A Black--Scholes Model with Long Memory

John A. D. Appleby, John A. Daniels and Katja Krol

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Abstract: This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH($\infty$) processes are sketched.

Date: 2012-02
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