Open AccessAn alternative tree method for calibration of the local volatility
Author(s) -
Wenxiu Gong,
Zhiting Xu
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020146
Subject(s) - trinomial tree , mathematical optimization , computer science , binomial options pricing model , volatility (finance) , tree (set theory) , local volatility , stochastic volatility , valuation of options , calibration , volatility smile , mathematics , algorithm , econometrics , statistics , mathematical analysis
In this paper, we combine the traditional binomial tree and trinomial tree to construct a new alternative tree pricing model, where the local volatility is a deterministic function of time. We then prove the convergence rates of the alternative tree method. The proposed model can price a wide range of derivatives efficiently and accurately. In addition, we research the optimization approach for the calibration of local volatility. The calibration problem can be transformed into a nonlinear unconstrained optimization problem by exterior penalty method. 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. Numerical results confirm the excellent performance of the alternative tree pricing model.