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- Title
Implied Binomial Trees with Cubic Spline Smoothing.
- Authors
TIAN, YISONG S.
- Abstract
Implied binomial trees are typically constructed by fitting a risk-neutral density (in the form of ending nodal probabilities) to observed option prices (for example, Rubinstein [1994]). This commonly used approach requires the solution of a high dimensional quadratic program with the number of unknowns proportional to the number of binomial periods. In this article, we propose a more efficient implementation of implied binomial trees by incorporating cubic spline smoothing in the quadratic program. Only a selected subset of ending nodal probabilities is treated as unknowns whereas the remainder is interpolated using cubic splines. The reduction in dimensionality of the quadratic program can substantially improve the efficiency of implied binomial trees without any loss in numerical accuracy. More important, our smoothing method can overcome the overfitting problem in the implied binomial tree scheme and minimize distortions to the extracted risk-neutral density even when option prices are observed with error.
- Subjects
MATHEMATICAL models of option; OPTIONS sales &; prices (Finance); SPLINE theory; STATISTICAL smoothing; CALIBRATION; PROBABILITY theory
- Publication
Journal of Derivatives, 2015, Vol 22, Issue 3, p40
- ISSN
1074-1240
- Publication type
Article
- DOI
10.3905/jod.2015.22.3.040