Материал: Хеджирование валютного курса
Планируется продолжение работ над данным исследованием, поскольку
получились неоднозначные результаты. Возможно при использовании более сложных
моделей, таких как моделей условных автокорреляций, которые относятся к классу
динамических, результаты получатся более удовлетворительными.
Приложение 1
Рисунок 1: Динамика цены фьючерсов на нефть и реального курса долл/руб (дневная)
Приложение 2
Рисунок 2: График остатков модели с фьючерсами на рубль
Рисунок 3: График остатков модели с фьючерсами на нефть
Рисунок 4: График остатков модели свопов на дефолт России по кредиту
Приложение 3
Рисунок 5: Распределение остатков модели фьючерсов на рубль
Рисунок 6: Распределение остатков модели фьючерсов на нефть
Рисунок 7: Распределение остатков модели кредитно-дефолтных свопов
Приложение 4
Таблица 8
Критерий длины лага для модели фьючерсов на рубль
|
Lag |
LogL |
LR |
FPE |
AIC |
SC |
HQ |
|
0 |
2701.076 |
NA |
3.11e-08 |
-11.60893 |
-11.59111 |
-11.60192 |
|
1 |
2754.945 |
107.0428 |
2.51e-08 |
-11.82342 |
-11.76997 |
-11.80238 |
|
2 |
2777.274 |
44.17828 |
2.32e-08 |
-11.90225 |
-11.81318 |
-11.86719 |
|
3 |
2812.637 |
69.66087 |
2.03e-08 |
-12.03715 |
-11.91244* |
-11.98806* |
|
4 |
2817.439 |
9.418009 |
2.02e-08 |
-12.04060 |
-11.88026 |
-11.97749 |
|
5 |
2822.057 |
9.018645 |
2.02e-08 |
-12.04326 |
-11.84729 |
-11.96612 |
|
6 |
2824.306 |
4.371346 |
2.03e-08 |
-12.03572 |
-11.80413 |
-11.94457 |
|
7 |
2827.954 |
7.061129 |
2.04e-08 |
-12.03421 |
-11.76698 |
-11.92903 |
|
8 |
2846.834 |
36.37987 |
1.91e-08 |
-12.09821 |
-11.79535 |
-11.97901 |
|
9 |
2850.073 |
6.214119 |
1.92e-08 |
-12.09494 |
-11.75645 |
-11.96171 |
|
10 |
2862.578 |
23.88015 |
1.85e-08 |
-12.13152 |
-11.75740 |
-11.98427 |
|
11 |
2864.801 |
4.226386 |
1.86e-08 |
-12.12388 |
-11.71413 |
-11.96260 |
|
12 |
2874.220 |
17.82360 |
1.82e-08 |
-12.14718 |
-11.70180 |
-11.97188 |
|
13 |
2882.879 |
16.31236 |
1.78e-08 |
-12.16722 |
-11.68621 |
-11.97789 |
|
14 |
2889.486 |
12.38996 |
1.76e-08 |
-12.17843 |
-11.66179 |
-11.97508 |
|
15 |
2893.076 |
6.701252 |
1.77e-08 |
-12.17667 |
-11.62440 |
-11.95929 |
|
16 |
2896.156 |
5.724597 |
1.77e-08 |
-12.17272 |
-11.58481 |
-11.94132 |
|
17 |
2904.903 |
16.17573 |
1.74e-08* |
-12.19313* |
-11.56960 |
-11.94771 |
|
18 |
2906.013 |
2.043241 |
1.76e-08 |
-12.18070 |
-11.52154 |
-11.92125 |
|
19 |
2907.214 |
2.201974 |
1.78e-08 |
-12.16866 |
-11.47387 |
-11.89519 |
|
20 |
2910.740 |
6.430114 |
1.78e-08 |
-12.16663 |
-11.43620 |
-11.87913 |
|
21 |
2913.881 |
5.701056 |
1.79e-08 |
-12.16293 |
-11.39688 |
-11.86141 |
|
22 |
2915.759 |
3.392618 |
1.81e-08 |
-12.15380 |
-11.35212 |
-11.83826 |
|
23 |
2916.286 |
0.946760 |
1.84e-08 |
-12.13886 |
-11.30155 |
-11.80930 |
|
24 |
2922.971 |
11.96107 |
1.81e-08 |
-12.15041 |
-11.27747 |
-11.80682 |
|
25 |
2928.467 |
9.785975 |
1.80e-08 |
-12.15685 |
-11.24827 |
-11.79923 |
|
26 |
2934.414 |
10.53937 |
1.79e-08 |
-12.16522 |
-11.22102 |
-11.79358 |
|
27 |
2941.630 |
12.72436 |
1.76e-08 |
-12.17905 |
-11.19922 |
-11.79339 |
|
28 |
2947.144 |
9.676047* |
1.75e-08 |
-12.18556 |
-11.17010 |
-11.78588 |
|
29 |
2948.783 |
2.862286 |
1.77e-08 |
-12.17541 |
-11.12431 |
-11.76170 |
|
30 |
2952.003 |
5.595091 |
1.78e-08 |
-12.17206 |
-11.08533 |
|
|
31 |
2954.471 |
4.266927 |
1.79e-08 |
-12.16547 |
-11.04311 |
-11.72370 |
|
32 |
2955.923 |
2.498314 |
1.81e-08 |
-12.15451 |
-10.99652 |
-11.69872 |
|
33 |
2956.952 |
1.760844 |
1.84e-08 |
-12.14173 |
-10.94811 |
-11.67192 |
|
34 |
2957.816 |
1.472849 |
1.86e-08 |
-12.12824 |
-10.89899 |
-11.64441 |
|
35 |
2963.167 |
9.067541 |
1.85e-08 |
-12.13405 |
-10.86917 |
-11.63619 |
|
36 |
2964.898 |
2.918192 |
1.87e-08 |
-12.12429 |
-10.82378 |
-11.61241 |
|
37 |
2968.367 |
5.818632 |
1.87e-08 |
-12.12201 |
-10.78587 |
-11.59610 |
|
38 |
2973.564 |
8.673384 |
1.87e-08 |
-12.12716 |
-10.75539 |
-11.58723 |
|
39 |
2975.137 |
2.612196 |
1.89e-08 |
-12.11672 |
-10.70932 |
-11.56276 |
|
40 |
2979.455 |
7.131171 |
1.89e-08 |
-12.11809 |
-10.67505 |
-11.55011 |
|
Замечания: * indicates lag order selected by the criterion. LR: sequential modified LR test statistic (each test at 5% level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion HQ: Hannan-Quinn information criterion |
||||||
Таблица 9
Критерий длины лага для модели фьючерсов на нефть
|
Lag |
LogL |
LR |
FPE |
AIC |
SC |
HQ |
|
0 |
2333.421 |
NA |
1.51e-07 |
-10.02762 |
-10.00980* |
-10.02060 |
|
1 |
2342.188 |
17.42122 |
1.48e-07 |
-10.04812 |
-9.994675 |
-10.02708* |
|
2 |
2345.533 |
6.617741 |
1.49e-07 |
-10.04530 |
-9.956227 |
-10.01024 |
|
3 |
2347.827 |
4.519224 |
1.50e-07 |
-10.03797 |
-9.913259 |
-9.988881 |
|
4 |
2353.516 |
11.15794 |
1.49e-07 |
-10.04523 |
-9.884894 |
-9.982122 |
|
5 |
2354.272 |
1.475125 |
1.51e-07 |
-10.03128 |
-9.835308 |
-9.954142 |
|
6 |
2359.308 |
9.791501 |
1.50e-07 |
-10.03573 |
-9.804136 |
-9.944576 |
|
7 |
2363.996 |
9.073783 |
1.50e-07 |
-10.03869 |
-9.771465 |
-9.933512 |
|
8 |
2374.097 |
19.46352 |
1.46e-07 |
-10.06493 |
-9.762076 |
-9.945729 |
|
9 |
2375.521 |
2.730687 |
1.47e-07 |
-10.05385 |
-9.715364 |
-9.920623 |
|
10 |
2382.144 |
12.64796 |
1.46e-07 |
-10.06513 |
-9.691015 |
-9.917881 |
|
11 |
2387.930 |
10.99953 |
1.45e-07 |
-10.07282 |
-9.663066 |
-9.911538 |
|
12 |
2390.509 |
4.880370 |
1.46e-07 |
-10.06670 |
-9.621324 |
-9.891401 |
|
13 |
2395.843 |
10.04899 |
1.45e-07 |
-10.07244 |
-9.591432 |
-9.883116 |
|
14 |
2398.394 |
4.784849 |
1.46e-07 |
-10.06621 |
-9.549571 |
-9.862862 |
|
15 |
2401.606 |
5.995388 |
1.46e-07 |
-10.06282 |
-9.510551 |
-9.845447 |
|
16 |
2403.101 |
2.777007 |
1.48e-07 |
-10.05205 |
-9.464144 |
-9.820647 |
|
17 |
2408.525 |
10.03251 |
1.47e-07 |
-10.05817 |
-9.434641 |
-9.812750 |
|
18 |
2411.377 |
5.249198 |
1.48e-07 |
-10.05323 |
-9.394071 |
-9.793786 |
|
19 |
2415.597 |
7.731489 |
1.48e-07 |
-10.05418 |
-9.359385 |
-9.780707 |
|
20 |
2419.063 |
6.322138 |
1.48e-07 |
-10.05188 |
-9.321461 |
-9.764389 |
|
21 |
2422.666 |
6.539738 |
1.48e-07 |
-10.05018 |
-9.284123 |
-9.748657 |
|
22 |
2426.708 |
7.301111 |
1.48e-07 |
-10.05036 |
-9.248672 |
-9.734812 |
|
23 |
2433.068 |
11.43360 |
1.47e-07 |
-10.06051 |
-9.223191 |
-9.730937 |
|
24 |
2437.641 |
8.183685 |
1.46e-07 |
-10.06297 |
-9.190028 |
-9.719381 |
|
25 |
2445.070 |
13.22722 |
1.44e-07* |
-10.07772* |
-9.169143 |
-9.720102 |
|
26 |
2445.521 |
0.800420 |
1.47e-07 |
-10.06246 |
-9.118251 |
-9.690817 |
|
27 |
2448.812 |
5.803413 |
1.47e-07 |
-10.05941 |
-9.079571 |
-9.673743 |
|
28 |
2455.293 |
11.37211 |
1.45e-07 |
-10.07008 |
-9.054609 |
-9.670387 |
|
29 |
2458.516 |
5.627820 |
1.46e-07 |
-10.06673 |
-9.015636 |
-9.653020 |
|
30 |
2464.281 |
10.01846* |
1.45e-07 |
-10.07433 |
-8.987600 |
-9.646590 |
|
31 |
2465.741 |
2.524102 |
1.47e-07 |
-10.06340 |
-8.941044 |
-9.621640 |
|
32 |
2467.416 |
2.881431 |
1.48e-07 |
-10.05340 |
-8.895413 |
-9.597615 |
|
33 |
2470.225 |
4.808663 |
1.49e-07 |
-10.04828 |
-8.854660 |
-9.578469 |
|
34 |
2472.582 |
4.014590 |
1.50e-07 |
-10.04121 |
-8.811963 |
-9.557378 |
|
35 |
2473.197 |
1.041619 |
1.52e-07 |
-10.02665 |
-8.761772 |
-9.528793 |
|
36 |
2477.235 |
6.809016 |
1.52e-07 |
-10.02682 |
-8.726307 |
-9.514935 |
|
37 |
2478.177 |
1.579569 |
1.54e-07 |
-10.01366 |
-8.677523 |
-9.487756 |
|
38 |
2483.859 |
9.482174 |
1.53e-07 |
-8.649127 |
-9.480967 |
|
|
39 |
2486.747 |
4.794516 |
1.54e-07 |
-10.01611 |
-8.608713 |
-9.462159 |
|
40 |
2488.600 |
3.061564 |
1.56e-07 |
-10.00688 |
-8.563851 |
-9.438903 |
|
Замечания: * indicates lag order selected by the criterion. LR: sequential modified LR test statistic (each test at 5% level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion HQ: Hannan-Quinn information criterion |
||||||
Таблица 10
Критерий длины лага для модели свопов на дефолт по кредиту
|
Lag |
LogL |
LR |
FPE |
AIC |
SC |
HQ |
|
0 |
2174.155 |
NA |
3.00e-07 |
-9.342604 |
-9.324788 |
-9.335591 |
|
1 |
2187.339 |
26.19695 |
2.89e-07 |
-9.382103 |
-9.328657* |
-9.361066* |
|
2 |
2188.575 |
2.444753 |
2.92e-07 |
-9.370213 |
-9.281137 |
-9.335152 |
|
3 |
2191.860 |
6.471346 |
2.93e-07 |
-9.367138 |
-9.242432 |
-9.318054 |
|
4 |
2196.327 |
8.760826 |
2.92e-07 |
-9.369146 |
-9.208809 |
-9.306037 |
|
5 |
2200.089 |
7.347025 |
2.93e-07 |
-9.368125 |
-9.172157 |
-9.290992 |
|
6 |
2202.214 |
4.130275 |
2.95e-07 |
-9.360058 |
-9.128461 |
-9.268901 |
|
7 |
2210.912 |
16.83521 |
2.89e-07 |
-9.380266 |
-9.113037 |
-9.275084 |
|
8 |
2222.658 |
22.63363 |
2.80e-07* |
-9.413583* |
-9.110724 |
-9.294377 |
|
9 |
2225.366 |
5.194546 |
2.81e-07 |
-9.408025 |
-9.069536 |
-9.274796 |
|
10 |
2228.544 |
6.068343 |
2.82e-07 |
-9.404489 |
-9.030369 |
-9.257234 |
|
11 |
2234.262 |
10.87143 |
2.80e-07 |
-9.411880 |
-9.002130 |
-9.250602 |
|
12 |
2237.244 |
5.642628 |
2.82e-07 |
-9.407500 |
-8.962120 |
-9.232198 |
|
13 |
2240.113 |
5.404990 |
2.83e-07 |
-9.402636 |
-8.921625 |
-9.213309 |
|
14 |
2244.461 |
8.154352 |
2.83e-07 |
-9.404134 |
-8.887493 |
-9.200783 |
|
15 |
2245.269 |
1.508307 |
2.86e-07 |
-9.390405 |
-8.838134 |
-9.173030 |
|
16 |
2247.059 |
3.325428 |
2.89e-07 |
-9.380899 |
-8.792997 |
-9.149500 |
|
17 |
2248.612 |
2.872650 |
2.92e-07 |
-9.370375 |
-8.746843 |
-9.124952 |
|
18 |
2250.609 |
3.675753 |
2.95e-07 |
-9.361759 |
-8.702596 |
-9.102311 |
|
19 |
2251.063 |
0.831569 |
2.99e-07 |
-9.346507 |
-8.651713 |
-9.073035 |
|
20 |
2252.654 |
2.902543 |
3.03e-07 |
-9.336148 |
-8.605724 |
-9.048652 |
|
21 |
2254.910 |
4.094303 |
3.05e-07 |
-9.328646 |
-8.562592 |
-9.027126 |
|
22 |
2256.927 |
3.642750 |
3.08e-07 |
-9.320115 |
-8.518430 |
-9.004570 |
|
23 |
2259.084 |
3.879231 |
3.10e-07 |
-9.312191 |
-8.474876 |
-8.982622 |
|
24 |
2261.370 |
4.089106 |
3.12e-07 |
-9.304816 |
-8.431871 |
-8.961223 |
|
25 |
2268.164 |
12.09852 |
3.09e-07 |
-9.316835 |
-8.408259 |
-8.959218 |
|
26 |
2269.598 |
2.541283 |
3.12e-07 |
-9.305799 |
-8.361593 |
-8.934158 |
|
27 |
2274.445 |
8.546776 |
3.11e-07 |
-9.309441 |
-8.329604 |
-8.923775 |
|
28 |
2280.865 |
11.26526 |
3.08e-07 |
-9.319847 |
-8.304380 |
-8.920158 |
|
29 |
2282.938 |
3.620665 |
3.11e-07 |
-9.311561 |
-8.260463 |
-8.897847 |
|
30 |
2284.558 |
2.815499 |
3.14e-07 |
-9.301326 |
-8.214598 |
-8.873588 |
|
31 |
2287.826 |
5.649735 |
3.15e-07 |
-9.298176 |
-8.175817 |
-8.856413 |
|
32 |
2288.387 |
0.965120 |
3.20e-07 |
-9.283384 |
-8.125395 |
-8.827598 |
|
33 |
2294.781 |
10.94640* |
3.17e-07 |
-9.293683 |
-8.100064 |
-8.823873 |
|
34 |
2296.906 |
3.619264 |
3.19e-07 |
-9.285619 |
-8.056369 |
-8.801784 |
|
35 |
2297.826 |
1.558108 |
3.24e-07 |
-9.272369 |
-8.007489 |
-8.774510 |
|
36 |
2299.759 |
3.259385 |
3.27e-07 |
-9.263479 |
-7.962969 |
-8.751596 |
|
37 |
2300.047 |
0.483521 |
3.32e-07 |
-9.247515 |
-7.911374 |
-8.721607 |
|
38 |
2305.070 |
8.382686 |
3.31e-07 |
-9.251915 |
-7.880144 |
-8.711984 |
|
39 |
2308.304 |
5.368222 |
3.32e-07 |
-9.248618 |
-7.841216 |
-8.694662 |
|
40 |
2310.086 |
2.943239 |
3.35e-07 |
-9.239079 |
-7.796046 |
-8.671099 |
|
Замечания: * indicates lag order selected by the criterion. LR: sequential modified LR test statistic (each test at 5% level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion HQ: Hannan-Quinn information criterion |
||||||
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Российские источники:
25. Колоколов А. (2011), «Хеджирование фьючерсами: многомерные GARCH с динамическими условными корреляциями», Квантиль, №9, стр.61-75.
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Электронные ресурсы:
28. Сайт Центрального Банка России // Режим доступа: <http://cbr.ru/DKP/?PrtId=e-r_policy>
. Сайт Московской биржи // Режим доступа: <http://moex.com/>