Stability Mechanism

How do we achieve a USD denomination of our perpetual bonds?

OPB is a dollar-denominated perpetual bond. When the collateral is hedged in a delta-neutral manner, the position is stable in dollar terms. This position is then tokenized as OPB, and yield payments are made directly to the token holders.

This means that users who mint or purchase OPB have downside protection on their principal, allowing them to hold a dollar-denominated instrument that continuously accrues value via funding rate yield.

What does Delta-Neutral mean?

A delta-neutral trading strategy means that a trader has no exposure to the price movement of a particular asset. The trader is long and short at the same time, cancelling out any P&L in either direction.

Example: When you own one Bitcoin valued at $10,000 and borrow another to sell for the same amount, you hold one Bitcoin and $10,000, and you also owe one Bitcoin. If Bitcoin's price rises to $15,000, your Bitcoin is worth $15,000, and with your $10,000, you have $25,000 total. To settle your debt, you'd buy a Bitcoin for $15,000, leaving you with $10,000 – the amount you started with. This outcome is the same whether Bitcoin's price rises or falls; being long and short simultaneously keeps your initial USD value unchanged.

As the above example shows, the price of the underlying asset can change without affecting the dollar value of the position. The position is always equal to the price at which the position was entered.

Delta Neutrality Using Inversely Priced Perpetual Swaps

Creating delta neutrality by going long on Bitcoin in the spot market and shorting a Bitcoin future introduces significant operational complexities. This is primarily because the prices in the spot and futures markets often differ markedly, necessitating continuous monitoring of the basis. Additionally, price changes require constant re-balancing of profit and loss from the profitable position to the losing one. Moreover, traditional futures have expiry dates, which means one needs to repeatedly re-enter the short position after each expiry. Fortunately, one of the most popular products in crypto trading is the inverse price perpetual swap. This product allows traders to achieve delta neutrality in a single transaction.

Inverse price perpetual swaps are margined in their base currency, as opposed to the quote currency. In the case of BTC/USD, this means the base currency is BTC. Therefore, going short in this context implies that you are simultaneously long and short.

Here is why.

Inverse Price Perpetuals (IPPs) consistently maintain a fixed dollar value, typically $1 per contract. This means to buy or sell a single contract, you must provide a margin of $1. However, since the margin for these contracts is in Bitcoin (BTC) rather than USD, you need to pledge the equivalent of $1 in Bitcoin. For instance, if Bitcoin's price is $10,000, then $1 equals 0.0001 BTC ($1/$10,000). Therefore, you would need 0.0001 BTC to trade one contract at this price level. Conversely, if Bitcoin's price increases to $20,000, the required amount to trade one contract reduces to 0.00005 BTC ($1/$20,000). This illustrates the inverse relationship: as the price of Bitcoin increases, the amount of Bitcoin needed for one contract decreases, and vice versa when the Bitcoin price falls.

Another crucial aspect of IPPs is that the Profit and Loss (P&L) is calculated in Bitcoin. For example, if you hold a short position in an IPP and the price of Bitcoin decreases, you gain Bitcoin. Conversely, if the price increases, you lose Bitcoin. The P&L formula for shorting an IPP can be summarized as follows:

\text{P&L}_{\text{short}} = \frac{n * v}{p_{ex}} - \frac{n * v}{p_{en}} ,

where n is the number of contracts, v is the value of each contract, p_en and p_ex is the entry and exit price respectively. Now say we are shorting 1 contract of an IPP using the $1 per contract example from above. Then v = 1 and n = 1. Assuming the current price is $10,000 then p_en = 10,000.In order to open this position we would need to margin 1 / 10,000 = 0.0001 BTC. Now say the price of Bitcoin falls to $5,000 and we exit our position then our P&L would be 0.0001 BTC=11500011100000.0001\text{ BTC} = \frac{1*1}{5000} - \frac{1 * 1}{10000}.

Together with our initial margin of 0.0001 BTC, which would be released after exiting this trade, our total account balance would be 0.0002 BTC. Since the price of Bitcoin is currently $5,000 in dollar terms, 0.0002 would buy $5000 * 0.0002 BTC = $1.Exactly as much as we started with.

From the example above it becomes clear how one can lock in a dollar value using inversely priced perpetual swaps.

Bringing It All Together

OPB is essentially a token representing a short position in an inversely priced perpetual swap, managed by OpenDelta. For instance, to mint $100 of OPB at a Bitcoin price of $10,000, a user deposits 0.01 BTC (calculated as 100/10,000) with OpenDelta. Subsequently, OpenDelta shorts an equivalent amount ($100) of Inversely Priced Perpetual Swaps (IPPs) on a derivatives exchange. In return, OpenDelta issues the user $100 worth of OPB. To redeem this amount, OpenDelta closes its $100 short position and returns the original margin (0.01 BTC), adjusted by the profit or loss incurred during the position's duration, to the user.

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