A Black--Scholes Model with Long Memory

Details A Black--Scholes Model with Long Memory A Black--Scholes Model with Long Memory

2012-02-24

arxiv.org/abs/1202.5574v1

Economy

Quantitative Finance

Pricing of Securities

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
sketched.

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