A Novel Decision Tree Approach for Option Pricing Using a Clustering Based Learning Algorithm

Decision tree analysis involves forecasting future outcomes and assigning probabilities to those events. One of the most basic fundamental applications of decision tree analysis is for the purpose of option pricing. The binomial tree would factor in multiple paths that the underlying asset's price can take as time progresses. The price of the option is calculated using the discrete probabilities and their associated pay-offs at maturity date of the option. In this work we came up with an approach to build a binomial decision tree that can be used to price European, American and Bermudian options and a methodology to train the decision tree using a clustering based learning algorithm that minimizes the mean square error (MSE) between the observed and predicted option prices. The training methodology involves clustering the options based on moneyness and fit a linear equation for each cluster to calculate the confidence that needs to be used in building the binomial decision tree for a particular strike price within the cluster. It is observed that the MSE for option price using the proposed model is less when compared to the Black-Scholes model for the proposed learning algorithm.