An alternative tree method for calibration of the local volatility

Abstract

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.