A Binomial Model of Asset and Option Pricing with Heterogeneous Beliefs
University of Technology Sydney (UTS) - School of Finance and Economics
University of Technology Sydney (UTS); Financial Research Network (FIRN)
July 12, 2010
Australian Centre for Financial Studies - Finsia Banking and Finance Conference 2010
This paper provides a theoretical framework for pricing assets in a multi-period economy with heterogeneous beliefs. The stock price dynamics follow a binomial lattice structure. Agents are allowed to differ in their beliefs of 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. Statically, divergence of opinions leads to lower risk premium, greater divergence of opinions regarding future return in the upstate (downstate) leads to lower (higher) expected return for the risky asset and the risk-free rate. Dynamically, we show that the consensus belief is a fair belief to price options since agents’ wealth share process is a martingale under the consensus belief. Furthermore, call option prices exhibit implied volatility skew when the optimistic (pessimistic) agent is also confident (doubtful) about future asset returns.
Number of Pages in PDF File: 26
Keywords: asset prices; heterogeneous beliefs; binomial trees; options;
JEL Classification: G12, D84
Date posted: July 12, 2010
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