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

Gonçalo Faria*, João Correia-da-Silva

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)125-159
Number of pages35
JournalReview of Derivatives Research
Volume17
Issue number2
DOIs
Publication statusPublished - 1 Jul 2014
Externally publishedYes

Keywords

  • Ambiguity
  • Option pricing
  • Stochastic volatility

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