Dynamic Network Token 

Research and results for reducing volatility in an ERC-20 token. 

1 Introduction

This paper will present the research conducted, methodology and results behind the Dynamic Network Token (DNT).

The first chapter will lay out the background and vision for the Dynamic Network Token. The second chapter will present the research regarding reduction of volatility, the concepts of burning and minting, along with methodology for implementing the functionality. The third chapter will present the results from implementing the functionality presented in the previous chapter. The fourth chapter is a conclusion along with notes regarding future work for the Dynamic Network Token.

1.1 Background of the Dynamic Network Token

The Dynamic Network Token started as a thesis project and evolved into a full scale crypto project. The idea for the project came from the observation of almost all cryptocurrencies or crypto assets being solely used as an investment, for speculation or a store of value. Of course, we also believe that a good means of payment should have the ability to preserve value and increase over time. Therefore our goal became to create a token with deflationary properties while also reducing volatility in favor of a more stable means of payment between parties in the network.

1.2 Vision of the Dynamic Network Token

The idea of a deflationary token, making it more attractive as an investment while also providing a good means of payment, is the core idea behind the Dynamic Network Token.

For this idea to become reality, we believe that a strong community where everybody is treated equal under the smart contract governing the Dynamic Network Token is necessary.  

2 Research & Methodology

2.1 Literature study

Volatility in cryptocurrencies is a fact, making them subject to speculation and an asset class mainly used for investing and trading. As the cryptocurrency space grows, different cryptocurrencies emerge, with different technologies and implementations.

Although different cryptocurrencies are designed to have unique functionality and utility, the problem of volatility seems to be a common denominator for all cryptocurrencies. To identify causes for volatility in cryptocurrencies, a literature study, studying different kinds of cryptocurrencies provides a suitable method for gaining knowledge. In this way, factors contributing to volatility can be derived and more closely examined to help with the implementation of functionality reducing volatility in the Dynamic Network Token. The literature study is based on Bitcoin, Ethereum and Tethers whitepapers and related articles.

To gain knowledge about the method that is used for the Dynamic Network Token, Binance and Helium were studied. The method is called burning and minting.

2.1.1 Whitepapers and reports

Bitcoin as of Q3 2021, is the most valuable asset according to market cap. Studying the Bitcoin whitepaper is a crucial step to gain insights and understandings to the implementation of the halving and hard cap, making Bitcoin a scarce and deflationary currency in regard to supply. Bitcoins hard cap and the shortage of coins added to circulation due to the halving, creates scarcity which is contributing to Bitcoin’s volatility.

Ethereum’s whitepaper was studied to understand the fundamentals of an ERC-20 token, what smart contracts are and a deeper understanding of the Ethereum ecosystem. One other key insight gained from Ethereum’s whitepaper, is the ability to develop and deploy a smart contract by using their blockchain as a host for the contract. Ethereum’s functionality provides a way for the Dynamic Network Token to be deployed.

Tether was studied for its stable value. This comes from its one-to-one ratio to the U.S Dollar, and how they make use of the proof of reserve method to ensure a one-to-one ratio. With this information regarding how they mint and burn tokens, a better understanding of how to keep a value stable and regulated in regard to another asset was achieved.

2.1.2 Burn and mint in other projects

To get a better understanding regarding burning and minting, research of other projects and their approaches was conducted. The focus of the research targeted projects using burning and minting functionality, and how these projects had implemented it. With different goals and ambitions, projects use different approaches to this area.

The projects chosen for studying these functionalities are Binance coin and the Helium token. Both projects are considered well established and have drawn a lot of capital to them and reside in the top 100 rankings by market capitalization as of April 2021. Helium was chosen mainly for its minting functionality, while Binance coin was chosen for its unique approach to burning.

Binance coin is the native coin of the Binance blockchain, whose approach to burning their coins is interesting. From the initial coin offering of Binance coin, the company announced that they would burn 50% of its total supply by buying back Binance coins and then burning them. In their 2021 Q1 report, Binance had burned around 13% of its total supply which was equivalent to 426,304,000 U.S Dollars. By studying how the price was affected after each burn and over time with more iterations of burns, knowledge regarding burning and its long and short-term effects on price could be obtained for Binance coin.

Figure 2.1: Chart over BNB burned vs price between July-17 and Sept-19. Source: Bitcoinsuisse.com.

Helium mints its tokens based on a basic algorithm which starts minting 5 million tokens each month and every second year, this amount is cut in half. This implies that Helium’s inflation rate will decrease 50% every second year until the minting is no longer affecting the price. By studying how the price reacts to this, a better understanding on how Heliums approach to minting can potentially decrease the volatility could be achieved.

2.2 Burning and Minting

The method for reducing the volatility in the Dynamic Network Token consists of implementing burning and minting functionality. The reason for choosing this method is partly because of the foundation for the functionality being incorporated in the ERC-20 standard as provided by Open-Zeppelin. But the main reason for choosing burning and minting as a method to reduce the volatility, is because the functionality is compliant with the quantity theory of money or “QTM”. This theory states that a greater quantity of money in a society, leads to a higher price in labour and commodities.

To make use of the QTM theory in a cryptocurrency with burning and minting functionality, the heightening price of labour and commodities when adding to the total quantity of the cryptocurrency is replaced with a fiat currency, for example the U.S dollar. This means that if minting occurs, its value in comparison to the U.S dollar should become lower and if burning occurs, its value should become higher. In essence, the QTM theory applied this way in a cryptocurrency dictates that minting twice as much of that currency, will halven the value of that currency in regards to its pairing, for example the U.S dollar.

In accordance with the QTM theory, the burning and minting functionality should have an impact on volatility. By burning tokens when a sell transaction occurs, the impact should be that the price is not affected as negatively and losing as much value in regard to its pairing. In the same way, by minting tokens, the price impact to the upside should be more controlled when a buy transaction occurs and reducing potential volatility.

How the implementation of the burning and minting should look is up to the developers of the project to decide. In the case with Binance, a quarterly burn will occur until the supply is cut in half. In the case with Helium, a minting will occur every month, adding five million tokens to the total supply.

However, these methods used by Binance and Helium are static approaches to burning and minting. They will occur based on a timeline and not happen dynamically. Therefore, these approaches are not suitable for a cryptocurrency trying to control volatility dynamically.

The burning and minting must be implemented in a way where it interacts with transactions rather than using a timeline. By utilizing the transfer function from the ERC-20 standard, this can be achieved.

With the use of the transfer function, a mathematical formula for deciding the number of tokens to be burned or minted needs to be chosen. This formula should behave in a way where the ratio is in favour for the burning, which in accordance with the QTM should result in a more deflationary cryptocurrency.  

As burning and minting affects the total supply, the number of tokens burned or mint must be realistic in proportion to the total supply. By looking at transactions of other cryptocurrencies such as Bitcoin, the median transaction is small. This should indicate that the average transaction for the Dynamic Network Token also will be small. To handle this when burning and minting, the mathematical formula should make use of logarithms and exponents, as their functionality enables a good relation between the number of tokens and their percentage as displayed in table 2.1 and 2.2.

2.2.1 Burning

Burning is the functionality that is reducing the supply of a token by removing tokens from the total supply. This can be done in different ways, for example with a condition or by executing a transaction.

The burning functionality is possible to implement in the standard contract for ERC-20 tokens by Open-Zeppelin, which makes it a suitable choice for the Dynamic Network Token. With the use of the existing burning functionality provided by Open-Zeppelin in combination with the transfer function integrated in the standard contract for ERC-20 tokens, the option to create a custom burn algorithm could be achieved based on the amount that is being transferred when a sale occurs.

To figure out when to burn, a condition that checks if the receiver is either the reserve- or owner-address will determine if the transaction in question is a sell-transaction, and the burn will be initiated.

If the condition is met, and the transaction is a sell-transaction, the first step before the actual exchange of tokens between the seller and the reserve address is the calculation of the burn. This calculation is based on a logarithmic or exponential function depending on the amount that is being sold, resulting in the amount to be burned.  

When the amount to be burned is calculated, it is reduced from the reserve address and is sent to the 0x0 address, resulting in the burning of the tokens. After this process is done, the transfer from the seller to the reserve is done, finishing the transaction.

Figure 2.1: Flow chart of the burning functionality

To get a good ratio between the amount that is being transferred and how many tokens should be burned, a logarithmic/exponential approach was chosen as mentioned in the introduction to this section. Because a logarithmic function behaves as an inverse to an exponential function, burning for smaller transactions which presumably will be the majority of transactions based on Bitcoin distribution in wallets, will experience a higher burn percentage than larger transactions. This will also result in a better distribution of tokens burned in regard to total supply, as a high percentage of a small transaction results in a small number because of the size of that number being small.

As mentioned in section 2.1.2, Binance Coin has an implemented approach to burning, which could be an approach used in the Dynamic Network Token. However, it would remove the functionality of being dynamic and would have a negative effect on users transacting the token. The goal is to encourage the use of the token and not intervene when transacting with the token but only intervene when capital gain is in place.

To calculate the number of tokens to be burned, the amounts of the last two transactions are added, where t1 being the previous transaction amount and t2 the current. The result is then stored in a variable totalAmount and can be described as . The totalAmount is then divided by the logarithm of itself and multiplied by four, resulting in:

                                                                  (1)

Where the result stored in the burn variable from (1) constitutes the number of tokens that will be burned.

Table 2.1: Table showing the logarithmic burn functionality.

As the log of one is zero and the log of a number below one is negative, the function to calculate the burn must be changed below one. With a condition checking if the log value is negative, the implementation of the function changes from dividing by log, to division with the exponent times four of the total amount resulting in:

                                                                (2)

Table 2.2: Table showing the exponential burn functionality.

2.2.2 Minting

Minting tokens can be viewed as the opposite to burning, meaning that there is an addition to the supply. By adding tokens to the total supply, the purchasing power of the token will decrease depending on how many tokens are added.  

Minting is a necessary functionality for any ERC-20 token using Open-Zeppelin as it provides the functionality for the creation of the initial supply. Thus, also making minting a part of the Open-Zeppelin standard contract.

The implementation of the minting utilizes the same transaction function as the burn functionality, i.e., the necessary transfer function of the ERC-20 standard contract. With the help of a condition checking that the transaction is a purchase from the reserve or owner address, the contract knows that it should initiate a mint based on the amount bought.

Mentioned in literature studies under section 2.1.2 is Heliums approach to minting. This is an inflationary approach that in theory decreases in the long run, but with the potential to stay inflationary. This would not be suitable for Dynamic Network Token, as it would make the token inflationary and not dynamic since their approach is to mint a static number of tokens each month which is divided by two every second year.

If the condition for a purchase transaction is met, a calculation of how many tokens that should be minted is done. The calculation for the minting is as with the burning, based on a logarithmic or exponential function with the difference being the percentage being lower.

When the calculation is done, the amount to be minted is transferred to the reserve address, adding to the total supply of the token. After the minting process is done, the actual transfer between the reserve and the buyer occurs, finalizing the transaction.

Figure 2.2: Flow chart of the minting functionality

The logarithmic minting uses the same functionality as the burning with the only difference being that the four is changed to an eight, giving a function of:

                                                                 (3)

This leads to an algorithm that will have a burn to mint ratio of approximate 2:1.

Table 2.3: Table showing the logarithmic minting functionality.

The exponential minting works in the same way as with the exponential burning.

The only difference being that the root of the division is multiplied by eight instead of four giving:

                                                                 (4)

Thus, creating an approximate 2:1 burn and mint ratio for the exponential functionality as well, resulting in more burning than minting regardless of the size of the transaction.

Table 2.4: Table showing the exponential minting functionality.

2.2.3 Burning and Minting Limits 

As the burning and minting functionality implemented in the Dynamic Network Token has a potential to burn or mint as long as there are transactions, there is a need for a limit. This limit will be set to control the maximum amount of tokens to be burned and the maximum amount of tokens to be minted.

By implementing threshold variables, we can make sure that the burning of tokens can never reduce the supply below a certain point. In the same way, we can make sure that the minting of tokens will not create a supply shock.  

For the token to become more deflationary, the maximum supply variable should create less potential to mint tokens then the minimum supply variable creates potential to burn tokens. By continuing the path of implementing a 2:1 ratio in favor reduction, the room for burning becomes larger than that of minting. 

The starting amount of tokens to be minted in the Dynamic Network is set to 42 000 000. This means that the maximum supply variable is set to 52 500 000, giving it a 1,25 or 25 % room to increase. The minimum supply however, is set to 21 000 000, giving it a 0,5 or 50% room to decrease.

2.3 Price simulation tools

2.3.1 Java program

To start simulating the price, a simple iterative Java-program was developed. The function of the program is to both simulate price with the regulations of burning and minting implemented from section 2.2.1, 2.2.2 and at the same time simulate price without regulation.

The result of running the program was the creation of two arrays containing regulated and unregulated price growth. These arrays, containing the price over N-transactions, were later used to calculate the standard deviation i.e., the volatility. With help of the two datasets, it could be used with the geometric Brownian motion equation to give a hypothetical price prediction for the token over N-days by using the calculated volatility as a parameter.

2.3.2 Black-Scholes model

Postulated in 1973 by Black and Scholes, the process governing the price S of an asset, can be formulated as a stochastic differential equation satisfying the geometric Brownian motion with a constant initial value of S0 > 0. This insight was the foundation to what would become the Black-Scholes model.

The Black-Scholes model is a model used in mathematical economics for predicting option prices. It utilizes the stochastic differential equation satisfying the geometric Brownian motion, where S is the price (S0 represents starting price), r is the interest rate (representation of the drift or () and  (Sigma) is the volatility calculated as the standard deviation of the logarithmic return. With all the parameters accounted for, the formula for the Black-Scholes model can be derived from the SDE satisfying the geometric Brownian motion by using the stochastic chain rule in the Itô formula, resulting in (8).

                                                         (8)

By satisfying the conditions for geometric Brownian motion in the Black-Scholes model, it can simulate a random walk with constant drift. Thus, price can be seen as governed dynamically by the geometric Brownian motion, as it creates a source of uncertainty and randomness in regard to the price. The result is a somewhat realistic simulation of price behavior for a stock, making it a good model for the simulation of price for the Dynamic Network Token.

3.6.5 Geometric Brownian motion program

To make use of the geometric Brownian motion (GBM), and applying it in practice, a Python program was developed. Using the datasets mentioned in 2.3.1, the standard deviation or  could be calculated, thus giving the volatility variable for the stochastic differential equation.

For the program to work, the two other parameters had to be applied. These two parameters where S0, representing the starting price and the r or , representing the interest rate.

The starting price S0 was chosen arbitrarily to start at 0.2, as the focus of the thesis is to control volatility and the actual price in practice will be determined on different factors that are not known at this time.

Interest rate in cryptocurrencies is somewhat unheard of, as there is no interest gained in just holding a cryptocurrency or token in a regular cryptocurrency wallet. There is, however, the possibility to put them into interest accounts, earning interest on holding your cryptocurrencies in these accounts. Therefore, the interest rate or  in the SDE was set based on the average yield from Bitcoin, Ethereum and Tether, holding your cryptocurrency in an interest account with the company BlockFi.

The average yield from Bitcoin, Ethereum and Tether on BlockFi as of Q3 2021, can be calculated as in (9) which will be used as thevariable, representing the interest rate.

 6 + 5,25 + 9,3 / 3 = 6,85                                                                   (9)

With all the parameter variables sorted out, the actual formula for solving the Black-Scholes PDE using GBM could be written. The equation was converted into a function in Python code, taking all the parameters needed as arguments, then performing the calculation of the price and returning it.

Figure 2.3: PDE solving for Black-Scholes equation converted into Python code.

By storing the value returned from the function in a variable, a loop where each iteration representing the daily price could be stored in an array, simulating the price development over time using the Black-Scholes model.

In the program, two arrays were created to represent price with and without the implemented functionality. This is because of the option to plot the simulated price with and without the burning and minting side by side, giving a good idea of how the price would behave over time.

3 Results

3.1 Price simulation

The method for reducing the volatility in price consisted of implementing the concepts of burning and minting as described in 2.2. By simulating transactions with and without this functionality, two results could be derived which in this chapter will be defined as the regulated and unregulated price.

3.1.1 Unregulated price

The unregulated price did not contain any burning or minting functionality. Using the Java-program developed for simulating transactions, the average standard deviation or  could be calculated over N-iterations. The resulting average standard deviation could then be used as the volatility parameter in the Black-Scholes model, used to create a simulation of the price for the Dynamic Network Token.

By running 15 iterations of the Java-program, 15 different scenarios for the volatility could be obtained and used for calculating the average standard deviation for unregulated price. The volatility calculated for the unregulated price, resulted in an average standard deviation of 0.44774127 over these 15 iterations.

The impact no regulation had on price growth resulted in high volatility. This is further validated by the high average standard deviation obtained over the 15 iterations.

3.1.2 Regulated price

The regulated price contained the burning and minting functionality, trying to reduce the volatility in price. By using the Java-program to simulate price over N-transactions, datasets could be obtained to calculate the average standard deviation which would be used as the volatility parameter in the Black-Scholes model for creating a simulation of the Dynamic Network Token.

Same as with the unregulated price, the price was simulated in 15 iterations, creating 15 different scenarios using the Java-program which was then used to calculate the average standard deviation. The volatility calculated for the regulated price, resulted in an average standard deviation of 0.38645927 over 15 iterations.

The impact regulation had on price growth resulted in a reduction of volatility in comparison to the unregulated price. As can be seen in (1), the average standard deviation for regulated price over 15 iterations was reduced by 6,128%.

3.2 Comparison of price simulations

To evaluate if the implemented functionality of burning and minting had an impact on the price, a simulation of both unregulated and regulated price using the average volatility derived from section 3.1.1 and 3.1.2 was plotted on the same graph. The standard deviation was also used to see the difference in volatility over 15 iterations, represented in figure 3.1.

Figure 3.1: Staple diagram showing the standard deviation ( for regulated and unregulated prices.

As can be seen in the staple diagram in figure 3.1, all 15 iterations of the regulated price had a lower standard deviation than the unregulated price. This resulted in a lower average standard deviation for the regulated price for the total of iterations in comparison to the average standard deviation for the total of iterations for the unregulated price.

By using the average standard deviation orfor both regulated and unregulated, we can calculate the difference between them to see the impact on the price volatility. By subtracting the unregulated volatility with the regulated volatility, the following result was obtained:

                                                           (1)

The results in (1) is a 6,128% difference between unregulated and regulated average standard deviation.

Figure 3.2: Simulation of price with and without regulation over 365 days using the average.

Using the average standard deviation for the regulated and unregulated price, a simulation over 365 days containing both types of prices could be plotted on a graph. In figure 3.2 the unregulated price experiences a much higher volatility than the regulated price. It can also be seen that the regulated price is going down over time in this specific simulation. However, the volatility fluctuations are much lower and the evolution more linear.

To illustrate the result further, figure 3.3 and 3.4 presents the five first iterations of the 15 iterations simulated, containing the regulated and unregulated price over 90 days.

Figure 3.3: Graph over five iterations of unregulated price simulated over 90 days.

As can be seen in figure 3.3, all the five iterations deviate rapidly from each other after 40 days. The only iteration that can be considered having low volatility is the first, and the rest of the iterations are experiencing high volatility.

Figure 3.4: Graph over five iterations of regulated price simulated over 90 days.

In contrast to figure 3.3, figure 3.4 containing the regulated price shows less of a deviation between iterations. With almost every iteration having a very similar evolution over the 90 days, it seems as if the regulated price is more predictable and less volatile than the unregulated price.

3.3 Evaluation of linear regression

To evaluate if the burning and minting functionality had an impact on the linear growth over time, a linear regression model was created and fitted to both the regulated and unregulated price simulations.

The results from the linear regression with regulation will be presented in 3.3.1 along with the evaluation of the R-squared and root mean squared error (RMSE).

In section 3.3.2 the result from the linear regression for the unregulated price will be presented, along with the evaluation of the R-squared and root mean squared error (RMSE).

In section 3.3.3 a comparison between the regulated and unregulated price fitted to the linear regression model using the average standard deviation from 3.1.1 and 3.1.2.  

3.3.1 Linear regression with regulation

The results obtained by creating a linear regression model and inserting the regulated price showed an improvement in the reduction of volatility. The price is following the linear regression line, with a few deviations, which indicates that our mathematical implementation to dynamically regulate the price is working.

By fitting the simulated price with regulation to the regression model, the results obtained from the chosen metrics for evaluation were as follows:

R2: 0.8608742733463043
RMSE: 0.031974880043300014

As can be seen, the R-squared value obtained is above 80% which can be considered high. A high R-squared for regulated price data indicates that it fits the regression model well. This is represented as well in figure 3.5, where there are no extreme deviations from the regression line.

Looking at the RMSE for the regulated price, the value obtained is low. This is generally a good result for an RMSE as it indicates the spread of the residuals is low. This is also shown in figure 3.5 as the concentration occurs around the line, meaning that there are less errors in deviation.

Figure 3.5: Graph over linear regression model with regulated price over 365 days.

Even though the price in the simulation went down over the one-year period (which is arbitrary due to the Wiener process in the geometric Brownian motion), the price is closely following the regression line, indicating a good fit and a reduction in volatility.  

3.3.2 Linear regression without regulation

The results shown from the linear regression without any regulation shows a very different story compared to the results from the regulated one. By looking at figure 3.6, the price simulation from the unregulated price is not following the regression line. There is also a lot of fluctuation in the price simulation due to the high standard deviation.

By fitting the simulated price without regulation to the regression model, results could be obtained from the chosen metrics for evaluation and were as followed:

R2: 0.2092963109804813

RMSE: 0.14663562653286338

The R-squared value that was obtained is very low, which implies that the unregulated price data does not fit the linear regression model very well compared to the regulated one. Shown in figure 3.6, the deviations from the regression line are big and are not following the regression, indicating a poor fitment.

The RMSE score obtained from the simulation was relatively high compared to the score with regulation. This indicates that the spread of the residuals is high and there is a low concentration around the regression line.

Figure 3.6: Graph over linear regression model without regulation of price over 365 days.

3.3.3 Comparison of regression models

By comparing these two regression models, the regulated price is experiencing less volatility than the unregulated price. This is due to the regulated price having a lower standard deviation or σ, making it fit the regression line better.

As a good score for R-squared was obtained in the regulated model and not the unregulated one, it implies that the regulated price follows the regression line with less fluctuation than the unregulated model.

Subtracting the R-squared from the regulated model with the R-squared from the unregulated model, we can see a difference of:

0.860874 - 0.209296 = 0,651578                                                                    (2)

The difference for the R-squared between the models is 0.651578 as can be seen in (2), indicating a big difference in the fitment to the regression line for the regulated and unregulated price.  

Comparing the RMSE score for both the regulated and unregulated models, the results showed that the RMSE score obtained from the regulated model was lower and prone to fewer errors. By subtracting the high value for the RMSE obtain from the unregulated price with the RMSE of the regulated price, the result is as follows:

0.146635 - 0.031974 = 0.114661                                                                    (3)

With a difference of 0.114661 as seen in (3), the unregulated model is more prone to errors and its residuals will be further away from the regression line than the regulated model as its RMSE is considerably lower.

4 Conclusion

To conclude the work regarding the reduction of volatility in an ERC-20, the results show promising potential. The regulated price managed to reduce the volatility during the simulations, and it was possible to implement the functionality in the ERC-20 smart contract governing the Dynamic Network Token. This conclusion in summary is satisfying, as we could in fact see the reduction of volatility in the simulations. Furthermore, the regulated price growth also became more stable and linear compared to the unregulated.

After a lot of research and testing indicating that the implemented functionality is working, we are now ready to start building up the community that will be the foundation for the Dynamic Network Token.

4.1 Future of the Dynamic Network

The road ahead is filled with possibilities for improvement and new development. Now we need the help of our community to identify areas and ideas for the Dynamic Network to grow. We look forward to building this network together with you and all the other participants.