Analytic Pricing of Volatility-Equity Options within Affine Models: An Efficient Conditioning Technique

26 Pages Posted: 24 Apr 2014 Last revised: 16 Jan 2015

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Alessandro Gnoatto

University of Verona - Department of Economics

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Date Written: January 16, 2015

Abstract

We price for different affine stochastic volatility models some derivatives that recently appeared in the market. These products are characterised by payoffs depending on both stock and its volatility. Using a Fourier-analysis approach, we recover in a much simpler way some results already established in the literature for the single factor specification of the volatility and we push forward our methodology, which turns out to be independent of the dimension of the problem, thanks to a simple conditioning with respect to the subfiltration generated by the variance path. For each product we provide a closed form solution based on the Fast Fourier Transform and we illustrate the results for realistic model parameter values. Also, our results highlight the great flexibility and tractability of the Wishart based stochastic volatility models.

Keywords: Finance, Target Volatility Options, Corridor Variance Swap, Double Digital Call, Affine Stochastic Volatility Models

JEL Classification: G13

Suggested Citation

Da Fonseca, José and Gnoatto, Alessandro and Grasselli, Martino, Analytic Pricing of Volatility-Equity Options within Affine Models: An Efficient Conditioning Technique (January 16, 2015). Available at SSRN: https://ssrn.com/abstract=2428628 or http://dx.doi.org/10.2139/ssrn.2428628

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Register to save articles to
your library

Register

Paper statistics

Downloads
162
Abstract Views
1,016
rank
180,809
PlumX Metrics