Ambiguous Volatility and Asset Pricing in Continuous Time

60 Pages Posted: 8 Jan 2013

See all articles by Larry G. Epstein

Larry G. Epstein

Boston University - College of Arts and Sciences

Shaolin Ji

Shandong University, School of Mathematics

Date Written: November 7, 2012

Abstract

This paper formulates a model of utility for a continuous time frame-work that captures the decision-maker’s concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are presented. First, we derive arbitrage-free pricing rules based on hedging arguments. Ambiguous volatility implies market incompleteness that rules out perfect hedging. Consequently, hedging arguments determine prices only up to intervals. However, sharper predictions can be obtained by assuming preference maximization and equilibrium. Thus we apply the model of utility to a representative agent endowment economy to study equilibrium asset returns. A version of the C-CAPM is derived and the effects of ambiguous volatility are described.

Keywords: ambiguity, option pricing, recursive utility, G-Brownian motion, robust stochastic volatility, sentiment, overconfidence, optimism

Suggested Citation

Epstein, Larry G. and Ji, Shaolin, Ambiguous Volatility and Asset Pricing in Continuous Time (November 7, 2012). CIRANO - Scientific Publications 2012s-29. Available at SSRN: https://ssrn.com/abstract=2197408 or http://dx.doi.org/10.2139/ssrn.2197408

Larry G. Epstein (Contact Author)

Boston University - College of Arts and Sciences ( email )

Department of Economics, Room 352
270 Bay State Road
Boston, MA 02215
United States
617-353-4142 (Phone)

Shaolin Ji

Shandong University, School of Mathematics ( email )

27 Shanda Nanlu
South Rd.
Jinan, Shandong 250100
China

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