配對交易是在同一時間買空賣空來投資一個配對的市場中立的投資策略。考慮在一些價差上交易的兩支相似的股票。
當兩個證券的相關性變弱時，交易者在表現較差的股票買空一個部位，在表現較好的股票賣空一個部位。
交易者將利用在此相關性中的失衡，並在價差縮減到一些平衡狀態的值時獲利。基於狀態空間模型方法，
我們假設價差會遵循一個有高斯噪音且可觀察到的均值回歸模型。

卡爾曼濾波器法是應用在估計模型參數。來自校正模型的預測值與價差的子序列觀測值比較來決定投資。
對於這樣基於狀態空間模型方法的投資策略我們表現一個經驗的研究。
模擬研究方法與基於不同價差所提出的投資策略的表現也會呈現出比較結果。

Pairs trading is a market-neutral investment strategy which matches its long and
short investments one pair at a time. Consider two similar stocks which trade at
some spread. When the correlation between the two securities become weak, a trader
take a long position on underperforming stock, and take a short position on
outperforming one. A trader will take advantage from out of equilibrium in the
correlation, and make profit as the spread narrows again to some equilibrium value.
Based on a state space model approach, we assume the spread follows a mean reverting
model observed with Gaussian noise.

Kalman Filter method is applied to estimate the
model parameters. Predictions from the calibrated model are compared with subsequent
observations of the spread to determine the investment decisions. We perform an
empirical study for such an investment strategy based the state space model approach.
A simulation study is also performed to compare the performance of the proposed
investment strategy based on different strategies.

誌謝ii
摘要iii
Abstract iv
1 Background and Motivation 1
2 Pair Selection 2
2.1 Minimum Distance 2
2.2 Cointegration 3
3 State Space Model 6
3.1 Spread Model 8
3.2 Kalman Filter 8
4 Trading Strategy 11
4.1 Strategy I 11
4.2 Strategy II 12
5 Simulation Study 14
6 Real Example 14
7 References 18

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