An Extension of CreditGrades Model Approach with Levy Processes

Quantitative Finance, Vol. 11, No. 12, 2011

Posted: 15 Nov 2008 Last revised: 27 Nov 2011

See all articles by Takaaki Ozeki

Takaaki Ozeki

Mizuho-DL Financial Technology Co., Ltd.

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd.

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Daisuke Yoshikawa

Hokkai-Gakuen University

Date Written: March 12, 2010

Abstract

This paper proposes an extended CreditGrades model called the Levy CreditGrades model, which is driven by a Levy process. In this setting, quasi closed-form formulae for pricing equity options to a reference firm and for calculating its survival probabilities are derived. Moreover, using three tractable Levy CreditGrades models, we compute implied volatilities on equity options and term structures of credit default swaps (CDSs) and we examine the jump risk effects of the firm's asset value on short term CDS spreads and equity volatility skew. As a result, with this extension, our model is found to have more significant abilities than the original model introduced by Finger et al. [2002] and Stamicar and Finger [2005], and it is more appropriate for pricing both equity and credit derivatives simultaneously.

Keywords: CreditGrades Model, Levy Process, Equity Option, Credit Default Swap, Wiener-Hopf Factorization

JEL Classification: G12, G13

Suggested Citation

Ozeki, Takaaki and Umezawa, Yuji and Yamazaki, Akira and Yoshikawa, Daisuke, An Extension of CreditGrades Model Approach with Levy Processes (March 12, 2010). Quantitative Finance, Vol. 11, No. 12, 2011. Available at SSRN: https://ssrn.com/abstract=1299317

Takaaki Ozeki

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

Daisuke Yoshikawa

Hokkai-Gakuen University ( email )

4-1-40, Asahi-machi, Toyohira-ku
Sapporo-shi
Hokkai-do, 062-8605
Japan

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