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Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization


  • Consiglio, Andrea

    (University of Palermo)

  • Carollo, Angelo

    (University of Palermo)

  • Zenios, Stavros A.

    (University of Cyprus)


Simulation models of economic, financial and business risk factors are widely used to assess risk exposures and support decisions. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the "curse of dimensionality". There is, however, an important issue that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage restriction. We formulate a moment matching model to generate multi-factor scenario trees satisfying no-arbitrage restrictions as a global optimization problem. While general in its formulation the resultant model is nonconvex and can grow substantially even for a modest number of assets and scenarios. Exploiting the special structure of the problem we develop convex lower bounding techniques for its solution. Applications to some standard problems from the literature illustrate that this is a reliable approach to stochastic tree generation and is used to price a European basket option in complete and incomplete markets.

Suggested Citation

  • Consiglio, Andrea & Carollo, Angelo & Zenios, Stavros A., 2014. "Generating Multi-factor Arbitrage-Free Scenario Trees with Global Optimization," Working Papers 13-35, University of Pennsylvania, Wharton School, Weiss Center.
  • Handle: RePEc:ecl:upafin:13-35

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    References listed on IDEAS

    1. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
    2. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    3. Consiglio, Andrea & Saunders, David & Zenios, Stavros A., 2006. "Asset and liability management for insurance products with minimum guarantees: The UK case," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 645-667, February.
    4. Hao-Chun Lu & Han-Lin Li & Chrysanthos Gounaris & Christodoulos Floudas, 2010. "Convex relaxation for solving posynomial programs," Journal of Global Optimization, Springer, vol. 46(1), pages 147-154, January.
    5. Ronald Hochreiter & Georg Pflug, 2007. "Financial scenario generation for stochastic multi-stage decision processes as facility location problems," Annals of Operations Research, Springer, vol. 152(1), pages 257-272, July.
    6. Consiglio, Andrea & De Giovanni, Domenico, 2008. "Evaluation of insurance products with guarantee in incomplete markets," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 332-342, February.
    7. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    8. John M. Mulvey & Hercules Vladimirou, 1992. "Stochastic Network Programming for Financial Planning Problems," Management Science, INFORMS, vol. 38(11), pages 1642-1664, November.
    9. repec:spr:pharme:v:21:y:2003:i:12:p:839-851 is not listed on IDEAS
    10. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    11. Pieter Klaassen, 2002. "Comment on "Generating Scenario Trees for Multistage Decision Problems"," Management Science, INFORMS, vol. 48(11), pages 1512-1516, November.
    12. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
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    Cited by:

    1. Staino, Alessandro & Russo, Emilio, 2015. "A moment-matching method to generate arbitrage-free scenarios," European Journal of Operational Research, Elsevier, vol. 246(2), pages 619-630.

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