A Black--Scholes Model with Long Memory

preprint2012arXivOpen access

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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A Black--Scholes Model with Long Memory

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