438
Views
0
CrossRef citations to date
0
Altmetric
Articles

Entropy binomial tree method and calibration for the volatility smile

, &
Pages 1591-1608 | Received 20 Nov 2019, Accepted 28 Feb 2020, Published online: 23 Apr 2020

References

  • Black F, Scholes M. The pricing of options and corporate liabilities. J Pol Econ. 1973;81(3):637–654. doi: 10.1086/260062
  • Boyle PP. Options: a Monte Carlo approach. J Financ Econ. 1997;4:323–338. doi: 10.1016/0304-405X(77)90005-8
  • Cox JC, Ross SA, Rubinstein M. Option pricing: a simplified approach. J Financ Econ. 1979;7:229–263. doi: 10.1016/0304-405X(79)90015-1
  • Brennan M, Schwartz ES. Finite difference methods and jump processes arising in the pricing of contigent claims: a synthesis. J Financ Quant Anal. 1978;13:464–474.
  • Chance DM. A synthesis of binomial option pricing models for lognormally distributed asset. J Appl Finance. 2008;18:38–56.
  • Diener F, Diener M. Asymptotics of the price oscillations of a European call option in a tree model. Math Finance. 2004;14:271-–293. doi: 10.1111/j.0960-1627.2004.00192.x
  • Rendleman J, Richard J, Bartter BJ. Two-state option pricing. J Finance. 1979;34:1093–1110. doi: 10.1111/j.1540-6261.1979.tb00058.x
  • Walsh JB. The rate of convergence of the binomial tree scheme. Finance Stoch. 2003;7:337–361. doi: 10.1007/s007800200094
  • Li YH, Li XS. Entropy binomial tree model for option pricing. Appl Math Inf Sci. 2013;7(1):151–159. doi: 10.12785/amis/070118
  • Jaynes ET. Information theory and statistical mechanics. Phys Rev. 1957;106:620–630. doi: 10.1103/PhysRev.106.620
  • Dupire B. Pricing with a smile. Risk. 1994;7:18–20.
  • Bouchouev I, Isakov V. Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets. Inverse Probl. 1999;15:95–116. doi: 10.1088/0266-5611/15/3/201
  • Hofmann B, Kramer R. On maximum entropy regularization for a specific inverse problem of option pricing. J Inverse Ill-Posed Probl. 2005;13:41–63. doi: 10.1515/1569394053583739
  • Wang Y, Zhang Y, Lukyanenko D, et al. Recovering aerosol particle size distribution function on the set of bounded piecewise-convex functions. Inverse Probl Sci Eng. 2013;21:339–354. doi: 10.1080/17415977.2012.700711
  • Jiang LS, Bian BJ. The regularized implied local volatility equations-A new model to recover the volatility of underlying asset from observed market option price. Discrete Continuous Dyn Syst, Ser B. 2012;7(6):2017–2046. doi: 10.3934/dcdsb.2012.17.2017
  • Korolev YM, Kubo H, Yagola AG. Parameter identification problem for a parabolic equation – application to the Black–Scholes option pricing model. J Inverse Ill-Posed Probl. 2012;20:327–337.
  • Wang YF. Computational methods for inverse problems and their applications. Beijing: Higher Education Press; 2007.
  • Atkinson K. An introduction to numerical analysis. 2nd ed. New York (NY): John Wiley & Sons; 1989.
  • Li Y. A new algorithm for constructing implied binomial trees: does the implied model fit any volatility smile? J Comput Finance. 2001;4:69–98. doi: 10.21314/JCF.2001.072
  • Derman E, Kani I, Chriss N. Implied trinomial trees of the volatility smile. J Deriv. 1996;3:7–22. doi: 10.3905/jod.1996.407952
  • Barle S, Cakici N. How to grow a smiling tree. J Financ Eng. 1999;7:127–146.
  • Crépey S. Calibration of the local volatility in a trinomial tree using Tikhonov regularization. Inverse Probl. 2003;19:91–127. doi: 10.1088/0266-5611/19/1/306
  • Talias K. Implied binomial trees and genetic algorithms [Ph.D. thesis]. Imperial College; 2005.
  • Charalambous C, Christofides N, Constantinide E, et al. Implied non-recombining trees and calibration for the volatility smile. Quant Finance. 2007;7(4):459–472. doi: 10.1080/14697680701488692
  • Lok UH, Lyuu YD. The waterline tree for separable local-volatility models. Comput Math Appl. 2017;73:537–559. doi: 10.1016/j.camwa.2016.12.008
  • Gong WX, Xu ZL. Non-recombining trinomial tree pricing model and calibration for the volatility smile. J Inverse Ill-Posed Probl. 2019;27(3):353–366. doi: 10.1515/jiip-2018-0005
  • Li XS. An efficient approach to nonlinear minimax problems. Chin Sci Bull. 1992;37(10):802–805.
  • Heston S, Zhou GF. On the rate of convergence of discrete-time contingent claims. Math Finance. 2000;10(1):53–75. doi: 10.1111/1467-9965.00080
  • Fiacco AV, McCormick GP. Nonlinear programming: sequential unconstrained minimization techniques. New York (NY): John Wiley & Sons; 1968.
  • Fletcher R. Practical methods of optimization. Chichester: Wiley; 1987.
  • Andersen L, Andreasen J. Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing. Rev Derivat Res. 2000;4:231–262. doi: 10.1023/A:1011354913068

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.