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arxiv: 1202.5574 · v1 · pith:EJNJTMY2new · submitted 2012-02-24 · 💱 q-fin.PR · math.CA· math.DS· math.PR· q-fin.CP

A Black--Scholes Model with Long Memory

John A. D. Appleby , John A. Daniels , Katja Krol This is my paper
classification 💱 q-fin.PR math.CAmath.DSmath.PRq-fin.CP
keywords longmemorymodelvolatilityarchassetasymptoticallyautoregressive
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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.

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