Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2008/6: Level dependent annuities: Defaults of multiple degrees

Aksel Mjøs () and Svein-Arne Persson ()
Additional contact information
Aksel Mjøs: SNF - Institute for Research in Economics and Business Administration, Postal: SNF - Institute for Research in Economics and Business Administration, Breiviksveien 40, N-5045 Bergen, Norway
Svein-Arne Persson: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Motivated by the risk of stopped debt coupon payments from a leveraged company in financial distress, we value a level dependent annuity contract where the annuity rate depends on the value of an underlying asset-process. The range of possible values of the asset is divided into a finite number of regions. The annuity rate is constant within each region, but may differ between the regions. We consider both in finite and finite annuities, with or without bankruptcy risk, i.e., bankruptcy occurs if the asset value process hits an absorbing boundary. Such annuities are common in models of debt with credit risk in financial economics. Suspension of debt service under the US Chapter 11 provisions is one well-known real-world example. We present closed-form formulas for the market value of such multi-level annuities contracts when the market value of the underlying asset is assumed to follow a geometric Brownian motion.

Keywords: Multi-level annuity; credit risk; financial distress

JEL-codes: G13; G32; G33

24 pages, March 12, 2008

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