Entropy binomial tree method and calibration for the volatility smile

Abstract

In this paper, we combine the maximum entropy principle with binomial tree to construct a non-recombining entropy binomial tree pricing model under the volatility that is a function of time, and give the rate of convergence. The model may yield an unbiased and objective probability. In addition, we research the calibration problem of volatility with the entropy binomial tree, and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results confirm the effectiveness of the entropy binomial tree pricing model.

Keywords:

• Entropy binomial tree
• volatility
• option pricing
• calibration
• nonlinear constrained optimization

2010 Mathematics Subject Classifications:

• 91G20
• 91G60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work is supported by National Natural Science Foundation of China [grant number 11571365].