Stochastic Volatility and Seasonality in ... - Interconti, Limited

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Table 3: Parameter estimates for soybean contracts, Full sample: Oct. 1984 – Mar. 1999. Volatility κ: 2.2708 θ : 0.1542 σ v : 0.7414 ν 1 : −0.4096 ν ∗ 1 : −0.2626 ν 2 : 0.2250 ν ∗ 2 : 0.1293 parameters: (0.2654) (0.0085) (0.0299) (0.0387) (0.0483) (0.0229) (0.0223) Convenience yield β : 0.8145 σ δ : 0.9933 α 0 : 0.0612 α 1 : −0.2683 α ∗ 1 : 0.1915 α 2 : 0.2338 α ∗ 2 : 0.2689 parameters: (0.2100) (0.1345) (0.0086) (0.0276) (0.0130) (0.0255) (0.0600) Correlations and risk ρ 12 : 0.3979 ρ 13 : 0.4078 ρ 23 : −0.0784 λ P : −0.6274 λ δ : −0.1282 λ v : −3.7829 premia parameters: (0.0110) (0.0461) (0.0772) (1.3001) (1.2286) (1.5610) 36 Correlation matrix of measurement errors (standard deviation estimates in diagonal): ⎛ ⎜ ⎝ ⎞ 0.9606 −0.3075 0.8040 0.0489 0.2150 2.4068 0.0164 0.1373 0.7310 3.4679 −0.2480 0.1719 0.1118 0.1053 0.0180 −0.1871 0.1153 0.1435 0.1549 0.8947 0.0265 −0.1236 0.0850 0.2187 0.2398 0.7175 0.9137 0.0279 −0.0638 0.0566 0.2922 0.3084 0.5302 0.7388 0.9238 0.0254 ⎟ −0.0688 0.0755 0.2306 0.2765 0.3838 0.5751 0.7466 0.8870 0.0193 ⎠ −0.1199 0.0808 0.1573 0.2042 0.2053 0.3663 0.4892 0.6014 0.8191 0.0116 Log-likelihood function value: 8468.59
Table 4: Parameter estimates for soybean contracts, 1. half: Oct. 1984 – Nov. 1991. Volatility κ: 0.7373 θ : 0.1103 σ v : 0.7626 ν 1 : −0.3825 ν ∗ 1 : −0.1448 ν 2 : 0.2461 ν ∗ 2 : 0.0861 parameters: (0.5038) (0.0110) (0.0282) (0.0371) (0.0423) (0.0332) (0.0186) Convenience yield β : 0.3186 σ δ : 0.7385 α 0 : 0.0872 α 1 : −0.2103 α ∗ 1 : 0.1571 α 2 : 0.2300 α ∗ 2 : 0.2454 parameters: (0.1921) (0.0887) (0.0090) (0.0336) (0.0139) (0.0335) (0.0516) Correlations and risk ρ 12 : 0.3549 ρ 13 : 0.4989 ρ 23 : −0.0638 λ P : −3.0441 λ δ : −1.9042 λ v : −5.4792 premia parameters: (0.0150) (0.1052) (0.0836) (2.0377) (1.6564) (1.8105) 37 Correlation matrix of measurement errors (standard deviation estimates in diagonal): ⎛ ⎜ ⎝ ⎞ 1.0093 −0.1240 0.8056 0.1506 0.2121 2.6630 0.0842 0.1804 0.6474 3.6959 −0.2235 0.1148 0.1393 0.0651 0.0142 −0.1720 0.0662 0.0958 0.0409 0.9347 0.0219 −0.1396 0.0662 0.1087 0.0256 0.8492 0.9599 0.0251 −0.1216 0.0656 0.1563 0.0505 0.7250 0.8476 0.9381 0.0244 ⎟ −0.1333 0.0901 0.0660 0.0475 0.5411 0.6404 0.7345 0.8644 0.0206 ⎠ −0.1787 0.0821 −0.0131 0.0266 0.3112 0.3578 0.4195 0.5321 0.8027 0.0129 Log-likelihood function value: 4205.60
Page 1 and 2: Stochastic Volatility and Seasonali
Page 3 and 4: 1 Introduction This paper sets up a
Page 5 and 6: The estimated commodity price model
Page 7 and 8: where β, κ, θ, λ P , λ δ , λ
Page 9 and 10: Solutions to the ordinary different
Page 11 and 12: The measurement equation relates th
Page 13 and 14: and, N ˆΓ ∼ W m (N, Γ) where W
Page 15 and 16: where T s and T l refer to the rele
Page 17 and 18: prices seems lower than that of sho
Page 19 and 20: [ INSERT FIGURE 2 ABOUT HERE ] As s
Page 21 and 22: where adverse weather conditions ma
Page 23 and 24: Inverse leverage effects The correl
Page 25 and 26: (with the relevant estimated standa
Page 27 and 28: as well as changes in government po
Page 29 and 30: Besides estimating model parameters
Page 31 and 32: Chambers, M. & Bailey, R. (1996).
Page 33 and 34: Kaldor, N. (1939). “Speculation a
Page 35 and 36: Appendix Lemma 1 Let p t = log P t
Page 37: Table 2: Summary statistics for soy
Page 41 and 42: 1100.00 Futures prices in cents per
Page 43 and 44: 1.00 0.75 0.50 0.25 0.00 - 0.25 α(
Page 45: 2.00 1.50 1.00 0.50 0.00 - 0.50 α

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