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Pricing A Class Of Exotic Options Via Moments And Sdp Relaxations

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  • J. B. Lasserre
  • T. Prieto‐Rumeau
  • M. Zervos

Abstract

We present a new methodology for the numerical pricing of a class of exotic derivatives such as Asian or barrier options when the underlying asset price dynamics are modeled by a geometric Brownian motion or a number of mean‐reverting processes of interest. This methodology identifies derivative prices with infinite‐dimensional linear programming problems involving the moments of appropriate measures, and then develops suitable finite‐dimensional relaxations that take the form of semidefinite programs (SDP) indexed by the number of moments involved. By maximizing or minimizing appropriate criteria, monotone sequences of both upper and lower bounds are obtained. Numerical investigation shows that very good results are obtained with only a small number of moments. Theoretical convergence results are also established.

Suggested Citation

  • J. B. Lasserre & T. Prieto‐Rumeau & M. Zervos, 2006. "Pricing A Class Of Exotic Options Via Moments And Sdp Relaxations," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 469-494, July.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:3:p:469-494
    DOI: 10.1111/j.1467-9965.2006.00279.x
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    Cited by:

    1. Khaliq, A.Q.M. & Voss, D.A. & Yousuf, M., 2007. "Pricing exotic options with L-stable Pade schemes," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3438-3461, November.
    2. Wong, Man Hong & Zhang, Shuzhong, 2014. "On distributional robust probability functions and their computations," European Journal of Operational Research, Elsevier, vol. 233(1), pages 23-33.

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