There is always a gap between application and theory, and this is true in every industry.

Because the market is made by people, there are thousands of factors that affect the market, and there are only a few parameters in the formula. How can it possibly describe all possibilities? At least one thing is something that the formula can never figure out - human psychological factors, the so-called following the trend, and the changes in the market caused by chasing the rise and killing the fall. Can the formula calculate it? Or how do you plan to get the value of each parameter? How do you determine the value of the risk-free rate r? Based on the inflation rate, or the bank deposit interest rate? How to get R? Based on where? Wait, all of this will affect your profits and the risk factor of your trading. Of course, the model is not useless. When using it, try to consider it from a comprehensive perspective. The data calculated by the model can become part of the analysis report~

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These two formulas are not contradictory but have different pertinence

In addition Let me explain that when I learned it, I learned it in English. The corresponding Chinese terminology in China is not accurate, but I will try my best to explain it and hope it will not cause misunderstanding.

The principle of futures pricing has prerequisites, and the pricing of different futures varieties will also be in Derived from basic formulas.

The information you gave is too general to judge the specific meaning of the formula, especially the first derivation formula. If you think it is needed in practice, you can derive it based on the mathematical model and actual practice. It is impossible for everyone to I’ve learned them all, but it’s impossible for every one of them to be a universal formula

If you don’t understand the first formula, you have to look at the explanation he gave for the model. This is not a universal basic formula. The models are all targeted and you didn’t give them. I can’t understand the information. The structure is a bit similar to the calculation of price changes in days.

The second one is to calculate compound interest based on continuous time periods. What is the compound interest interval of r? Continuous... To put it bluntly, it is derived from something similar to a limit value. It is a bit like making the desired time period infinitely smaller until the limit is continuous. This is a mathematical conceptual process and is also purely mathematical. .

As a basic formula to calculate the future futures price f=s*e^(r-R)(T-t)

For example, here I take t=0 (current) T=0.25 years (that is, 3 months) Then the futures price after 3 months should be f=s*e^(r-R)*0.25. If T is not in years, it must be converted into years because the definition of continuous compound interest is in years.

Sorry, I must apologize because r-R my explanation was incorrect. It’s been so long since I’ve read those theories that I’ve forgotten them a bit, but I thought about them carefully that day, haha, and I remembered them. I'm so sorry! I hope it has not affected your normal understanding and learning.

Your formula is not a basic formula. R here refers to the expected return of R% of the asset value within the limited period of the contract. The basic formula is F = S e^rT. That is to say, if you invest The value after S and T should be F under the interest rate r. However, if you want to pay R as a reward, you must reduce the payment to get the real price of s in the future. This formula is mainly used in stock index futures. where R refers to the average dividend rate of the stock index. because R is known, so we could calculate the present value of the yield R in (T-t):Se^-R(T-t).

Then we calculate the value generated by r, according to the basic formula, the present value is Fe^-r(T-t)

Fe^-r(T-t) is the cash inflow, and Se^-R(T-t)can be considered as cash outflow in the investment. Let inflow = outflow, we may got a equation and derive the final result: F=Se^(r-R)(T-t)

Other types of futures have different If you are interested in the formula name, send me your email address and I will send you my information. It is all in English, but it is not difficult and you can understand it.

The second formula also exists, but it calculates the value of the futures contract rather than the pricing, which is related to the calculation of profit or loss. The parameter settings are also different. I won’t say any more, lest you become more confused.

The use of e. e is a constant, it seems to be 2.63.. (I can’t remember clearly, it must be greater than 2). The decimal part does not loop infinitely. Generally, if we really need the result, we will directly use e on the calculator. If you have not entered a specific value with reserved digits, it will be inaccurate if you have reserved it.

Futures pricing has nothing to do with leverage trading magnification. e is a constant that will not change... This is basic common sense in mathematics.

The magnification factor of futures is not necessarily 10. Different types of margin requirements are different. For example, rubber may be 5-6%, etc. Financial futures are also different and cannot be the same. And this has nothing to do with futures pricing...just the rules of leverage trading. Do you need specific examples? For example, if a spot price is 10 yuan per ton, the corresponding three-month futures price may be 12 yuan according to the formula. If the margin is 10%, you have to spend 1.2 yuan to trade this contract. This is a leveraged transaction. The problem of multiple amplification...

Assuming that this formula is the truth formula, it is perfect and correct. So if the three-month futures price is calculated to be 12, and if the current market price is 11, ignoring the handling fee, what should I do? operate? Of course it is buying, because the price will definitely rise to 12 yuan in three months, which corresponds to short selling. Do you understand this? It has nothing to do with the magnification of leveraged trading.

Foreign exchange is also divided into real offer and derivatives. Leveraged transactions are derivatives. What is real offer? When you go to the bank to exchange U.S. dollars and travel to the United States for consumption, the U.S. dollars exchanged are real offer transactions...

Which formula should you choose if you face an exam? Look at the definition of r given in his question. It is the r of continuous compound interest (this continuous compound interest is compounded continuously in English that I randomly translated. You can look up the information to find the corresponding term by yourself). Then you must use the model with e. Because this model is the final formula derived from compound interest calculations, the value of r when placed on other formulas will be wrong. For the first formula, you see how r is defined. If it is the same as the one given in the question, then bring the first formula. I hope I made it clearer

But it seems like what I said above is just a As for which model is more reasonable and which one is better to use, it depends on other data information and the analyst's own choice. For actual market operations, I think it is not very useful. If the market follows the model in such a disciplined manner, no one will not make money. Haha, so he is right. There is no need to be serious, just memorize the conclusions. If you want to understand the model, at least a master's degree or above. If you can design the model and get a doctorate... You don't need these levels to take the exam for a professional qualification certificate. You don't need to go into details if you know the basic conclusions.