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Semistatic hedging and pricing American floating strike lookback options

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  • San‐Lin Chung
  • Yi‐Ta Huang
  • Pai‐Ta Shih
  • Jr‐Yan Wang

Abstract

We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta‐hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.

Suggested Citation

  • San‐Lin Chung & Yi‐Ta Huang & Pai‐Ta Shih & Jr‐Yan Wang, 2019. "Semistatic hedging and pricing American floating strike lookback options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 418-434, April.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:4:p:418-434
    DOI: 10.1002/fut.21986
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    References listed on IDEAS

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    1. Tze Leung Lai & Tiong Wee Lim, 2004. "Exercise Regions And Efficient Valuation Of American Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 249-269, April.
    2. Jason Fink, 2003. "An examination of the effectiveness of static hedging in the presence of stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(9), pages 859-890, September.
    3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    4. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    5. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    6. Figlewski, Stephen & Gao, Bin, 1999. "The adaptive mesh model: a new approach to efficient option pricing," Journal of Financial Economics, Elsevier, vol. 53(3), pages 313-351, September.
    7. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
    8. Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
    9. Akihiko Takahashi & Akira Yamazaki, 2009. "A new scheme for static hedging of European derivatives under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(5), pages 397-413, May.
    10. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    11. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Hull, John & White, Alan, 1988. "The Use of the Control Variate Technique in Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 237-251, September.
    14. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
    15. R. C. Heynen & H. M. Kat, 1995. "Lookback options with discrete and partial monitoring of the underlying price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 273-284.
    16. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-1163.
    17. Chung, San-Lin & Shih, Pai-Ta & Tsai, Wei-Che, 2013. "Static hedging and pricing American knock-in put options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 191-205.
    18. Geunhyuk Chang & Jangkoo Kang & Hwa‐Sung Kim & In Joon Kim, 2007. "An efficient approximation method for American exotic options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(1), pages 29-59, January.
    19. Eberlein, Ernst & Papapantoleon, Antonis, 2005. "Equivalence of floating and fixed strike Asian and lookback options," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 31-40, January.
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