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Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs

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  • Jingtang Ma
  • Dongya Deng
  • Harry Zheng

Abstract

In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature.

Suggested Citation

  • Jingtang Ma & Dongya Deng & Harry Zheng, 2016. "Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 593-603, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:593-603
    DOI: 10.1080/14697688.2015.1046397
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    References listed on IDEAS

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    1. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
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