutions of these options through the change of numeraire technique and examine the effects of both jump risks and stochastic interest rate on the option price with numerical experiment. The model can be seen as an extension of Stulz (1982), Johnson (1987) and Lindset (2006).

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Authors and Affiliations

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

    Guohe Deng

  2. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Lihong Huang

Authors
  1. Guohe Deng
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  2. Lihong Huang
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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, the “985” Project of Hunan University and the Guangxi Natural Science Foundation under Grant No. 0991091.

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Deng, G., Huang, L. A Poisson-Gaussian model to price European options on the extremum of several risky assets within the HJM framework. J Syst Sci Complex 23, 769–783 (2010). https://doi.org/10.1007/s11424-010-7205-y

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  • DOI: https://doi.org/10.1007/s11424-010-7205-y

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