A Black--Scholes Model with Long Memory

Economy – Quantitative Finance – Pricing of Securities

Scientific paper

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John Appleby and John Daniels were partially funded by the Science Foundation Ireland grant 07/MI/008 "Edgeworth Centre for Fi

Scientific paper

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

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