Nonparametric predictive inference for European option pricing based on the binomial tree model

Abstract

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.

Keywords:

• CRR Binomial Tree Model
• European option
• imprecise probability
• nonparametric predictive inference
• option pricing

Acknowledgement

This work was carried out while Ting He studied for PhD at Durham University, with funding from the Chinese Scholarship Council. The authors are grateful to two reviewers of this article for comments that improved the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.