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A Closed-Form Solution for Options with Ambiguity about Stochastic Volatility

Gonçalo Faria () and Joao Correia-da-Silva

FEP Working Papers from Universidade do Porto, Faculdade de Economia do Porto

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 (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. Consistently, in the former (and more natural) scenario, ambiguity aversion decreases the option's implied volatility, which helps to explain the variance premium puzzle.

Keywords: Option Pricing; Stochastic Volatility; Ambiguity; Variance Premium Puzzle (search for similar items in EconPapers)
JEL-codes: C61 D81 G13 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2011-05
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Journal Article: A closed-form solution for options with ambiguity about stochastic volatility (2014) Downloads
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