Is Paradigm Chengfang Perpetual Contract a new category of derivatives, or is it just an improvement on existing derivatives?
Recommended reading: ” Paradigm reimagines new derivatives: Chengfang perpetual contract “
Original title: “How to understand Paradigm’s power perpetual contract”
Written: 0x76
Paradigm, a top investment institution, released a paper last week introducing a new type of financial derivative “Chengfang Perpetual Contract”. Once the paper was published, it triggered extensive discussions in the core user community of the blockchain.
So, is Chengfang perpetual contract a new category of derivatives or just an improvement on existing derivatives. Is it closer to option derivatives, or more like the perpetual contracts we are familiar with. This article will try to analyze the meaning and value of this new type of derivative product for readers by using as concise language as possible. (Note: This article assumes that the reader has a certain understanding of the basics of futures, options and perpetual contracts, so I will no longer take up space to introduce the basics of derivatives.)
Of course, readers who wish to learn more about the “Chengfang Perpetual Contract” are still recommended to directly read the original text of the paper or the Chinese translation of the reprint, as well as the reference links cited in the article.
Linear and convex functions
At present, all financial derivatives, no matter how the specific structure design of their products changes, the core of which is to construct a mapping function from the price of the underlying asset to the price of the derivative. Under this idea, mainstream derivatives can be divided into the following two categories according to their mapping function types:
The first category is linear function derivatives. The price of derivatives will change linearly according to changes in spot prices. The corresponding product is the futures contract in traditional finance, so I won’t introduce too much here.
The second category is a derivative of the convex function type. Its typical feature is that the price of derivatives has a non-linear relationship with the changes in spot prices. For example, when the spot price rises, the price of derivatives rises even more. In mathematics, convex functions also have clear geometric characteristics. Under the premise of not pursuing rigorous mathematical definitions, convex functions can be simply understood as a function that curves upward or downward.
The figure below is a randomly generated convex function of a function image that curves downward. If we use this function to construct a derivative, the x-axis represents the spot price and the y-axis represents the price of the derivative. Then the holders of this derivative will get a kind of asymmetric risk and return. When the spot price rises, the derivative holders’ income will increase even more, and when the spot price falls, the derivative holdings The rate of loss will be even smaller.
Readers may have discovered that this risk-return model is very similar to the profit and loss model of call options. Therefore, the core feature of all option derivatives can also be summarized as the asymmetry between risk and return. This property is often called convexity (geometric description) or Gamma value (algebraic description).
This asymmetric risk and return combination brought by convex functions provides investors with a very ideal portfolio risk management tool. Therefore, convex financial products (option products) have always occupied a large market share in the traditional financial market, and are often used by professional investment institutions to adjust the risk exposure of investment portfolios or construct more complex derivative products .
However, the disadvantage is that traditional options products are subject to the specific realization of call and put transactions, so it is always difficult to completely get rid of the shortcomings of continuous expiration of products and the need to exercise rights. Although the industry has been conducting relevant explorations, trying to build a “perpetual option” product with no expiration date, the effect has not been very satisfactory.
The “Power Perpetual Contract” proposed by Paradigm’s latest paper is the latest answer to this classic proposition. It tries to combine the structure of the perpetual contract product that has been successfully verified, and by adjusting its core function from a linear function to a convex function, it tries to solve the problem that the former “perpetual option” has not been able to really solve. That is: structure A derivative category that does not expire and does not require exercise, and at the same time has convexity.
Reconstruction of traditional derivatives
We refer to the above ideas and use the classic funding model of perpetual contracts to reconstruct the products of the two mapping functions respectively, and then we will get two new derivative forms.
It can be seen from the above table that the so-called exponent perpetual contract is to use the capital fee mechanism of the perpetual contract to construct a product with asymmetric risk exposure similar to the option risk model. This “power perpetual contract”, which combines the capital fee mechanism and the risk exposure of options, has the following obvious advantages over traditional option products:
The product structure is more pure, and there are no additional links such as delivery period and exercise price. Buyers and sellers can simply trade convex risk exposures;
The problem of liquidity fragmentation in the same trading pair is fundamentally solved, and the trading efficiency is greatly improved;
The underlying logic is simpler, which facilitates product realization on public chains with limited computing resources;
Unify the underlying functions of the convex function class and linear function class derivatives. As can be seen from the above table, y = x is actually a special form when n=1. Therefore, a derivatives agreement can simulate two different risk exposures of futures and options by relying only on the same underlying mapping function formula;
How does the Chengfang perpetual contract reflect the four risk exposures of option trading
We know that traditional options products contain four different risk exposures. They are: buying call options, selling call options, buying put options, and selling put options.
The image of their pricing function is as follows (the red curve is the valuation curve):
Next, we will try to construct four function images similar to traditional option functions by adjusting the value of n.
Buy call option
When n>1, the function image will protrude downward. When the spot price rises, the multi-party of the power perpetual contract has a faster increase in income and a slower loss when the spot price falls, which can better simulate the risk exposure of call options. (In this example, n=3, and the y value corresponding to the purchase price is used as the origin of the y axis)
Sell ​​call options
In the function in the above figure, if the trader does not choose to go long but short, the profit and loss function will be exactly the opposite of the above figure. That is, the function image is flipped according to the x axis.
The income characteristics of its holders are also similar to that of selling call options. When the price drops, the increase in income is slower, while the loss can grow rapidly when the price rises, which corresponds to the traditional option type of sold call options.
Buy put option
How to construct put options through the power perpetual contract seems to be not mentioned in the paper. So we try to take n as a negative value less than zero, and we will get a function graph in which the loss increases slowly when the spot price rises, and the income increases rapidly when the spot price falls. (N is -0.4 in the figure below)
The profit and loss model of the long holder of this curve is very similar to the income model of traditional put options, except that the function curve no longer intersects with the x-axis, so it forms the characteristic that the income can grow indefinitely when losing money.
Put option
In the same way, the empty square in the function above holds the reflection function of the original function on the x-axis. Its income increases slowly when the price rises, and its loss expands rapidly when the price falls, which corresponds to the risk-return model of selling put options.
Pricing of Chengfang Perpetual Contract
At the end of the article, we need to briefly discuss the pricing of the power perpetual contract.
The reason why options need to be priced is closely related to the nature of their convex functions. As mentioned above, the holder of the convex function obtains a risk exposure in which the return and risk do not match. Therefore, if you want to buy a party whose potential profit is greater than the potential risk position, only by paying a certain premium to its counterparty can the unfairness of the transaction be eased and the transaction can be concluded.
This premium is expressed as the purchase price of the option in traditional options. In the Chengfang perpetual contract, it will be expressed as a regular payment of funds to the short side. This form of regular payment of funds by multiple parties is equivalent to multiple parties “renting” this asymmetric risk exposure to the short party within a certain period of time. And its lease time can be adjusted freely and is no longer restricted by the expiration date of traditional options.
At the same time, due to the existence of this premium, the transaction price of the function will be higher than the function image itself, which is why the function image in the paper will have two curves at the same time. The blue line in the figure below is the function image itself, the yellow line is the theoretical transaction price after considering the premium, and the part of the yellow line higher than the blue line is the risk premium paid by the long side of the power perpetual contract to the short side.
So the next question is naturally, how much should the yellow line be higher than the blue line to be a reasonable premium? The paper discusses this problem in detail with a complicated formula, and here readers can temporarily ignore the complicated mathematical formula, as long as they know what factors affect the size of this premium.
Like traditional option products, the price of the power perpetual contract, which is the premium mentioned above, will be affected by the volatility of the underlying assets and the risk-free interest rate. The higher the volatility of the underlying assets, the higher the premium paid by the buyer of the power perpetual contract, that is, the greater the distance between the yellow line and the blue line. In addition, the greater the absolute value of n, which represents the degree of curve curvature, the greater the imbalance between product returns and risks, and the higher the premium.
This article is only based on the basic theoretical derivation, trying to discuss the possible application scenarios of the Chengfang perpetual contract. If there are any deficiencies, please criticize and correct the professional. My personal first impression of this innovation is that if this model can really be implemented and commercialized, and has not been falsified in the application stage, then it may be an innovation that is as important as the spot AMM transaction mechanism. .
I look forward to a professional team to commercialize the idea of ​​Chengfang perpetual contract and enable it to be tested in the real market environment.
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