In fact, there is no perfect market, and any arbitrage requires costs. Therefore, there is a risk-free arbitrage interval in the normal market, and there is no profit in this interval. Once it exceeds this interval, there will be profits.

First, we list the cost of a spot arbitrage:

1. Bilateral handling fees for futures market transactions

2. The impact cost of futures trading

3. Bilateral transaction fees for buying and selling stocks

4. Stamp duty on stock transactions

5. The impact cost of stock trading

6. Stock portfolio simulation index tracking error

7. Borrowing spread cost

We use Tc to represent the cost of a spot arbitrage, which makes a no-arbitrage interval appear on the basis of the theoretical price. Only when the actual price is higher than the upper bound of the no-arbitrage interval or lower than the lower bound of the no-arbitrage interval will there be arbitrage opportunities.

The upper limit of the no-arbitrage interval is equal to the theoretical price of stock index futures plus the arbitrage cost, that is

Se^(r-q)(T-t)+Tc

The lower limit of the no-arbitrage interval is equal to the theoretical price of stock index futures minus the arbitrage cost, i.e.

Se^(r-q)(T-t)-Tc

In this way, the no-arbitrage interval is

[se^(r-q)(t-t)-tc,se^(r-q)(t-t)+tc]