Article2013

Ambiguous Volatility and Asset Pricing in Continuous Time

236 citations0/0 files storedReview of Financial Studies

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

Abstract

We formulate a model of utility for a continuous-time framework that captures aversion to 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. Because ambiguous volatility implies market incompleteness, hedging arguments determine prices only up to intervals. In order to obtain sharper predictions, we apply the model of utility to a representative agent endowment economy and study equilibrium asset returns. A version of the consumption capital asset pricing model is derived, and the effects of ambiguous volatility are described.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 2007Brownian Motion and Stochastic Calculus 2009The Impact of Uncertainty Shocks 1989Maxmin expected utility with non-unique prior 1987The Pricing of Options on Assets with Stochastic Volatilities 2003Stochastic Differential Equations 2007The Impact of Uncertainty Shocks 1989Optimal consumption and portfolio policies when asset prices follow a diffusion process

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2013Ambiguous volatility, possibility and utility in continuous time 2016Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities 2014Financial markets with volatility uncertainty 2016Moral Hazard in Dynamic Risk Management 2018Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix 2021Ambiguity about volatility and investor behavior

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