基于Black-Scholes方程的股指期货期现套利模型及交易算法

Stock index futures arbitrage model based on Black-Scholes equation and corresponding trading algorithm

为了适应股指期货期现套利高频交易需要,解决传统协整理论不能很好捕捉交易信号的问题,构建了基于Black-Scholes方程的期现套利模型及算法。首先使用修正跟踪误差指标确定交易所交易基金投资组合最优化权重并用广义既约梯度算法求解;然后构建了基于Black-Scholes方程的套利模型和算法交易系统。实证检验显示,该算法实现了1.52%的单日净收益率和5%的止损发生率,且止损发生率与波动性正相关。证明该算法在市场条件稳定的条件下能够很好地捕捉交易信号和控制交易行为,如果市场发生较大异常波动,算法的适用性将受到影响。

To meet the practical need of high frequency index future-spot arbitrage and overcome the disadvantage of the arbitrage algorithms based on traditional cointegration theory, which is failing to recognize many trading signals, a new index future-spot arbitrage model and trading algorithm were established. Based on modified tracking error model and Generalized Reduced Gradient （GRG） algorithm, an optimized weighting ETF （Exchange Trade Fund） portfolio was built and then the arbitrage model and the algorithm trading system based on Black-Scholes equation were formulized. The empirical results show that, the algorithm realized a daily net yield of I. 52% and a stop-loss rate of 5%, and the stop-loss rate is positively correlated with the market volatility. It is proved that this algorithm has a good control on recognizing the trading signal and executing trading orders under stable market condition while its practicability will be discounted under the market turmoil.