General Closed-Form Basket Option Pricing Bounds

56 Pages Posted: 8 Jan 2014 Last revised: 19 Jun 2015

See all articles by Ruggero Caldana

Ruggero Caldana

Independent

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Sir John Cass Business School - City, University of London

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 8, 2014

Abstract

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known in closed-form. Moreover, the basket value is not required to be positive. We test our new bounds on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality. In particular, our new lower bound turns out to be fast and accurate.

Keywords: Basket option, Lower Bound, Non Gaussian models, Upper Bound, Fourier Transform, Exotic option

JEL Classification: G12, G13

Suggested Citation

Caldana, Ruggero and Fusai, Gianluca and Gnoatto, Alessandro and Grasselli, Martino, General Closed-Form Basket Option Pricing Bounds (January 8, 2014). Available at SSRN: https://ssrn.com/abstract=2376134 or http://dx.doi.org/10.2139/ssrn.2376134

Ruggero Caldana

Independent ( email )

No Address Available

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Sir John Cass Business School - City, University of London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

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

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