Predictive inference

Negative binomial distribution

Bayesian probability

Binomial options pricing model

Statistics

Frequentist inference

Poisson distribution

Economics

Computer science

Probability distribution

Binomial (polynomial)

Operations research

Trinomial tree

Mathematics

Binomial distribution

Inference

Nonparametric statistics

Econometrics

Mathematical analysis

Operations management

Artificial intelligence

Tree (set theory)

Valuation of options

Purchasing

Bayesian inference

Journal of the Operational Research Society

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 article, 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 utilising 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 European option pricing based on the binomial tree model