Pricing Range Notes within Wishart Affine Models

36 Pages Posted: 11 Aug 2013 Last revised: 4 Jan 2014

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Martino Grasselli

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

Date Written: January 3, 2014

Abstract

We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multi-factor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same data-set, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.

Keywords: affine term structure models, Wishart models, Range Accrual Notes, model risk

JEL Classification: C63, G13

Suggested Citation

Chiarella, Carl and Da Fonseca, José and Grasselli, Martino, Pricing Range Notes within Wishart Affine Models (January 3, 2014). Available at SSRN: https://ssrn.com/abstract=2308636 or http://dx.doi.org/10.2139/ssrn.2308636

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

José Da Fonseca (Contact Author)

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)

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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