Convertible Bonds Valuation in a Jump Diffusion Setting with Stochastic Interest Rates

Quantitative Finance, 2015, 15(1), 115-129

23 Pages Posted: 4 Jul 2009 Last revised: 9 Feb 2019

See all articles by Laura Ballotta

Laura Ballotta

Bayes Business School (formerly Cass) - City, University of London

Ioannis Kyriakou

Bayes Business School (formerly Cass), City, University of London

Date Written: August 12, 2014

Abstract

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie, Pan and Singleton [Duffie, D., Pan, J. and Singleton, K., Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 2000, 68, 1343-1376] with tractable behaviour. We define the firm's optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates.

Keywords: Convertible bonds pricing, Stochastic interest rates, Affine jump diffusion model, Optimal call strategy

JEL Classification: G12, G13, C63

Suggested Citation

Ballotta, Laura and Kyriakou, Ioannis, Convertible Bonds Valuation in a Jump Diffusion Setting with Stochastic Interest Rates (August 12, 2014). Quantitative Finance, 2015, 15(1), 115-129, Available at SSRN: https://ssrn.com/abstract=1426524 or http://dx.doi.org/10.2139/ssrn.1426524

Laura Ballotta

Bayes Business School (formerly Cass) - City, University of London ( email )

Faculty of Finance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

HOME PAGE: http://www.city.ac.uk/people/academics/laura-ballotta

Ioannis Kyriakou (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

Faculty of Actuarial Science & Insurance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom
+44 (0)20 7040 8738 (Phone)
+44 (0)20 7040 8881 (Fax)

HOME PAGE: http://www.bayes.city.ac.uk/experts/I.Kyriakou

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