L_{i} = PP_{i} ∫_{t}^{T} dx ∫_{t}^{Ti} dx’σ(t, x) σ(t, x’) D(x, x′; t, T_{FR})

M_{ij} = P_{i}Pj ∫_{t}^{Ti} dx ∫_{t}^{Tj} dx’σ(t, x) σ(t, x’) D(x, x′; t, T_{FR})

This definition allows the residual variance in

Theorem: Hedge parameter for bond in the field theory model equals

Δ_{i} = -∑_{j=1}^{N} L_{j} M_{ij}^{-1}

Corollary: Residual variance, the variance of the hedged portfolio equals