A Binomial Model of Asset and Option Pricing with Heterogeneous Beliefs

Journal of Management Science and Engineering, Forthcoming

Australian Centre for Financial Studies - Finsia Banking and Finance Conference 2010

27 Pages Posted: 12 Jul 2010 Last revised: 23 Sep 2016

Xuezhong He

University of Technology Sydney (UTS) - School of Finance and Economics; Financial Research Network (FIRN)

Lei Shi

University of Technology Sydney (UTS); Financial Research Network (FIRN)

Date Written: September 22, 2016

Abstract

This paper provides a difference-in-opinions equilibrium framework for pricing asset and option in a multi-period binomial economy with heterogeneous beliefs. Agents agree to disagree about their beliefs on the probability and asset return in each state of nature. By constructing a consensus belief, we examine the impact of heterogeneous beliefs on market equilibrium. We show that agents’ wealth shares are expected to remain the same under the consensus belief, although they are expected to increase under their own beliefs. Also large disagreement leads to lower risk premium, while high disagreement on the future return in up state (down state) leads to lower (higher) risk-free rate and expected return for the risky asset. Furthermore, under the consensus belief, the implied volatility of the call options exhibits some observed patterns widely documented
in option markets.

Keywords: asset prices; heterogeneous beliefs; binomial trees; options;

JEL Classification: G12, D84

Suggested Citation

He, Xuezhong and Shi, Lei, A Binomial Model of Asset and Option Pricing with Heterogeneous Beliefs (September 22, 2016). Journal of Management Science and Engineering, Forthcoming; Australian Centre for Financial Studies - Finsia Banking and Finance Conference 2010. Available at SSRN: https://ssrn.com/abstract=1638773 or http://dx.doi.org/10.2139/ssrn.1638773

Xue-Zhong 'Tony' He

University of Technology Sydney (UTS) - School of Finance and Economics ( email )

Haymarket
Sydney, NSW 2007
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Lei Shi (Contact Author)

University of Technology Sydney (UTS) ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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