# OPTIHEDGE - t to the value of the asset in question The...

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EC3070 FINANCIAL DERIVATIVES OPTIMAL HEDGE RATIO If an asset has been hedged, then the movements in its spot price and in the accompanying short hedge should constitute compensating variations. The optimum size of the hedge will be a function of the variances of the spot price and the futures price and of the covariance of the two. Let S = S t 2 S t 1 denote the change in the spot price between times t 1 and t 2 , and let F = F τ | t 2 F τ | t 1 be the change in the futures price. Also, let h denote the hedge ratio, which is the ratio of the value of the futures contract at time
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Unformatted text preview: t to the value of the asset in question. The change in the value of the hedger’s position between time t 1 and t 2 is ∇ S − h ∇ F. We may denote the variance of ∇ S by σ 2 S and the variance of ∇ F by σ 2 F . Then, the variance of the hedger’s position is ν = σ 2 S + h 2 σ 2 F − 2 hρσ S σ F , where ρ is the correlation between ∇ S and ∇ F and where, consequently, ρσ 2 S σ 2 F is the covariance of ∇ S and ∇ F . The value of h which minimises ν is h = ρ σ S σ F . 1...
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