Futures price = spot price+financing cost
If the corresponding asset is a stock portfolio that pays cash dividends, then the party who buys the futures contract does not receive dividends because it does not immediately hold the stock portfolio. On the contrary, the contract seller gets dividends because he holds the corresponding stock portfolio, thus reducing his position cost. Therefore, futures prices should be adjusted downward by the amount equivalent to dividends. Results The futures price is a function of the net position cost, that is, the financing cost minus the corresponding asset income. That is:
Futures price = spot price+financing cost-dividend income
Generally speaking, when the financing cost and dividend income are expressed by continuous compound interest, the pricing formula of index futures is:
F=Se^(r-q)(T-t)
These include:
F= the value of the futures contract at time t;
S= the value of the underlying assets of the futures contract at time t;
An investment due at time r = t is a risk-free interest rate calculated by continuous compound interest (%);
Q= dividend yield, calculated by continuous compound interest (%);
T= expiration time of futures contract (year)
T= time (year)
Consider a three-month S&P 500 futures contract. Assuming that the dividend yield of the stock used to calculate the index is converted into continuous compound interest of 3% per year, the present value of the S&P 500 index is 400, and the risk-free interest rate of continuous compound interest is 8% per year. Where r=0.08, S=400, T-t=0.25, q=0.03, and the futures price f is:
F=400e^(0.05)(0.25)=405
We call this equilibrium futures price the theoretical futures price. In practice, it may deviate from the theoretical price, because the conditions assumed by the model cannot be fully met. However, if these factors are taken into account, empirical analysis proves that there is no significant difference between the actual futures price and the theoretical futures price.
The content of this article comes from: China Law Publishing House "General Knowledge Series of Legal Life"