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["株式高頻度取引シミュレ－タ"]
["2022.1.14"]
[]
["石黒真木夫＠統計数理研究所名誉教授"]
[]
["コンピューターを駆使した超高速の金融取引をHFT、ハイ・フリークエンシー・トレーディングと称します。高速取引ともいうようです。"]
[]
["HFT が株式市場でどう働くものなのか体感できるシミュレータです。"]
[]
["株価変動に関して「ティックデータ」なるものがあります。"]
["NET上にマイクロ秒単位での株式ティックデータをもCSVファイルで提供しているサイトがあるようですが"]
["このソフトはそれらしい価格変動をする２銘柄の株価をシミュレーションで作ってHFTの実験ができるように作られています。"]
[]
["簡単のためにすべての株の価格が一定時間間隔で入手でき、、"]
["毎時刻に手持ちの株を売る事と任意の株を買うことが可能で手数料はかからないものとし、"]
["次の時刻に売買による持ち株数の変化が反映されるとしました。"]
[]
["株価変動は２次自己回帰モデルで生成した平均ゼロの時系列に一定値を加えて作るようになっています。"]
["特性根の位置を与えることによって系列の「暴れ方」を指定できます。詳細は「株式市場に潜むマクスウェルの魔.pdf」に書きましたが、"]
[]
["偏角で「基本周波数」を与えます。たとえば偏角を36度とすると基本周波数は36度/360度=0.1、波長 1/0.1=10 の波となります。"]
["絶対値を 0 に近づけることで変動の乱雑度が増し、1に近づけると滑らかな変動をするようになります。"]
["ですから特性根を、たとえば、偏角36度、絶対値1の複素数とするときれいな周期10の波にしたがって変動する系列が得られます。"]
[]
["次の「シミュレーションシート」では系列 LEFT は絶対値 0.9、偏角 43度、系列 RIGHT は絶対値 0.8、偏角 40度 の特性根で指定した場合の例になっています。"]
["このシートをコピーして黄色のセルを書き替えて「market」ボタンをクリックすると株価系列が書き替えられ、その状況で投資戦略が異なる投資家０，１、…がどんな資産形成をするか観察できます。"]
[]
["ただし、「投資家m」 は「情報m」に基づいて株式売買するものとし、「情報m」を以下のように定義します。"]
[]
["情報m ＝　（現在のLEFT銘柄の価格/ m時点前のLEFT銘柄の価格) / （現在のRIGHT銘柄の価格/ m時点前のRIGHT銘柄の価格)"]
[]
["投資家m は「情報m」>1 の場合、銘柄　RIGHT の半分を売って得た資金で銘柄　LEFT を買います。"]
["投資家m は「情報m」<1 の場合、銘柄　RIGHT の半分を売って得た資金で銘柄　LEFT を買います。"]
["投資家m は「情報m」=1 の場合は売買しません。"]
[]
["投資家０は常に「情報０=1」を受け取ることになり一切売買をしないことになります。"]
["投資家1は直近の株価の動きの基づいて素早い売買をする超高頻度売買投資家で。"]
["投資家２～も投資家１とおなじ行動をとるのですが、手に入る株価変動情報は直近の株価の動きを捉えてないというわけです。"]

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