Comparison of pricing models

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In October 1997, Robert Merton and Myron Scholes were awarded the Nobel Prize in Economics for their formula for calculating the price of European options. Although Fisher Black also contributed to the development, his untimely death prevented him from sharing the honor.

The invention of the pricing formula has led toincreased interest in options trading and caused the explosive growth in derivatives trading. In the early 70s, the mathematical approach in options trading was revolutionary in itself, and allowed to move away from subjective-intuitive estimates when determining the price of a contract.

The authors relied on 6 assumptions for their model, most are associated with a risk-free interest rate, but 2 of them are of particular interest to us. These assumptions are about the availability of an immediate short sale of the underlying asset and the continuity of trading.

Now there is a huge variety of services that provide convenient tools for options evaluating according to the Black-Scholes model, including calculation of “Greeks”, expected volatility (IV), and strategy building. Options are traded on many world exchanges, and have huge turnover, especially options on the S&P 500 index.

But what about cryptocurrency options?

The above model is utilized by centralized cryptocurrency exchanges, where order book has a market maker that quotes ATMs and close contracts with a given spread, adhering to delta neutrality* of the total portfolio. It is necessary to use historical volatility to evaluate in accordance with the model, that is the variance of the underlying asset over a certain period of time. But as we know, in the real world, the past does not determine the future, or in other words, if the market is in a sideways trend today, this does not mean that it will not change tomorrow. For this reason, market makers set their own prices, and services for traders provide the ability to convert prices into expected volatility (IV). The market is partly about the possession of information and the ability to analyze it, so expected volatility has become a tool for assessing market expectations, and its weighted strike value is often dictated by the exchange itself.

Exchange-traded options use the classic model, but what about decentralized options?

With the rapid development of DeFi, there have been attempts to create protocols for options trading based on smart contracts, and some of these projects are successfully functioning. They are built on the principle of creating an individual contract between the buyer and the seller. For example, user Alice wants to buy a Call option for ETH / USDT with a strike of 360, and user Bob wants to write the same contract. In order to guarantee the execution of the option agreement, Alice is obliged to contribute 360 ​​USDT tokens to the contract in order to ensure the possibility of buying 1 ETH at a price of 360 USDT on the expiration day if the ETH / USDT rate is above 360. Bob, in turn, must contribute 1 ETH to the contract to ensure Alice can buy 1 ETH. For this operation, Bob receives a premium, which he sets himself when the transaction is made, and the transaction is completed only if the premium suits both participants.

Many may ask, what is the disadvantage of this approach? The problem is that participants block 200% in total of the strike price in a smart contract, which has an extremely negative effect on the return on investment. In order to increase profitability, sellers try to increase premiums, which repels buyers and negatively affects the growth of protocol liquidity and the interest of traders. In order to somehow reduce the premiums, some protocols position themselves as a hedging tool, offering to trade OTM (Out-the-Money) strikes. But despite the decrease in the premium, the payback gap is only widening for buyers, and in the long term, the purchase of such instruments is unprofitable.

Attempts to use barriers to address these decentralized problems are also highly controversial. For example, there is no physical delivery of an asset in such protocols, and the seller and the buyer contribute 20% to the contract, and after the price moves in one direction or another by the specified value, the contract either closes or asks for replenishment from the unprofitable side for prolongation. But such contracts cannot be called options, they are more like a deposit built into each contract.

In the DYMMAX protocol, we wanted to combine the strengths of each approach. We use the parimutuel betting with fixed odds pricing model to calculate option premiums, and a 24-hour prolonged auction instead of the classic order book. The model is based on a shared money pool, which does not require the full collateral for the contract, but guarantees payments to all participants in any market scenario.

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The DYMMAX protocol also has a significantly different contract quotation model. It lacks the usual market maker in the order book for each contract, but instead has a shared pool of liquidity for the entire auction, the volume of which affects the final premiums. This means that everyone can supply liquidity in any proportion, and receive a proportional benefit from this. At the beta stage, there is no possibility of liquidity delivery, but the product release includes an interface for liquidity providers with risk management.

In the following articles, we will take a closer look at the protocol’s use case and the capabilities it brings to the DeFi market.

  1. Delta neutrality — creation of a portfolio that is insensitive to the movement of the underlying asset by including various options with the resulting delta close to zero.

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