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Generalized Binomial Trees

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  • Jackwerth, Jens Carsten

Abstract

We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the volatility parameter. Implied binomial trees can accommodate only related European options with the same time-to-expiration. The generalized binomial trees introduced here can accommodate any kind of related options (European, American, or exotic) with different times-to-expiration.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11635.

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Date of creation: 19 Aug 1996
Date of revision: 12 May 1997
Handle: RePEc:pra:mprapa:11635

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Keywords: Generalized; Binomial; Tree; Trees;

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References

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  1. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  2. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  5. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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Citations

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Cited by:
  1. Emmanuel Jurczenko & Bertrand Maillet & Bogdan Negrea, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
  2. Zsembery, Levente, 2003. "A volatilitás előrejelzése és a visszaszámított modellek
    [Forecasting of volatility and implied models]
    ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 519-542.
  3. Moriggia, V. & Muzzioli, S. & Torricelli, C., 2009. "On the no-arbitrage condition in option implied trees," European Journal of Operational Research, Elsevier, vol. 193(1), pages 212-221, February.
  4. Dasheng Ji & B. Brorsen, 2011. "A recombining lattice option pricing model that relaxes the assumption of lognormality," Review of Derivatives Research, Springer, vol. 14(3), pages 349-367, October.
  5. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
  6. Kim, In Joon & Park, Gun Youb, 2006. "An empirical comparison of implied tree models for KOSPI 200 index options," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 52-71.
  7. Ahmed Loulit, 2004. "Approximating equity volatility," Working Papers CEB 04-028.RS, ULB -- Universite Libre de Bruxelles.
  8. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1250058-1-1.
  9. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, . "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
  10. Jackwerth, Jens Carsten & Rubinstein, Mark, 2003. "Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns," MPRA Paper 11638, University Library of Munich, Germany, revised 2004.

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