General Formulas for Valuing Stocks and Bonds with Structural Changes
59 Pages Posted: 14 Apr 2009 Last revised: 10 Jan 2010
Date Written: April 12, 2009
Previous studies have documented the impacts on asset valuations under pricing environments with structural changes which is modeled by regime switching. Below, I extend previous models by providing general formulas for valuing assets in the setting of affine factor processes augmented with regime switching (ARS). Based on the extended version of Feyman-Kac theorem, I find closed forms for the prices of both stocks and bonds under ARS with an arbitrary number of factors and regimes. Compared with the other two setups in finance which both work for single-regime scenarios: the linearity generating processes and the affine jump-diffusion models, I document that ARS is more flexible in modeling to accomodate empirical regularities. Next, I investigate several applications which illustrate the power of the general formulas in terms of i) establishing links among existing models in different areas; and ii) providing a convenient way to conceive new tractable models with desired features. A calibrated three-regime consumption-based Peso problem model shows that regime switching provides a simple way to understand the empirically observed yield curves.
Keywords: regime switching, affine processes, within-the-regime jumps, Feyman-Kac theorem
JEL Classification: C60, G12, G13
Suggested Citation: Suggested Citation