Review of Derivatives Research

, Volume 17, Issue 2, pp 125–159 | Cite as

A closed-form solution for options with ambiguity about stochastic volatility



We derive a closed-form solution for the price of a European call option in the presence of ambiguity about the stochastic process that determines the variance of the underlying asset’s return. The option pricing formula of Heston (Rev Financ Stud 6(2):327–343, 1993) is a particular case of ours, corresponding to the case in which there is no ambiguity (uncertainty is exclusively risk). In the presence of ambiguity, the variance uncertainty price becomes either a convex or a concave function of the instantaneous variance, depending on whether the variance ambiguity price is negative or positive. We find that if the variance ambiguity price is positive, the option price is decreasing in the level of ambiguity (across all moneyness levels). The opposite happens if the variance ambiguity price is negative. This option pricing model can be used to address various empirical research topics in the future.


Option pricing Stochastic volatility Ambiguity 

JEL Classification

C61 D81 G13 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.CEF.UP and Faculdade de EconomiaUniversidade do PortoPortoPortugal
  2. 2.RGEAUniversidad de VigoVigoSpain

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