In the Blockchain concept, assets (i.e. tokens) should not be printable; i.e. the supply of assets should be bounded to a limited value or should be an observable and measurable formula that can justify the supply increase or decrease.

Therefore,as of the launch of 1XMM project, digital assets do not have interest rate features, aka yield curves (note that creation of digital interest rate curves is a step in Asagaia development plan). 1xMM Pools intend to simulate the concept of “cost of carry”, using options and the varying cost of premia in time.

1xMM Pools offer the possibility to user to accrue the performance of constant maturity options, either a call if a user believes that the asset potential is positive, or a put if a user believes that the asset potential is negative.

The total amount of 1XMM tokens is 650 million tokens, that will be distributed across various blockchains thanks to the integration of LINK protocol into 1XMM smart contract (ERC677 standard).

75% of the total supply will be used for pools / liquidity / cash management, of which 10% will be used to garantee some liquidity on 1XMM token, 25% will be used by Asagaia to raise more capital in the short / medium term to (1) finance Asagaia projects, and (2) to improve liquidity on 1xMM Pools (i.e. stake coins on the different pools to ensure minimum positions and therefore yield possibilities).

The remaining 40% of the 1XMM tokens will be used exclusively for the 1XMM pools, in order to serve attractive yield to 1XMM holders ( provided that users are in the right direction). Since we are expecting 1XMM price to have stable growth, 1XMM liquidity on 1XMM pools may mostly be on the short side; our trading team will be in charge of moving liquidity on the 1XMM pools to try to offer an average of 5% p.a. yield to 1XMM holders.

Note that: our projections should allow us to serve an interest between 3% and 6% p.a. for the coming 15 years, depending on liquidity deposited on the 1XMM pools. These projections cannot be guaranteed, in any case, since they depend on the market conditions and the trading team’s ability to manage the liquidity on pools.

1XMM smart contract offers the possibility to deposit ETH, or any other ERC20 coins, onto the 1XMM contract so that 1XMM holders can exchange their 1XMM tokens against these “staked tokens”. The “staked tokens” will be purchased using 1xMM Pools revenues.

The “staked tokens” can be exchanged at any time, as long as “staked tokens” are available (i.e. when all the quantity has been withdrawn, there will be no more possibility for users to get “staked tokes”), and at a pre-fixed rate. The pre-fixed rate depends on market conditions but will be, in general, more attractive than market exchange rate offered for the “staked token”. For example, if ETH/1XMM is exchanged at 1,500.00, the pre-fixed rate could be 1,450.00.

The 1XMM tokens which are exchanged via this process will be automatically burnt. The main objective of auto-exchangeability is to sustain 1XMM value thanks to the attractive exchange rate and the auto-burnability of the token.

1XMM tokens which are sent back to the smart contract are automatically burnt. In general, this burn process is the result of the auto-exchange process.

The main objective of the auto-burn feature is to sustain 1XMM value by reducing the supply of 1XMM tokens. The auto-burn is an intrinsic feature of the 1XMM token contract.

In 1xMM Pools, users predict whether an asset’s value will rise or fall. This decision shapes their position and determines their yield when staking tokens.

Users earn yield if the asset's price moves as expected. For example, those with a long position profit if the price rises, while those with a short position lose. If the price moves against their prediction, they incur a loss.

Each position involves a constant maturity option (a call or put), and yield is based on its value change over the fixing period (cf. accrued yield computation). If the price rises, long users earn the accrued performance of the call option, while short users cover this cost. The maturity of the involved constant maturity option depends on the term of the position selected by a user; e.g. if a user wants to stake for 2 weeks, he will be receiving the performance of a 2 weeks constant maturity option.

A constant maturity option never expires and maintains a fixed time to maturity (e.g., 1 day or 1 week), allowing users to enter or exit the pool anytime. At 1xMM, we believe these options best reflect an asset’s expected cost of carry, which we define as its expected internal rate of return.

The Volatility

For each term, we get forward and option prices from Deribit for reference pairs (BTC/USD, ETH/USD, SOL/USD and BNB/USD), for all available terms.

Using this market data information, SABR smiles are calibrated to create reference volatility surfaces. A volatility surface for a pair X, defined at a time t, allows to get the implied Black & Scholes volatility for any option base on X and priced at time t:

For other pairs (i.e. non-reference pairs), we compute the correlated At-The-Money ("ATM") volatilities, and then we calibrate a SABR smile to fit the correlated volatilities Out-of-The-Money ("OTM") and In-The-Money ("ITM") - the process for OTM and ITM may change in time. Once the volatility surfaces are computed, we can compute the premium of all the constant maturity vanilla options.

The Premium

Using the volatility surfaces, we compute strike, by term T, for each option such as:

The strike approach defined above aims at considering the Futures market forecast in the options's premium. Indeed, if the Futures market has a positive view about a pair (i.e. the Futures price is bigger than the spot price), the Put options will be in the money while the Call options will be out of the money.

Then, we can compute the premia:

When time reaches next fixing period, $t_{i+1} = t_i + fixing\_period$, we compute the new premium of each option (i.e. the “Performance premium”) such as:

This methodology allows to track the performance of the spot in the yield which will be exchanged between parties. Long users are paid the accrued value of Calls "Performance premia", while Short users are paid the accrued value of Puts "Performance premia".

First, let’s set:

1. We compute the amount to be paid by Payers:

$$Payer_{t_{i+1},T} = AccrualFactor \times Notional_{Payer,T,t_i} \times Premium(X,t_{i+1},T)$$

Where $Notional_{Payer,T,t_i}$ is the notional for Term T at time $t_i$.

And

$$Payment_{t_{i+1}} = \sum_{T} Payer_{t_{i+1},T}$$

2. Then, we compute the distribution of Payment amongst Receiver

With the elements above, we can compute the total performance to be distributed to the receiver side:

$$Receiver_{t_{i+1},T} = D(T) \times Payment_{t_{i+1}}$$

Where

$$D(T) = \frac{\sum_{T} AccrualFactor \times Premium(X,t_{i+1},T) \times Notional_{Receiver,T,t_i}}{AccrualFactor \times Premium(X,t_{i+1},T) \times Notional_{Receiver,T,t_i}}$$

3. Finally, we can compute the Accrued Yield for each term:

$$AccruedYield_{t_{i+1},T} = \frac{Receiver_{t_{i+1},T}}{Notional_{Receiver,T,t_i}}$$

Example:

We have the following positions:

Term	Short	Long
1D	100,000	100,000
1W	65,000	50,000
2W	40,000	40,000
3W	25,000	75,000
1M	0	25,000

Total Short Positions = 230,000

Total Long Positions = 290,000

Let’s assume the following market parameters (we assume same volatility for all tenors) for a fixing period of 5 minutes:

Data	t	t + 5 min
Spot	3,600	3,580
Volatility	30%	32%
Forward Yield	10% p.a.	10% p.a.

Strikes at t (in this case, forward yield being positive, we have adjusted the strikes for the Calls, then we looked for put strikes such as Call = Put):

Term	$$K_{t_i,T}$$	$$K_{t_{i+1},T}$$
1D	3,600.986	3,581.177
1W	3,606.904	3,588.239
2W	3,613.808	3,596.478
3W	3,620.712	3,604.717
1M	3,629.589	3,615.310

Values of Premia at t + 5 min

Term	Calls	Puts
1D	0.4258%	0.9759%
1W	1.5126%	2.0290%
2W	2.2506%	2.7281%
3W	2.8190%	3.2579%
1M	3.4241%	3.8138%

Since spot went down, Long side (i.e. calls) pays the Short side (i.e. the puts); the average performance to be paid is: 1.4230%

The performance by term:

Side	Term	1D	1W	2W	3W	1M
Short	D(T)	75.7523%	14.8145%	6.2616%	3.1716%	0%
	Receiver	3.543	0.693	0.293	0.148	0
	Accrued Yield (in bps)	0.354	0.107	0.073	0.059	0
Long	Payer	3.389	0.503	0.271	0.404	0.110

Note: Accrued Yield seems small but it corresponds to the 5 minutes accrual. E,g, for a 1D term on the short side, 0.272 bps is equivalent to 0.783% return over 1D.

When users select a term for their staking position, users commit to remain in the position for a minimum period of time. This feature has been implemented to ensure more stable liquidity profiles in the pools and for other users. Nobody wants to see users going into a 1 day position and exit the position after 5 minutes.

Furthermore, if a user exits the position before the term, and if this user is generating profit on the position, it is not fair to let the user leave with the full benefit since he didn't remain in the position for the expected period of time, and his/her revenues may not be reflecting the real income at the period end.

Note that the one-off, fixed, penalty depends on pools and can be changed over time. Penalty rules can also be changed over time.