Download pdf
Numerical methods base on trinomial trees for option pricing
- 1 Imperial College London
* Author to whom correspondence should be addressed.
Abstract
This paper investigates the approach to pricing European options, starting with one-step binomial tree pricing (a relatively simple way to calculate option value). In the next step, an additional possible rate of change of stock price is added to make the model more realistic, resulting in the one-step trinomial tree model. The model bounds the option price under the no-arbitrary principle. The paper then analyzes the circumstances under which options have a fixed price by completing the market and giving the solution formula of option price through the model. Last, put-call parity is used to prove the rationality of one-step trinomial model so that the model effectively prevents the occurrence of risk-free arbitrage in the market. This helps traders to price options reasonably in the market and maintains the stability of the options market.
Keywords
Numerical Methods, Trinomial Trees, Option Pricing
[1]. Paul Clifford, Yan Wang, Oleg Zaboronski. (2010). Pricing options using trinomial trees. Working paper, available from https://warwick.ac.uk/fac/sci/maths/people/staff/oleg_zaboronski/fm/ trinomial_tree_2010_kevin.pdf
[2]. Fei Lung Yuen, Hailiang Yang. (2010). Option pricing with regime switching by trinomial tree method. Journal of Computational and Applied Mathematics. Volume 233, Issue 8, Pages 1821-1833.
[3]. John Hull. (2018). Options, Futures, and Other Derivatives (Tenth edition). Harlow, UK Pearson.
[4]. Barnett, W., & Saliba, M. (2004). A free market for kidneys: options, futures, forward, and spot. Managerial Finance, 30(2), 38-56.
[5]. Fabozzi, F. (1981). Handbook of financial markets--securities, options, futures. Dow Jones-Irwin.
Cite this article
Zhang,Z. (2024). Numerical methods base on trinomial trees for option pricing. Theoretical and Natural Science,43,113-119.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).