General Formulas for Valuing Stocks and Bonds with Structural Changes

59 Pages Posted: 14 Apr 2009 Last revised: 10 Jan 2010

See all articles by Du Du

Du Du

Hong Kong University of Science & Technology (HKUST)

Date Written: April 12, 2009

Abstract

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

Du, Du, General Formulas for Valuing Stocks and Bonds with Structural Changes (April 12, 2009). Available at SSRN: https://ssrn.com/abstract=1365744 or http://dx.doi.org/10.2139/ssrn.1365744

Du Du (Contact Author)

Hong Kong University of Science & Technology (HKUST) ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

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