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An exact subexponential-time lattice algorithm for Asian options

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Abstract

Asian options are popular financial derivative securities. Unfortunately, no exact pricing formulas exist for their price under continuous-time models. Asian options can also be priced on the lattice, which is a discretized version of the continuous- time model. But only exponential-time algorithms exist if the options are priced on the lattice without approximations. Although efficient approximation methods are available, they lack accuracy guarantees in general. This paper proposes a novel lattice structure for pricing Asian options. The resulting pricing algorithm is exact (i.e., without approximations), converges to the value under the continuous-time model, and runs in subexponential time. This is the first exact, convergent lattice algorithm to break the long-standing exponential-time barrier.

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Authors and Affiliations

  1. Department of Information and Finance Management, National Chiao-Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan, 300, Republic of China

    Tian-Shyr Dai

  2. Department of Computer Science and Information Engineering and Department of Finance, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd, Taipei, 106, Taiwan

    Yuh-Dauh Lyuu

Authors
  1. Tian-Shyr Dai
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  2. Yuh-Dauh Lyuu
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Correspondence to Yuh-Dauh Lyuu.

Additional information

An early version of this paper appeared in the Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, 2004.

T.-S. Dai was supported in part by NSC grant 94-2213-E-033-024.

Y.-D. Lyuu was supported in part by NSC grant 94-2213-E-002-088.

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Dai, TS., Lyuu, YD. An exact subexponential-time lattice algorithm for Asian options. Acta Informatica 44, 23–39 (2007). https://doi.org/10.1007/s00236-006-0033-9

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