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Short maturity conditional Asian options in local volatility models

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Abstract

In this paper, we study the option pricing problem for the conditional Asian option that appears as a recent market product, offering a cheaper and new alternative to the regular Asian option. We develop the new characteristics of short-maturity asymptotic for the prices of the conditional Asian option provided that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money and at-the-money using fixed strike conditional Asian options are presented, respectively, which provide the linear approximation description of call/put option price. Moreover, the approximating solution for the corresponding variational problem under the well-known Black–Scholes model is also given. The theoretical results derived in the paper are practically relevant and numerical experiments are shown to validate the theoretical outcomes of the paper.

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Acknowledgements

Nian Yao was supported in part by the Natural Science Foundation of China 11371283, and Mingqing Xiao was supported in part by NSF-DMS 1419028, 1854638 of the United States. The first author, Nian Yao, would like to thank the hospitality from the Department of Mathematics, Southern Illinois University Carbondale during her visit from March 2017–August 2018, and this joint work is conducted during the visit. Also, the authors would like to thank Prof. Dan Pirjol, Prof. Wen Yang, and Prof. Jingyi Wang for the helpful discussions with the first author. The authors are also grateful to the editor and the referees for their careful reading of this manuscript as well as for their many suggestions that lead to the significant improvement of this manuscript.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, Guangdong Province, China

    Nian Yao, Zhichao Ling & Jieyu Zhang

  2. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901, USA

    Mingqing Xiao

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  1. Nian Yao
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  2. Zhichao Ling
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Correspondence to Mingqing Xiao.

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Yao, N., Ling, Z., Zhang, J. et al. Short maturity conditional Asian options in local volatility models. Math Finan Econ 14, 307–328 (2020). https://doi.org/10.1007/s11579-020-00257-y

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