A Continuity Correction for Discrete Barrier Options
AbstractThe payoff of a " barrier option" depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult. We show, however, that discrete barrier options can be priced with remarkable accuracy using continuous barrier formulas by applying a simple continuity correction to the barrier. The correction shifts the barrier away from the underlying by a factor of exp(bet sig sqrt dt), where bet approx 0.5826, sig is the underlying volatility, and dt is the time between monitoring instants. The correction is justified both theoretically and experimentally. Copyright Blackwell Publishers Inc 1997.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Mathematical Finance.
Volume (Year): 7 (1997)
Issue (Month): 4 ()
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- Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
- Fusai, Gianluca & Recchioni, Maria Cristina, 2007. "Analysis of quadrature methods for pricing discrete barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 826-860, March.
- Emmanuel Gobet, 2009. "Advanced Monte Carlo methods for barrier and related exotic options," Post-Print hal-00319947, HAL.
- N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
- Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
- Lindset, Snorre & Persson, Svein-Arne, 2008. "Continuous Monitoring: Look before You Leap," Discussion Papers 2008/8, Department of Business and Management Science, Norwegian School of Economics.
- Chris Kenyon & Andrew Green, 2013. "Collateral-Enhanced Default Risk," Papers 1302.4595, arXiv.org.
- Ye Li & Peter Jan Engelen & Clemens Kool, 2012. "A Barrier Options Approach to Modeling Project Failure: The Case of Hydrogen Fuel Infrastructure," Working Papers 13-01, Utrecht School of Economics.
- Christian Skaug & Arvid Naess, 2007. "Fast and accurate pricing of discretely monitored barrier options by numerical path integration," Computational Economics, Society for Computational Economics, vol. 30(2), pages 143-151, September.
- Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
- Gobet, Emmanuel & Menozzi, Stéphane, 2010. "Stopped diffusion processes: Boundary corrections and overshoot," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 130-162, February.
- Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers 99s-15, CIRANO.
- L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Papers 0804.0162, arXiv.org.
- Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
- Yan Dolinsky & Yuri Kifer, 2009. "Binomial Approximations for Barrier Options of Israeli Style," Papers 0907.4136, arXiv.org.
- Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
- Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
- Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
- Janssen, A.J.E.M. & van Leeuwaarden, J.S.H., 2007. "Cumulants of the maximum of the Gaussian random walk," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1928-1959, December.
- Adi Ben-Meir & Jeremy Schiff, 2012. "The Variance of Standard Option Returns," Papers 1204.3452, arXiv.org.
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