Option Pricing on Non-Recombining Implied Trees Assuming Serial Dependence of Returns

The non-recombining implied tree is calibrated taking into account serial dependence of stock returns. Effectively, the model becomes non-Markovian. Unlike typical preference-free option pricing models, a parameter related to the expected return of the underlying asset appears in our model. We calibrate the non-Markovian model using European calls on the FTSE 100 index for year 2003. Results strongly support our modelling approach. Pricing results are smooth without evidence of an over-fitting problem and the derived implied distributions are realistic. Also, results for the pricing of American call options indicate that the non-Markovian model outperforms the equivalent Markovian model and also the ad-hoc procedure of smoothing Black-Scholes implied volatilities proposed by Dumas et al. (1998).