Articlegreen2014

Stationarity and Ergodicity for an Affine Two-Factor Model

Mátyás Barczy · Leif Döring · Zenghu Li · Gyula Pap

36 citations0/0 files storedAdvances in Applied Probability

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Stochastic processes and financial applications Mathematical Dynamics and Fractals Stochastic processes and statistical mechanics

Abstract

We study the existence of a unique stationary distribution and ergodicity for a two-dimensional affine process. Its first coordinate process is supposed to be a so-called α-root process with α ∈ (1, 2]. We prove the existence of a unique stationary distribution for the affine process in the α ∈ (1, 2] case; furthermore, we show ergodicity in the α = 2 case.

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1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 1983Stochastic Differential Equations and Diffusion Processes 1991Brownian motion and stochastic calculus 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 2003Affine processes and applications in finance

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