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

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 1.52% 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.