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@sin32775
Created July 20, 2021 20:13
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# モンテカルロで見える世界\n",
"\n",
"インターネット上から金融関連の価格データを手に入れ、そのデータにトレンドが在るか無いかを見てきました。\n",
"\n",
"トレンドがあれば、確定的トレンドと確率的トレンドに分類され、また、時間との関係では定常時系列と非定常時系列に分類されました。\n",
"\n",
"確定的トレンド、確率的トレンド、定常時系列、または時間トレンド、ランダムウォーク、AR(1)が時系列分析の3種の神器でした。\n",
"\n",
"## モンテカルロ・シミュレーションの利用  \n",
" \n",
" 日経平均株価の動きの3つのモデルは  \n",
" \n",
" $1.P_{t} = P_{t-1} + σw_{t}$ \n",
" \n",
" $2.P_{t} =a + βP_{t-1} + σw_{t}$ \n",
" \n",
" $3.P_{t} = P_{t-1} + σB_{t}$ \n",
" \n",
" です。 \n",
" \n",
" $P_{t}$は t 時の価格である。 \n",
" \n",
" $P_{t-1}$はtよりも1単位時間前の価格です。\n",
" \n",
" $w_{t}$は平均ゼロ、分散1の正規分布に従う確率変数であり、σは定数です。 \n",
" \n",
"$B_{t}$は+1,-1からなるベルヌーイ過程である。シミュレーションではσ=0.00632とする。  \n",
" \n",
" ## ランダムウォーク  \n",
" \n",
" ランダムウォーク・モデルは  \n",
" \n",
" $P_{t} = P_{t-1} + σw_{t}$ \n",
" \n",
" で与えられる。\n",
" \n",
" ここではα= 0としてドリフト無しランダムウォークを検討する。\n",
" \n",
" σは一定である。  \n",
" \n",
" まず1年間の$P_{t}$の動きを人工的に生成してみよう。\n",
" \n",
" np.randomというモジュールの中にある乱数生成器normalを用いて確率変数$w_{t}$を生成する。 \n",
" \n",
" 株価の初期値 P を1とする。 \n",
" \n",
" 株式市場の1年の営業日数を250日とし、250個の株価の動きを生成してみよう"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.00632455532034\n"
]
}
],
"source": [
"%matplotlib inline\n",
"import pandas as pd\n",
"import numpy as np\n",
"sigma=0.1/np.sqrt(250)\n",
"print(sigma)\n",
"P=[1]\n",
"for i in range(1,250):\n",
" w=np.random.normal(0,1)\n",
" P.append(P[i-1]+sigma*w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"これでPの時系列が生成できた。価格の差分を取り、その平均、標準偏差、歪度、尖度を確かめてみます。"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean -0.00006 std 0.00629 skew -0.12995 kurt 0.02848\n"
]
}
],
"source": [
"price=pd.Series(P)\n",
"dp=price.diff().dropna()\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dp.mean(),dp.std(),dp.skew(),dp.kurt()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"平均はほぼゼロ、標準偏差はほぼ予定通り、歪度と尖度もほぼゼロに近い。次に結果をグラフで確かめてみます。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f751b1ea4a8>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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gJ1IS/B8IumDj8TjxeDxcwHups2IX0traSiqVIpvNhrNnZ+vq6goXJw7G2L3wwgszdqUQ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\nzMzMzBLhws7MzMwsES7szMzMzBLxP54k3KUMHwYsAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f751b56deb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.figure(figsize=(10,5.2))\n",
"plt.subplot(121)\n",
"price.plot(color='darkgray')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.subplot(122)\n",
"dp.hist(color='lightgreen')\n",
"mx=round(dp.max(),2)\n",
"mn=round(dp.min(),2)\n",
"plt.xticks([mn,0,mx])\n",
"plt.xlabel('$P_t-P_{t-1}$')\n",
"plt.ylabel('frequency')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"左側のチャートは1日目の価格、2日目の価格といった具合に250日間の価格の推移を描いていて、右側の頻度図は日々の価格の変化の大きさに対する頻度を表示している。 \n",
"\n",
"価格の差分は1回の試行の結果としては、かなりきれいな正規分布である。\n",
"\n",
"#### プログラムコードの解説\n",
"\n",
"P=[1]\n",
"\n",
" for i in range(250): \n",
" w=np.random.normal(0,1)\n",
" \n",
" P.append(P[i-1]*(1+sigma*w))\n",
"\n",
"生成された活くを格納する容器の準備を整えている\n",
"\n",
"[1]は初期値を1に設定している。\n",
"\n",
"for文以下は250回繰り返す\n",
"\n",
"平均ゼロ、分散1の確率変数を生成する。\n",
"\n",
"価格の1期間更新している。\n",
"\n",
"P=[] 価格の配列の初期化 \n",
"\n",
"high=[0]*250 価格の上限の配列の初期化\n",
"\n",
"low=[1]*250 価格の下限の配列の初期化\n",
"\n",
"for j in range(10000): for文以下を10000回繰り返す\n",
"\n",
"P0=100 価格の初期値を100回に設定\n",
" \n",
" for i in range(250): for文以下を250回繰り返す\n",
"\n",
"w=np.random.normal(0,1) 標準正規文に従う確率変数の生成\n",
"\n",
"P0=P0*(1+sigma*w) 価格の更新\n",
"\n",
"if P0>high[i]: 上限の更新\n",
"\n",
"high[i]=P0 if P0<low[i]: 下限の更新\n",
"\n",
"low[i]=P0 P.append(P0) 最終日の価格をPに保存\n",
"\n",
"price=pd.Series(P) リストPを Seriesに変換しpriceとして保存\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"次に250個の価格データを生成した上述の過程を10000回繰り返すことで、1日目、2日目の価格の最大値、最小値を250日目まで求めることで価格の推移の期間構造を求めよう\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"P=[]\n",
"dP=[]\n",
"high=[0]*250\n",
"low=[1]*250\n",
"for j in range(10000):\n",
" P0=1\n",
" for i in range(250): \n",
" w=np.random.normal(0,1)\n",
" dp=sigma*w\n",
" P0=P0+dp\n",
" if P0>high[i]:\n",
" high[i]=P0\n",
" if P0<low[i]:\n",
" low[i]=P0\n",
" dP.append(dp)\n",
" P.append(P0)\n",
"price=pd.Series(P)\n",
"dprice=pd.Series(dP)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"価格の時系列はpriceに、価格差の時系列はdpriceにpandasシリーズとして格納した。確認のためにグラフにしてみます。"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean 0.00000 std 0.00633 skew 0.00095 kurt 0.00038\n"
]
},
{
"data": {
"image/png": 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VMH1ocFgw37pybMdyQIANVmeMMcb0BitgesG6ompiI0KoqG3i4Tc2U9/cSvig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\nfpAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f75176ccf60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(9,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"このモンテカルロシミュレーションでは250日間の価格をまず生成し、それを10000回繰り返すことで、時系列の特性を得ようとしました。 \n",
"\n",
"左の図は250日間の価格の推移の特性を調べています。\n",
"\n",
"10000回の試行の内の1日目の価格の最大値と最小値をプロットし、それを2日目、3日目にも行い、250日目まで繰り返すと価格の推移の期間構造が得られます。\n",
"\n",
"価格の最大値と最小値の幅がほぼ直線的(緩やかな曲線)に増加しているのが分かります。\n",
"\n",
"右図は250日目の価格の頻度を表している。分布はほぼベル型です。\n",
"\n",
"価格差の平均はゼロ、標準偏差は0.00633と設定値そのものである。歪度と尖度もほぼゼロです。  \n",
"\n",
"このモンテカルロシミュレーションから得られた時系列の特性は実際の価格の動きの特性を説明しているであろうか? \n",
"\n",
"前回の結果を思い出してほしい"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Material 9 変化率の最大値、最小値の期間構造のグラフ参照\n",
"\n",
"最小値(low)のグラフは割とスムーズだが最大値(high)のグラフは凸凹である。\n",
"\n",
"一方、シミュレーションではほぼ曲線的に下落、上昇している。\n",
"\n",
"パラメータが一定のシミュレーションでは現実の世界を説明できないが、そんなに外れてもいない。  \n",
"\n",
"次に得られた時系列から1日間隔の変化率とそれを1日ずらした変化率の散布図を描いてみよう"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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qhEdwtITlCBsT2R1N3OkC2jY0fWaKEZsNxpY64ClkmmwQioFSY6Bt3NzxVhos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\nChuiCHChUChsiP8ff7p8jt4+skYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7513f07400>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(5,5))\n",
"mx=round(dprice.max(),2)\n",
"mn=round(dprice.min(),2)\n",
"plt.scatter(dprice,dprice.shift(1),alpha=0.01)\n",
"plt.xlabel('$P_{t-1}/P_{t-2}-1$')\n",
"plt.ylabel('$P_t/P_{t-1}-1$')\n",
"plt.xticks([mn,0,mx])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"まん丸の円が描かれた。実際のデータとはだいぶ違う。2つの変化率には相関がないことが見て取れます。\n",
"\n",
"これが分散不均一性もボラティリティ・クラスタリングも無い世界である。  \n",
"\n",
"このように、実際の時系列を分析する際には、モデルの厳密さにこだわるのではなく、まずは大まかな傾向をつかもうとするだけで新しい発見があります。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## AR(1)過程の生成  \n",
"\n",
"1次の自己回帰モデルは  \n",
"\n",
" $P_{t} =a + βP_{t-1} + σw_{t}$  \n",
"\n",
"で与えられる。このβを指定することで、AR(1)モデルがどのような性質をもっているのかを調べてみよう。\n",
"\n",
"プログラムのコードはランダムウォークの時とほとんど変わらないです。\n",
"\n",
"βを指定することによりαを決めなければならないが、これは期待値(μ)から求めることができる\n",
" \n",
" AR(1)の期待値$E(P_{t})$は  \n",
" \n",
" $E(P_{t})= E(α)+E(βP_{t-1}) +E(σw_{t})$\n",
" \n",
" で与えられる。\n",
" \n",
"$E = (P_{t}) = \\mu $とすると、\n",
" \n",
" $E(a) = a$、$E(w_{t})$であるから、 \n",
" \n",
" $$\\mu = \\frac{a}{1- \\beta } $$\n",
" \n",
" となる。価格の初期値を1と設定すると、  \n",
" \n",
" α=(1-β)である。分散は  \n",
" \n",
" $var(P_{t})=E(P_{t}-μ)^{2} = E(P_{t}^{2})-μ^{2}$\n",
" \n",
" であり、α=0であれば\n",
" \n",
" $$var(P_{t})= \\frac{ \\sigma ^{2}_{z}}{1- \\beta ^{2}} $$\n",
" \n",
" である。期待値も分散も時間とは独立している。\n",
" \n",
" ここがランダムウォークとは違う点である。  \n",
" \n",
" 次にdef分を用いて、ar1というm個の価格から成るAR(1)の時系列を標準偏差をsigma、回帰係数をbeta、初期値をp0で指定してn個生成する関数を作ってみよう。\n",
" \n",
" また、単位時間ステップ毎に価格の最大値と最小値も計算しておこう"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def ar1(beta,sigma,n,m,p0):\n",
" P=[]\n",
" dP=[]\n",
" high=[0]*m\n",
" low=[p0]*m\n",
" alpha=(1-beta)*p0\n",
" sigma_w=sigma*p0\n",
" for j in range(n):\n",
" P0=p0\n",
" for i in range(m): \n",
" w=np.random.normal(0,1)\n",
" P1=beta*P0+alpha+sigma_w*w\n",
" dp=P1-P0\n",
" P0=P1\n",
" if P0>high[i]:\n",
" high[i]=P0\n",
" if P0<low[i]:\n",
" low[i]=P0\n",
" dP.append(dp)\n",
" P.append(P0)\n",
" price=pd.Series(P)\n",
" dprice=pd.Series(dP)\n",
" return price,dprice,high,low"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"まず最初はbeta=0.9999、sigma=0.00632、n=10000、m=250、p0=1として時系列を生成します。 \n",
"\n",
"価格差の平均はゼロ、標準偏差は0.00632、歪度、尖度ともにゼロ近辺という結果になりました。  \n",
"\n",
"β< 1である特徴が僅かながら現れているだろうか"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean 0.00000 std 0.00633 skew -0.00001 kurt -0.00054\n",
"price std 0.09906\n"
]
},
{
"data": {
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AHy3ayZ/umUJZ9WmeX3sQgG/eMoy0y+hYZ66MqrYB+SKSALwiImO6HFcRuaz3rao+BTwF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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7513e25668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"price,dprice,high,low = ar1(0.9999,sigma,10000,250,1)\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))\n",
"print(\"price std %2.5f\"%price.std())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"価格差の平均はゼロ、標準偏差は0.00632、歪度、尖度ともにゼロ近辺という結果になった。  \n",
"\n",
"β< 1である特徴が僅かながら現れているだろうか。\n",
"\n",
"結果はランダムウォークとほぼ同等である。区別はできない。次に結果を価格差の散布図にしてみます。1単位時間差を見ています。"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"([<matplotlib.axis.XTick at 0x7f75140a7a58>,\n",
" <matplotlib.axis.XTick at 0x7f7513c875c0>,\n",
" <matplotlib.axis.XTick at 0x7f7513c82160>],\n",
" <a list of 3 Text xticklabel objects>)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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XRVq/S+l45yNpGZP8VmVZszquGI4KyqpiZW2dL9/c4Et/HLbhRcJ8+PU1uHZ7meWNdQZV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\nMVHAkUiLiQKORFrM/w+VfoSf2IDZngAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f75140ec470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(3,3))\n",
"mx=round(dprice.max(),2)\n",
"mn=round(dprice.min(),2)\n",
"plt.scatter(dprice,dprice.shift(1),alpha=0.01)\n",
"plt.xlabel('$P_{t-1}/P_{t-2}-1$')\n",
"plt.ylabel('$P_t/P_{t-1}-1$')\n",
"plt.xticks([mn,0,mx])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"また、散布図による、価格差の特性は綺麗な円形を示している。  \n",
"\n",
"次にAR(1)の特徴をさらに明確につかむために、βの値を動かしてみよう。\n",
"\n",
"β= 0.99、0.5、1.003、1.005について実験してみよう。まず最初はβ=0.99から始めよう"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean -0.00000 std 0.00633 skew 0.00122 kurt -0.00668\n",
"price std 0.04473\n"
]
},
{
"data": {
"image/png": 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iY0XkHRHZISLbReRbru33ikixiGx2/Vzqcc7dIpIvIrtF5GL/RW/MyGUl/5P0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\nRaAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7545315c18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"price,dprice,high,low = ar1(0.99,sigma,10000,250,1)\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))\n",
"print(\"price std %2.5f\"%price.std())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果は価格差の平均ゼロ、標準偏差000634、歪度と尖度はほぼゼロである。  \n",
"\n",
"β= 0.99では、ある日数を経過する価格の変化率の最大値と最小値の幅が一定値に留まるようになる。\n",
"\n",
"これが中心回帰、定常確率過程の特徴である。それでも定常性を得るために50日程度かかっているのが分かる。  \n",
"\n",
"次にβ= 0.5にしてみよう"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean 0.00000 std 0.00730 skew 0.00070 kurt -0.00035\n",
"price std 0.00729\n"
]
},
{
"data": {
"image/png": 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DIrJbRFa4XxcF7XO/iGwWkY0icn67B2nalz1+OO6ErI6Bql59mPUK3NbI8lXA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\nCgNFURRFURwqDBRFURRFcfx/DEBrQ5XRcLgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7513a55240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"price,dprice,high,low = ar1(0.5,sigma,10000,250,1)\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))\n",
"print(\"price std %2.5f\"%price.std())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果は価格差の平均ゼロ、標準偏差000730、歪度と尖度はほぼゼロである。  \n",
"\n",
"β= 0.5ではほぼ瞬間的に中心回帰の定常確率過程の特徴が見えてくる。\n",
"\n",
"次にAR(1) が発散するβが1を超える場合を見てみよう。最初はβ=1.003にしてみよう"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean 0.00000 std 0.00633 skew 0.00057 kurt 0.00336\n",
"price std 0.15265\n"
]
},
{
"data": {
"image/png": 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8AJThapl/n6p2DPxLMcb0xoo8sL3qBK+X1hAdHsoDiyc4HccYb/susEZEVgIC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\nGUs0IAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7513f4ee10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"price,dprice,high,low = ar1(1.003,sigma,10000,250,1)\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))\n",
"print(\"price std %2.5f\"%price.std())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果は価格差の平均ゼロ、標準偏差0.00633、歪度と尖度はほぼゼロである。  β= 1.003ではまだ発散には至っていない。\n",
"\n",
"むしろランダムウォークとの区別が難しい。β= 1.005ではどうだろうか"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean -0.00000 std 0.00636 skew -0.00215 kurt 0.00121\n",
"price std 0.20891\n"
]
},
{
"data": {
"image/png": 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z75VjONbc2rHPgLhot+IacybfB5aLyFJAgEtw5srojogMBZ7EOxiXAo+o6m9F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\npM4Y/pIkdcbwlySpM4a/JEmd+QFbLEsb83O1BQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7551f0ef98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"price,dprice,high,low = ar1(1.005,sigma,10000,250,1)\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(1,2,1)\n",
"plt.plot(high,label=\"high\",linestyle='--')\n",
"plt.plot(low,label=\"low\",color='darkgray')\n",
"plt.title('max$P_t$-min$P_t$')\n",
"plt.xlabel('t')\n",
"plt.ylabel('$P_t$')\n",
"plt.legend(loc='upper left')\n",
"plt.subplot(1,2,2)\n",
"price.hist(bins=100,color='pink')\n",
"plt.xlabel('$P_{250}$')\n",
"plt.ylabel('frequency')\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))\n",
"print(\"price std %2.5f\"%price.std())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果は価格差の平均ゼロ、標準偏差000636、歪度と尖度はほぼゼロである。β= 1.005では発散の一歩手前である。  \n",
"\n",
"βの違いは、AR(1)の動きの特性に大きな影響を与えたであろうか? \n",
"\n",
"β> 1であってもその程度が小さければ、価格過程は破たんすることが無いことが分かる。\n",
"\n",
"またそれは観測期間にも左右されることも分かる。\n",
"\n",
"期間が短ければ、βが1よりも大きくても破たんせずにすむ確率は上がる。また、β< 1で1近辺の場合はどうであろうか? \n",
"\n",
"ランダムウォークとの区別はうまく行くだろうか? これもまた難しいという結果になった。  \n",
"\n",
"自己回帰モデルの最大の特徴は価格の中心回帰の動きである。\n",
"\n",
"ランダムウォークの価格の動きは時間の経過とともに分散が大きくなるのに対して、自己回帰モデルではある点に収束する。\n",
"\n",
"そのために将来の予測を行うためには便利です。 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ベルヌーイ試行  \n",
" \n",
" 金融資産の価格の動きの大きさがx に定められていると、上昇は+ x 、下落は- x となる。\n",
" \n",
" このように結果が2つしかない実験をベルヌーイ試行とよび、とびとびな2つの値から成る独立な離散時間の確率変数列をベルヌーイ過程とよぶ。\n",
" \n",
" このような2つのとびとびな確率変数からなる確率過程の性質を乱数生成器を用いて調べてみます。\n",
" \n",
" ここではx を5とした時の1万個の確率変数を発生させその和を求め、それを1日分の取引としました。"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x7f7517677240>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GcfHeoargMtxMaAB49uyZ7X59OT/VFR5PS2a20gP4gYGBqF67f//+RBeHiJLg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\npNb/AYEHsrx25gdIAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f751126bf60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def bernoulli(p,x,N,p0):\n",
" s = (np.random.binomial(1, p, N)-0.5)*x\n",
" P0=p0\n",
" P=[]\n",
" for i in range(N):\n",
" P0=P0+s[i]\n",
" P.append(P0)\n",
" return P\n",
"P=bernoulli(0.5,5,10000,0)\n",
"plt.figure(figsize=(10,6))\n",
"plt.plot(P,color='darkgray')\n",
"plt.xlabel('steps $t$')\n",
"plt.ylabel('$\\sum_1^t B_t \\cdot 5$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"実際の価格の動きに似た動きが再現できていると思う。これはランダムウォークであり、一定の方向に価格が上昇したり下落しているのは確率的トレンドである。  \n",
"\n",
"\n",
"つぎにこの実験を10000回繰り返し、1回1回の実験で生成した確率変数の和をヒストグラムとして描いてみます。"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean -0.01500 std 352.97407 skew -0.02056 kurt 0.03577\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f750aaf9588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N=10000\n",
"M=10000\n",
"Q=[]\n",
"for j in range(N):\n",
" P=bernoulli(0.5,5,M,0)\n",
" Q.append(P[M-1])\n",
"plt.figure(figsize=(8,5))\n",
"plt.figure.left=-0.1\n",
"plt.hist(Q,normed=True,histtype='stepfilled',color='pink',bins=25)\n",
"plt.xlabel('$\\sum_1^t B_t \\cdot 5$')\n",
"plt.ylabel('probability density function')\n",
"price=pd.Series(Q)\n",
"dprice=price.diff()\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果はかなり正規分布に近いベル型の形をしている。次に1日の取引の回数を3000回に減らして、その実験の回数は10000回とします。"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean 0.00200 std 194.97902 skew 0.02862 kurt 0.06520\n"
]
},
{
"data": {
"image/png": 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DrmczpKrOrKpDmj+PTgD+oar+G94nWxB6cAFwQZIvAvcBL27+5TdqrYhXAH8O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\nFhMESZLUYoIgSZJaTBAkSVLL/wffRNkoIFL9vwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7517632f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N=10000\n",
"M=3000\n",
"Q=[]\n",
"for j in range(N):\n",
" P=bernoulli(0.5,5,M,0)\n",
" Q.append(P[M-1])\n",
"plt.figure(figsize=(8,5))\n",
"plt.figure.left=-0.1\n",
"plt.hist(Q,normed=True,histtype='stepfilled',color='pink',bins=25)\n",
"plt.xlabel('$\\sum_1^t B_t \\cdot 5$')\n",
"plt.ylabel('probability density function')\n",
"price=pd.Series(Q)\n",
"dprice=price.diff()\n",
"print(\"mean %2.5f std %2.5f skew %2.5f kurt %2.5f\"\\\n",
"%(dprice.mean(),dprice.std(),dprice.skew(),dprice.kurt()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"分布の形状は分布の幅が狭くなっている。これは1日の価格の動きが取引の回数に依存することを示しています。\n",
"\n",
"2番目の特徴は、ベル型の形は維持しているが、分布の滑らかさは維持されていない。\n",
"\n",
"これが最も重要な点で、これこそが本題です。  \n",
"\n",
" ボラティリティは取引数と関係があるということです。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
},
"latex_envs": {
"LaTeX_envs_menu_present": true,
"autocomplete": true,
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 1,
"hotkeys": {
"equation": "Ctrl-E",
"itemize": "Ctrl-I"
},
"labels_anchors": false,
"latex_user_defs": false,
"report_style_numbering": false,
"user_envs_cfg": false
},
"toc": {
"colors": {
"hover_highlight": "#DAA520",
"navigate_num": "#000000",
"navigate_text": "#333333",
"running_highlight": "#FF0000",
"selected_highlight": "#FFD700",
"sidebar_border": "#EEEEEE",
"wrapper_background": "#FFFFFF"
},
"moveMenuLeft": true,
"nav_menu": {
"height": "137px",
"width": "252px"
},
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 4,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false,
"widenNotebook": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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