For simplicity, the following analysis is based on the following assumptions:

1, without transaction costs and taxes.

2. Market participants can borrow and lend funds at the same risk-free interest rate.

3. There is no default risk for forward contracts.

4. Allow spot short selling.

5. When arbitrage opportunities appear, market participants will participate in arbitrage activities, thus making arbitrage opportunities disappear. The theoretical price we calculate is an equilibrium price without arbitrage opportunities.

6. The margin account of the futures contract pays the same risk-free interest rate. This means that no one can spend money to get long and short positions in forward and futures locally.

(2) Symbol

The symbols used mainly include:

T: Expiration time of forward and futures contracts, in years.

T: Current time, in years. The variables T and T are calculated from a certain date before the contract takes effect, and T-T represents the remaining time when the distance in the forward and futures contracts expires in years.

S: the price of the underlying asset at time T.

K: The delivery price of a forward contract.

F: the long value of the forward contract at time t.

F: The theoretical forward price and theoretical futures price of forward contracts and futures contracts at time t are called forward prices and futures prices respectively, unless otherwise specified.

R: The risk-free interest rate (annual interest rate) at time t is calculated by continuous compound interest due at time t, where all interest rates are continuous compound interest unless otherwise specified.