In finance, option pricing is one of the main topics. A basic model for option pricing is the Binomial Tree Model, proposed by Cox, Ross, and Rubinstein in 1979 (CRR). This model assumes that the underlying asset price follows a binomial distribution with a constant upward probability, the so-called risk-neutral probability. In this paper, we propose a novel method based on the binomial tree. Rather than using the risk-neutral probability, we apply Nonparametric Predictive Inference (NPI) to infer imprecise probabilities of movements, reflecting more uncertainty while learning from data. To study its performance, we price the same European options utilizing both the NPI method and the CRR model and compare the results in two different scenarios, firstly where the CRR assumptions are right, and secondly where the CRR model assumptions deviate from the real market. It turns out that our NPI method, as expected, cannot perform better than the CRR in the first scenario, but can do better in the second scenario.

Nonparametric predictive inference for American option pricing based on the binomial tree model.', Communications in statistics theory and methods. .

This article considers a novel exotic option pricing method for incomplete markets. Nonparametric predictive inference (NPI) is applied to the option pricing procedure based on the binomial tree model allowing the method to evaluate exotic options with limited information and few assumptions. As the implementation of the NPI method is greatly simplified by the monotonicity of the option payoff in the tree, we categorize exotic options by their payoff monotonicity and study a typical type of exotic option in each category, the barrier option and the look-back option. By comparison with the classic binomial tree model, we investigate the performance of our method either with different moneyness or varying maturity. All outcomes show that our model offers a feasible approach to price the exotic options with limited information, which makes it can be utilized for both complete and incomplete markets.

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