value is distributed in gaussian, ˆ S ≡ 1 ρ ρ 1 , ω ≡ x y f(z; ˆ S) = ∞ −∞ dx ∞ −∞ dyδ(z − x y )f(x, y; ˆ S) = ∞ −∞ dx ∞ −∞ dyδ(z − x y )((2π)N | ˆ S|)− 1 2 e− 1 2 ωT ˆ S−1 ω = 1 πγ{(z−z0 γ )2 + 1} (γ ≡ (1 − ρ2)1 2 , Z0 ≡ ρ) Cauchy distribution (a kind of t-distribution) The density function of price f(z; S) can be calculated as follows 201312݄2݄༵