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Computing lower bounds on basket option prices by discretizing semi-infinite linear programming

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Abstract

The problem of finding static-arbitrage bounds on basket option prices has received a growing attention in the literature. In this paper, we focus on the lower bound case and propose a novel efficient solution procedure that is based on the separation problem. The computational burden of the proposed method is polynomial in the input data size. We also discuss the case of possibly negative weight vectors which can be applied to spread options.

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References

  1. Carmona, R., Durrleman, V.: Pricing and hedging spread options. SIAM Rev. 45, 627–685 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. d’Aspremont, A., El Ghaoui, L.: Static arbitrage bounds on basket option prices. Math. Program. Ser. A. 106, 467–489 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Daum, S., Werner, R.: A novel feasible discretization method for linear semi-infinite programming applied to basket option pricing. Optimization. 60, 1379–1398 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Grötschel, M., Lovász, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Springer-Verlag, Berlin (1988)

    Book  MATH  Google Scholar 

  5. Hobson, D., Laurence, P., Wang, T.-H.: Static-arbitrage optimal subreplicating strategies for basket options. Insur. Math. Econ. 37, 553–572 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hobson, D., Laurence, P., Wang, T.-H.: Static-arbitrage upper bounds for the prices of basket options. Quant. Financ. 5, 329–342 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Laurence, P., Wang, T.-H.: Sharp upper and lower bounds for basket options. Appl. Math. Financ. 12, 253–282 (2005)

    Article  MATH  Google Scholar 

  8. Nemhauser, G., Wolsey, L.: Integer and combinatorial optimization. Wiley, New York (1999)

    MATH  Google Scholar 

  9. Peña, J., Saynac, X., Vera, J.C., Zuluaga, L.F.: Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition. Algorithmic Oper. Res. 5, 65–74 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Peña, J., Vera, J.C., Zuluaga, L.F.: Static-arbitrage lower bounds on the prices of basket options via linear programming. Quant. Financ. 10, 819–827 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Peña, J., Vera, J.C., Zuluaga, L.F.: Computing arbitrage upper bounds on basket options in the presence of bid-ask spreads. Eur. J. Oper. Res. 222, 369–376 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (1986)

    MATH  Google Scholar 

  13. Tankov, P.: Improved Frechet bounds and model-free pricing of multi-asset options. J. Appl. Probab. 48, 389–403 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors thank Professors Peña and Zuluaga for sending their code and paper. Kim’s work was supported by the National Research Foundation of Korea, funded by the Ministry of Education (NRF-2014R1A1A2054868).

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Authors and Affiliations

  1. Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea

    Hyunseok Cho & Kyoung-Kuk Kim

  2. Industrial Engineering, Seoul National University, Seoul, South Korea

    Kyungsik Lee

Authors
  1. Hyunseok Cho
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  2. Kyoung-Kuk Kim
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  3. Kyungsik Lee
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Correspondence to Kyoung-Kuk Kim.

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Cho, H., Kim, KK. & Lee, K. Computing lower bounds on basket option prices by discretizing semi-infinite linear programming. Optim Lett 10, 1629–1644 (2016). https://doi.org/10.1007/s11590-015-0987-z

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  • DOI: https://doi.org/10.1007/s11590-015-0987-z

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