基于概率约束的稀疏统计套利模型研究——以中国市场为例

Research on Sparse Statistical Arbitrage Model with Probability Constraint:Take the Chinese Market as an Example

经典的套利模型只研究两资产间的价格行为,本文基于不确定优化的视角,针对多资产的配对交易问题和中国市场限制卖空的特点,构建了带有概率约束的稀疏统计套利模型(QM-SSAM),进一步引入融券卖空,构建了考虑双向卖空的双概率稀疏统计套利模型(M-SSAM)。考虑到模型是NP-Hard,利用分布式鲁棒及无限对偶理论将原模型近似为约束稀疏锥规划问题,并提出用于求解近似模型的混合量子粒子群启发式算法。实证中通过上证50,深证100,沪深300及中证500历史数据检验了模型及算法的有效性和敏感性。研究发现,利用Fama-French三因子模型安全逼近的QM-SSAM-FF3模型相比于利用CAPM模型逼近的QM-SSAM-CAPM更符合预先的波动性要求;QM-SSAM-FF3的收益性和安全性取决于风险因子的权衡,实证结果表明[1.0e-1,1.0e+1]是较为理想的参数估值区间;结合up-up,up-down等五种不同的市场情形,QM-SSAM-FF3在不同指数环境下都可以取得正的套利收益,其中在沪深300指数表现最佳,年化平均收益和方差达到了0.5660和0.0396。在不同行业条件下,M-SSAM-FF3模型套利成功率为86%。

Classical arbitrage has studied the price spread between two assets.Construct a sparse optimal arbitrage model with one probability constraint from the perspective of uncertain optimization,considering the short selling restrictions in Chinese market.Short selling is further introduced to construct a two-probability sparse statistical arbitrage model(M-SSAM)with two-way short selling.Because of the NP-hard property of the original model,the original model is approximated as constrained sparse cone programming by distributed robust and infinite duality theory.Then a heuristic algorithm of mixed quantum particleswarm optimization(QPSO)is proposed to solve the approximate models.In numerical experiments,we test validity and sensitivity of the models and algorithm by the SSE 50,SZSE 100,CSI 300,CSI 500 index historical data.It is found that the QM-SSAM-FF3 model approximated by Fama-French model is more in line with the requirement of volatility in advance than the QM-SSAM-CAPM model approximated by CAPM model.The profitability and security of QM-SSAM-FF3 depend on the balance of risk factors.The empirical results show that[1.0e-1,1.0e+1]is an ideal parameter valuation range.Combined with five different market situations such as up-up,up-down and others,QM-SSAM-FF3 can achieve positive arbitrage returns in different index environments,among which the best performance is in CSI 300 index,with annual average returns and variance reaching 0.5660 and 0.0396.Under different industry conditions,the arbitrage success rate of M-SSAM-FF3 model is 86%.