Nonparametric Predictive Inference for European Option Pricing based on the Binomial Tree Model

He, T.; Coolen, F.P.A.; Coolen-Maturi, T.

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 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.

Citation

He, T., Coolen, F., & Coolen-Maturi, T. (2019). Nonparametric Predictive Inference for European Option Pricing based on the Binomial Tree Model. Journal of the Operational Research Society, 70(10), 1692-1708. https://doi.org/10.1080/01605682.2018.1495997

• Journal Article Type: Article
• Acceptance Date: Jun 26, 2018
• Online Publication Date: Feb 22, 2019
• Publication Date: Aug 1, 2019
• Deposit Date: Jun 26, 2018
• Publicly Available Date: Feb 22, 2020
• Journal: Journal of the Operational Research Society
• Print ISSN: 0160-5682
• Electronic ISSN: 1476-9360
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 70
• Issue: 10
• Pages: 1692-1708
• DOI: https://doi.org/10.1080/01605682.2018.1495997
• Public URL: https://durham-repository.worktribe.com/output/1323502