Regime switching affine processes with applications to finance

Misha Beek (), Michel Mandjes (), Peter Spreij () and Erik Winands ()
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Misha Beek: University of Amsterdam
Michel Mandjes: University of Amsterdam
Peter Spreij: University of Amsterdam
Erik Winands: University of Amsterdam

Finance and Stochastics, 2020, vol. 24, issue 2, No 2, 309-333

Abstract: Abstract We introduce the notion of a regime switching affine process. Informally this is a Markov process that behaves conditionally on each regime as an affine process with specific parameters. To facilitate our analysis, specific restrictions are imposed on these parameters. The regime switches are driven by a Markov chain. We prove that the joint process of the Markov chain and the conditionally affine part is a process with an affine structure on an enlarged state space, conditionally on the starting state of the Markov chain. Like for affine processes, the characteristic function can be expressed in a set of ordinary differential equations that can sometimes be solved analytically. This result unifies several semi-analytical solutions found in the literature for pricing derivatives of specific regime switching processes on smaller state spaces. It also provides a unifying theory that allows us to introduce regime switching to the pricing of many derivatives within the broad class of affine processes. Examples include European options and term structure derivatives with stochastic volatility and default. Essentially, whenever there is a pricing solution based on an affine process, we can extend this to a regime switching affine process without sacrificing the analytical tractability of the affine process.

Keywords: Affine processes; Regime switching; Markov modulation; Markov chain; Derivatives pricing; 60G20; 91G80 (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-020-00419-2

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