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Pricing and Hedging American Options Using Approximations by Kim Integral Equations

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  • Siim Kallast

    ()

  • Andi Kivinukk

    ()

Abstract

We present an approximation method for pricing and hedging American options written on a dividend-paying asset. This method is based on Kim (1990) equations. We demonstrate that a simple approximation of the Kim integral equations by quadrature formulas leads to an efficient and accurate numerical procedure. This approximation is accompanied by the Newton--Raphson iteration procedure in order to compute the optimal exercise boundary at each time point. The proposed sequence of approximations converges monotonically, convergence is fast and accuracy is high, even for long maturity options. We compare numerically our results with other competing approaches by different authors.

Suggested Citation

  • Siim Kallast & Andi Kivinukk, 2003. "Pricing and Hedging American Options Using Approximations by Kim Integral Equations," Review of Finance, Springer, vol. 7(3), pages 361-383.
  • Handle: RePEc:kap:eurfin:v:7:y:2003:i:3:p:361-383
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    Citations

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    Cited by:

    1. Detemple, Jérôme & Emmerling, Thomas, 2009. "American chooser options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 128-153, January.
    2. Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    3. repec:bpj:jossai:v:4:y:2016:i:2:p:149-168:n:4 is not listed on IDEAS
    4. Shen, Yang & Sherris, Michael & Ziveyi, Jonathan, 2016. "Valuation of guaranteed minimum maturity benefits in variable annuities with surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 127-137.
    5. Doriana Ruffino & Jonathan Treussard, 2006. "Lumps and Clusters in Duopolistic Investment Games: An Early Exercise Premium Approach," Boston University - Department of Economics - Working Papers Series WP2006-044, Boston University - Department of Economics.
    6. Fabozzi, Frank J. & Paletta, Tommaso & Stanescu, Silvia & Tunaru, Radu, 2016. "An improved method for pricing and hedging long dated American options," European Journal of Operational Research, Elsevier, vol. 254(2), pages 656-666.
    7. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    8. Carl Chiarella & Andrew Ziogas, 2006. "American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach," Research Paper Series 174, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. Thomas Adolfsson & Carl Chiarella & Andrew Ziogas & Jonathan Ziveyi, 2013. "Representation and Numerical Approximation of American Option Prices under Heston Stochastic Volatility Dynamics," Research Paper Series 327, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    11. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12.
    12. Song-Ping Zhu & Jing Zhang, 2012. "How should a convertible bond be decomposed?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 113-149, November.
    13. repec:eee:spapps:v:127:y:2017:i:10:p:3447-3464 is not listed on IDEAS
    14. Liu, Yanchu & Cui, Zhenyu & Zhang, Ning, 2016. "Integral representation of vega for American put options," Finance Research Letters, Elsevier, vol. 19(C), pages 204-208.
    15. repec:gam:jrisks:v:6:y:2018:i:1:p:5-:d:128119 is not listed on IDEAS
    16. Andrew Ziogas, 2005. "Pricing American Options Using Fourier Analysis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 29.

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