Implied binomial trees and calibration for the volatility smile
In this paper we capture the implied distribution from option market data using non-recombining binomial trees allowing the local volatility to be a function of the underlying asset and of time. We elaborate on the initial guess for the volatility term structure, and use non-linear constrained optimization to minimize the least square error function on market prices. The proposed model can accommodate European options with single maturities and, with minor modifications, options with multiple maturities. It can provide a market-consistent tree for option replication with transaction costs (often this requires a non-recombining tree) and can help pricing of exotic and Over The Counter (OTC) options. We test our model using options data of the FTSE-100 index obtained from LIFFE. The results strongly support our modelling approach
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