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

• Type: Article in International Scientific Journal
• Date: 2014

Authors

João Correia-da-Silva (Author) FEP; Gonçalo Faria (Author) Other

Journal

Title: Review of Derivatives Research

Vol. 17

Pages: 125-159

ISSN: 1380-6645

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 14 Citations

ISI Web of Science

Scopus - 14 Citations

Other information

Authenticus ID: P-009-K5D

DOI: 10.1007/s11147-014-9097-9

Abstract (EN): 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.

Type (Professor's evaluation): Scientific