Wednesday, September 17, 2008

Return Elasticity of Drift

This would represent the mean reversion factor for the process

E.g.

ΔS(t) = ρ ΔS(t – 1) + ε

ΔS(t) – ΔS(t – 1) = ρ ΔS(t – 1) – ΔS(t – 1) + ε

ΔΔS(t) = (ρ – 1) ΔS(t – 1) + ε


As the sapling interval becomes smaller

ρ ≈ 1 – c Δt (Assuming an exponentially decaying function proportional to the sampling interval)

Then,

ΔΔS(t) = – c ΔS(t - 1) Δt + ε

Best regards, Suminda Sirinath Salpitikorala Dharmasena

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