# Changes to Everlasting Options

Rolled out in Sept 2021, the everlasting options have been running as a beta version for over 4 months. Now with the launch of Deri V3, it will finish the beta stage and kick off the official journey. A few changes are to be made with the launch.

- Funding period = 7 day (was 1 day for V2)
- Switched to a Greek-based margin mechanism
- Lower transaction fee for OTM options

**Funding Period**

The concept of funding period was introduced for perpetual futures by Bitmex, as a lever to force the market back to the targeted price. It was set up as a Funding Fee = (Mark — Index) paid every 8 hours. The premium/discount component of the funding can be thought of as a “penalty function” for the discrepancy between the trading price and the index price (the target). The key parameter here is the degree of the penalty, which is solely determined by the funding period: the shorter the period is, the higher degree of penalty is enforced. Currently most of the centralized exchanges adopt a funding period of 8 hours for perpetual futures. This was largely a result of trails-and-errors. A funding period of 1 day was first tried out but was not enough to bring the trading price back in line with the index. Then 8-hour was tried and kept thereafter.

When it comes to everlasting options, things are more complicated. Mathematically, every everlasting option is equivalent to a portfolio of classical options. For a continuously-funded everlasting option, the corresponding portfolio is of a continuous spectrum of classical options. That is, a continuously-funded everlasting call (or put) option with strike *K* and funding period *T* is equivalent to a portfolio consisting of all classical call (or put) options with strike K and t ∈ (0, ∞)with an exponentially decaying weight density:

For example, the figure below illustrates the spectrum of everlasting calls with funding periods T = 1day, 7day, 10day, respectively.

During the beta stage of Deri’s everlasting options, we adopted the 1-day funding period. However, our numerical analysis based on trading practices has indicated that a 7-day funding period better satisfies the purposes of the everlasting option trading. Therefore, in Deri V3, we will roll out the everlasting options with 7-day funding period. Please note that the daily funding fee of a 7-day everlasting option is 1/7 of (mark — payoff).

The figure below shows the theoretical prices of 1-day V.S. 7-day EO. The 7-day EO are not bound to track the intrinsic value as closely as the 1-day EO.

The figure below shows that the 7-day EO has lower daily funding near the ATM range, but higher daily funding for ranges far away from the ATM point, compared with the 1-day EO.

**Greek-based margin requirements**

Designing a proper margin requirement algorithm for nonlinear derivatives such as everlasting options is not easy. Traditionally, most margin requirement algorithms are essentially scenario-based: the required maintenance margin is to cover the loss of the position associated with a specific risk scenario, e.g. underlying price changing by 5%. This is straightforward for futures or any linear derivatives. However, it is more complicated for nonlinear derivatives such as everlasting options, since the margin ratio is usually a variable depending on the underlying price. (Please note this issue does not exist for classical options, for which sellers simply post margins to cover the option values.) The tricky part is, we want two properties to be satisfied by the margin requirement algorithm. simultaneously:

- The required margin should be able to cover the loss of the position due to an unfavorable underlying price change (e.g. 5% or 4%)
- When the underlying price changes in a direction favorable to a position, if the margin requirement is to be increased, the increment should not be greater than the profit increment. Otherwise, there could be a small chance of an unreasonable scenario: price changes favorably to a position, but it gets liquidated because the increment of the margin requirement has surpassed that of the profit.

When everlasting options were rolled out in Deri V2, we adopted a margin algorithm that applies a discount for out-of-money options, per the out-of-money ratio. While this algorithm holds the first property very well, it fails to hold the second one. Therefore, in Deri V3, we are upgrading to a Greek-based margin system for the everlasting options. With 𝚫and 𝛤, we can estimate the change of the option value due to the underlying price change from S to $S+ 𝛿S, with a second-order Taylor expansion:

And the margin system works as follows: the trader is required to post 𝛿*C* (or 𝛿 P) as margin for a call (or put) position, with respect to a specific risk scenario, e.g. 𝛿S/S =5%. Please note that the ATM point needs to be handled specially since the function is not second-order continuous at this point.

Another small change is the *unfavorable underlying price change* adopted for the margin calculation. Considering Deri Protocol is deployed on high-speed blockchain network like BSC and adopting highly-sensitive oracles for BTC and ETH, a price change of 4% is adopted for V3, instead of the 5% used in Deri V2.

**Transaction Fee**

With a longer funding period adopted, we will apply a lower transaction fee for the OTM options.

The rationale behind the transaction fee is to set it as the minimum value ruling out the chance of front running. That is, we assume the DPMM can be front run by a price change of 0.2%. (This is a reasonable assumption when an oracle of 0.1% deviation threshold is adopted. However, if the oracle is less sensitive than 0.1%, i.e. with a larger deviation threshold, then the assumption should be revised accordingly.)

Then the front-run revenue by trading an everlasting option is:

where S is the underlying price and 𝚫 is the delta of the option (gamma risk is ignored). To rule out the possibility of front running, we need to have:

where Cost is the cost of transaction fee for a round trade (open & close).

For ITM options, we just treat them as futures (i.e. assuming 𝚫=1) and charge the transaction fee per notional (=S): we set the transaction fee to be fITM=0.1% of the notional so that the cost is

which set Revenue — Cost = 0 and thus rules out the possibility of front-run.

For OTM options, we charge the transaction fee (FeeRatio=fOTM) per mark price M:

Therefore we have the following “benefit-cost analysis” for the front-runners:

where 𝛀=sΔ/i is a key ratio of the option. If we let revenue-cost ratio equals to 1, then we have:

The figure below illustrates how 𝛀 changes per the underlying price for a typical option.

On the OTM side, we have 𝛀 ≈12.5, then we can set f=1.5% to keep the DPMM safe.

Please note that previously the OTM transaction fee ratio for the V2 everlasting options was set to 4% based on the same rationale. The ratio was higher due to a higher 𝛀 of the 1-day funding period options. The characteristics of 𝛀 is behind the conclusion mentioned in the first sector that a 7-day funding period better satisfies the purposes of the everlasting option trading.

**About Deri Protocol**

Deri Protocol = (Perpetual Futures + Everlasting Options) x Decentralized.

Deri is the DeFi way to trade derivatives: to hedge, to speculate, to arbitrage, all on chain. With Deri Protocol, trades are executed under AMM paradigm and positions are tokenized as NFTs, highly composable with other DeFi projects. Having provided an on-chain mechanism to exchange risk exposures precisely and capital-efficiently, Deri Protocol has minted one of the most important blocks of the DeFi infrastructure.