2013 5 219 JOURNAL OF XIAMEN UNIVERSITY Arts & Social Sciences No. 5 2013 General Serial No. 219 300 郑 鸣 1, 朱 德 贞 1 2, 倪 玉 娟 1. 361005 2. 200001 Helmer Longstaff 1991 300 1 300 300 2 3 300 F752. 62 A 0438-0460 2013 05-0124 - 08 引 言 2010 4 300 300 2012 300 76 A 1983 Cornell French F = Se r - q T - t S r q T - t Cox Ingersoll Ross 1985 Hemler Longstaff 1991 NYSE Wang 2007 225 200 2013-05 - 11 郑 鸣, 男, 福 建 福 州 人, 厦 门 大 学 经 济 学 院 教 授 博 士 生 导 师 ; 朱 德 贞, 女, 福 建 福 州 人, 厦 门 大 学 经 济 学 院 博 士 研 究 生 ; 倪 玉 娟, 女, 安 徽 滁 州 人, 海 通 证 券 研 究 所 分 析 师, 经 济 学 博 士 124
5 300 1997 Hemler Longstaff Hemler Longstaff Gay Jung 1999 Brailsford Cusack 1997 2008 2011 2007 B - S 2011 Helmer Longstaff 300 一 股 指 期 货 的 一 般 均 衡 定 价 模 型 Hemler Longstaff 1991 max C E t e -ρs ln C s ds t dw = w dq /q - Cdt ρ C dq /q = uxdt + σ 槡 YdZ 1 Z 1 X Y dx = a + bx dt + c 槡 XdZ 2 dy = d + ey dt + f 槡 YdZ 3 a d > 0 b e < 0 Z 2 Z 3 W Merton 1971 J W X Y t = e -ρt /ρ ln W + G X Y t dw = μx - ρ Wdt + σ W 槡 YdZ 1 W W X Y F W r V τ W τ V r A τ = F W r V τ = We -ρt A τ e = C τ = B τ = B τ r +C τ V 1 + β τ 2 e 2 β + e τ - 1 + 2 2 e τ - 1 β + e τ - 1 + 2 2 α+β η2 ψ + β - γ τ 2ψe 2 ψ + β - γ e ψτ - 1 + 2ψ 2δ ξ2 B τ 2 1 - e ψτ ψ + β - γ e ψτ - 1 + 2ψ α = μα - σ2 d β = - b γ = e - b δ = σ 2 d η = 槡 μc 125
2013 ξ = σ 槡 f = 槡 β 2-2η 2 ψ = 槡 γ + β 2 + 2ξ 2 β δ η ξ > 0 γ < β A τ B τ C τ lna τ = 0 B τ = τ C τ = 0 F = We γ -ρ τ 二 计 量 模 型 的 设 定 H - L Helmer Longstaff 1991 NYSE 1983 1 1987 11 1 L t = lna τ + B τ r + C τ V L t = ln F W r V τ eρτ W OLS L t = α + βr t + λv t + ε t 2 α β λ ε t lna τ = 0 B τ = τ C τ = 0 α = 0 β = τ λ = 0 2 L t = α + bτr t + λv t + ε t 3 β = bτ Wald α = 0 b = 1 λ = 0 Helmer Longstaff 1991 α t β t γ t lna τ B τ C τ τ τ t lna τ B τ C τ α τ β τ γ τ α τ lna 0 'τ + lna 0 τ 2 β τ β' 0 τ + β 0 τ 2 λ τ C' 0 τ + C 0 τ 2 α 1 = lna 0 ' α 2 lna 0 β 1 = B' 0 β 2 = B 0 λ 1 = C' 0 + λ 2 = C 0 L t = α 1 τ t + α 2 τ 2 t + β 1 τ t r t + β 2 τ 2 t r t + λ 2 τ 2 t V t + ε t 2007 MS - ARMA Krolzig 1998 M s t 1 M y t = y 1t y Kt ' t = 1 T p MS - ARMA 126 y t = μ s t + β s t X t + u t u t ~ N 0 σ s t
5 300 s t i j M p ij j = 1 p ij = Pr S t +1 = j s t = i = 1 i j 1 M MS - ARMA s t MS - ARMA MS - ARMA L t = λ s t L t -1 + α 1 s t τ t + α 2 s t τ 2 t + β 1 s t τ t r + β 2 s t τ 2 t + λ 1 s t τ t V t + λ 2 s t τ 2 t V t + μ t -1 - θ 1 s t μ t -1 4 u t ~ N 0 σ s t s t ARMA AIC SC HQ 三 实 证 结 果 300 2010 4 19 2010 4 19 2012 10 24 300 W t 300 F t 300 r t t 1 1 V t 300 300 5 τ 300 t 10 τ 10 /365 ρ t 300 t 300 5 Wind 1 2 A 5 7 t 300 1 300 300 300 2 / 3 300 A A 4 300 127
2013 1 A 2 300 1 300 L t 300 2806. 18 2798. 17 0. 0228 0. 0036 0. 0387 0. 0415 0. 032 1 F t W t ρ t L t τ t r t V t 2806. 18 2798. 17 0. 0228 0. 0036 0. 0387 0. 0415 0. 0320 2776. 00 2768. 79 0. 0035 0. 0030 0. 0389 0. 0400 0. 0236 3606. 00 3548. 57 0. 1641 0. 0353 0. 0972 0. 0924 0. 2020 2195. 00 2184. 89 0. 0000-0. 0181 0. 0000 0. 0174 0. 0067 330. 84 326. 73 0. 0374 0. 0055 0. 0258 0. 0137 0. 0251 0. 1786 0. 1236 2. 2657 1. 3180 0. 1543 0. 5426 2. 6298 2. 0780 2. 0157 7. 8334 8. 3344 1. 8852 3. 3524 12. 3301 r t V t τ L t - 0. 19 0. 17 0. 45 1% V t r t - 0. 2193 H - L OLS 3 L^ t = 0. 0005 + 1. 0684τr t + 0. 0418V t T 1. 20 6. 57 4. 96 τr t V t 1% V t L t τr t L t Wald a = 0 b = 1 λ = 0 LinResF 1 610 = 43. 179 1% 128
5 300 MS - ARMA 2 Markov Switching - ARMA OXMETRICS 6 MS - ARMA T AR - 1 0. 638 * 9. 290 MA - 1-0. 217 * - 3. 430 4 AIC SC τ t r 0. 01 ** 2. 190 HQ τ t V 0. 831 1. 220 τ 2 t V - 12. 436 *** - 1. 999 τ t s = 0 0. 134 * 5. 970 0 1 τ t τ t s = 1 0. 212 * 2. 780 σ s = 0 0. 0029 σ 14. 600 τ 2 t τ 2 t r p 0 1 0. 1272 *** 1. 979 2 0 1 在 状 态 0 时 的 概 率 ; p{0 1} 表 示 t 期 在 状 态 0 时,t + 1 0. 1272 1 2 仍 然 在 状 态 1 时 的 概 率 ( 3) 对 模 型 残 差 进 行 ARCH 效 0. 0201 0 0 应 和 自 相 关 效 应 检 验, 发 现 并 不 存 在 条 件 异 方 差 和 自 0. 9799 1 1 0. 8729 0 1 3 σ s = 1 0. 0069 * 6. 610 p 0 0 0. 9799 * 41. 900 注 : ( 1) * ** *** 和 分 别 表 示 在 1% 5% 和 10% 的 显 著 性 水 平 ( 2) p{0 0} 表 示 t 期 在 状 态 0 时,t + 1 仍 然 相 关 效 应, 可 认 为 文 章 运 用 的 MS - ARMA 模 型 较 好 地 解 决 了 自 相 关 和 异 方 差 问 题, 模 型 的 结 论 可 信 0 1 0. 0029 0. 0069 1 3 1 Lt 0 Lt ^ L 2 s t =0 { 0. 638 * L t -1 +0. 212 * τ t +0. 01 **** τ t r t +0. 831τ t V t -12. 436 *** τ 2 t V t + μ t -1-0. 21 * μ t -1 =1 t = 0. 638* L t -1 +0. 134 * τ t +0. 01 **** τ t r t + 0. 831τ t V t - 12. 436 *** τ 2 t V t + μ t -1-0. 21 * μ t -1 L t ARMA τ t τ t r t L t τ t V t τ 2 V L t τ t 0 0. 134 1 0. 212 1 τ t L t L t 4 s t 129
2013 4 0 1 注 : 横 轴 1-613 分 别 代 表 日 期 2010-4 - 19 日 到 2012-10 - 24 L t L t = ln Fe ρτ /W ^ F^ t = W t e L t - ρτ Bias = F t - F^ t 11 MS - ARMA 7 MS - AR- MA 5 5 四 结 论 Helmer Longstaff 1991 300 2010 4 19 2012 10 24 1 Wald 2 5 7 3 MS - ARMA 130
5 300 τ t τ t r t Lt τ t V t τ 2 t V Lt 4 11 7 300 MS - ARMA 2007 5 2011 300 7 2008 300 6 Brailsford T. J. and A. J. Cusack 1997 A Comparison of Futures Pricing Models In a New Market The Case of Individual Share Futures Journal of Futures Markets 17. Cornell B. and K. R. French 1983 Taxes and the Pricing of Stock Index Futures Journal of Finance 38 3. Cox J. C J. E. Ingersoll Jr. and S. A Ross. 1985 An Intertemporal General Equilibrium Model of Asset Prices Econometrica 53. Gay G. D. and D. Y. Jung 1999 A Further Look at Transaction Costs Short Sale Restrictions and Future Market Efficiency The Case of Korean Stock Index Futures Journal of Futures Markets 19. Hemler M. L. and F. A. Longstaff 1991 General Equilibrium Stock Index Futures Prices Theory and Empirical Evidence The Journal of Financial and Quantitative Analysis 26 3. Krolzig. H. M 1998 Predicting Markov - switching vector antoregressive processes Mimeo Institue of Economic and Statistics University of Oxford. Merton R. C. 1971 Optimum Consumption and Portfolio Rules in a Continuous Time Model Journal of Economic Theory 12. Wang Janchuang 2007 Testing the General Equilibrium Model of Stock Index Futures International Research Journal of Finance and Economics 10. On the Pricing of Hushen 300 Index Futures in China ZHENG Ming 1 ZHU De-zhen 1 NI Yu-juan 2 1. School of Economics Xiamen University Xiamen 361005 Fujian 2. Insitute of Haitong Securities Co. Ltd Shanghai 200001 China Abstract Stock index futures play an important role in risk management and market efficiency improvement and reasonable pricing is the prerequisite for this role. This paper studies the pricing of Hushen 300 index futures using Helmer & Longstaff s general equilibrium model of pricing of stock index futures in fluctuation of interests and market and the Markov-Switching Model. Our findings are 1 The timing of dividend payout of Hushen 300 listed companies has obvious seasonality. Therefore the time-variant dividend yield is crucial in the pricing of Hushen 300 index futures. 2 The volatility of stock index has significant explanatory power on the pricing of index futures which suggests that the volatility of stock index should be considered in the pricing of index futures. 3 The general equilibrium model performs better than the Cost and Carry Model on the pricing of Hushen 300 index futures. Key words pricing of stock index futures general equilibrium model Cost and Carry Model Markov-Switching Model 131