A Word of Warning
This article assumes familiarity with standard derivatives concepts: Futures pricing, Options valuation and Greeks (particularly Delta), and the mechanics of Cash-and-Carry arbitrage. If you are new to derivatives trading more broadly, it would be worth building that foundation first. The discussion that follows is aimed at traders who already know their way around a derivatives market but are encountering Deribit's specific contract design for the first time.
Deribit Keeps Its Books in Crypto
The central and most important point to grasp from the outset is this: Deribit denominates all P&L and margin in cryptocurrency, not in US dollars. This is a deliberate architectural choice, not an oversight, which has cascading consequences for every product on the exchange. Before diving into the mathematics, it is worth setting the context. On most derivatives exchanges — supporting financial products or commodities — contracts are quoted in a fiat currency (typically USD). For example, a CME Bitcoin Future is quoted and settled in US Dollars. This is intuitive for anyone whose mental accounting is anchored in fiat terms. However, Deribit took a different view and eliminated all reliance on fiat currencies by using crypto as sole unit of account. It is a crypto maximalist solution that creates complexity for anyone who is accustomed to thinking in USD terms, and that complexity impacts on how futures and options positions behave.
Futures
How Standard Crypto Futures Work
On most exchanges, a Bitcoin Future contract is quoted in USD per BTC, and you specify the size of your position in BTC. If you buy one BTC worth of futures at 50kUSD and the Future price rises to 55kUSD, your P&L is simply 5kUSD, expressed and settled in USD. The quantity and price are in BTC, and the P&L flows naturally from the multiplication of the two. This is a linear, easy-to-follow structure, which most derivatives traders are familiar with.
How Deribit Futures Work: The Inverse Structure
On Deribit, the contract structure is inverted. The quantity of a Futures position is expressed in USD, not in BTC. You are not buying 1 BTC worth of Futures but rather 50kUSD worth of Futures. The price, however, is still quoted in USD per BTC. This immediately raises a question: if both quantity and price are in USD, how does the exchange create a purely Crypto P&L? The answer is that the settlement mechanics introduce the inverse of the price.
To see this precisely, let us establish some notation. Let $X_T(t)$ denote the price of a Deribit Future contract observed at time $t$ for a contract expiring at time $T$. This is quoted in USD per BTC, just as you would expect. We will also use $X(t)$ to denote the Spot price of BTC in USD. When you enter a Futures position, the entry price is $X_T(t_0)$, where time $t_0$ represents the moment of trade.
The P&L of holding $Q$ USD notional worth of a Deribit BTC Futures contract, expressed in BTC, is:
$$ P_{\text{BTC}}(t) = Q \left[ \frac{1}{X_T(t_0)} - \frac{1}{X_T(t)} \right] $$
This formula is the heart of the inverse structure. The P&L is not computed by subtracting prices, but by subtracting the reciprocals of prices, and then scaling by the USD notional. More than an algebraic curiosity, it is the mechanism by which the P&L is kept in BTC. If the Future price rises, $1/X_T(t)$ falls, the bracket becomes positive, and the position is in profit as expected from a long position.
To convert this into USD terms, you simply multiply by the current Spot price:
$$ P_{\text{USD}}(t) = Q \left[ \frac{1}{X_T(t_0)} - \frac{1}{X_T(t)} \right] X(t) $$
This is the formula that determines what your position is worth in US Dollars at any point in time, even though the exchange is tracking it in BTC.
A Worked Example
Suppose you go long 100kUSD notional of a BTC Futures contract at an entry price of 50kUSD. One week later, the Future price has risen to 55kUSD. Your BTC P&L is then:
$$ P_{\text{BTC}} = 100 \left[ \frac{1}{50} - \frac{1}{55} \right] \approx 0.1818 \text{ BTC} $$
Assuming the Spot price has moved from 47.3kUSD to 52kUSD that final 0.1818 BTC is worth approximately 9.45kUSD. But compare this with what you would get with a standard USD-settled contract, you can calculate a discrepancy: (100 / 47.3) x (55 - 50) = 10.57kUSD.
The USD Delta: Why It Matters
For a trader managing a portfolio across multiple instruments, the most practically important quantity is the Delta of the position i.e. how much does the USD value of the position change as BTC moves? To compute this, we differentiate $P_{\text{USD}}$ with respect to $X(t)$:
$$ \frac{\partial P_{\text{USD}}}{\partial X} = \frac{Q}{X_T(0)} + \frac{Q}{X_T(t)} \left[ \frac{X(t)}{X_T(t)} \frac{\partial X_T}{\partial X} - 1 \right] $$
The second term in this expression might look alarming, but it collapses to zero as a consequence of cash-and-carry arbitrage. What remains is elegantly simple:
$$ \frac{\partial P_{\text{USD}}}{\partial X} = \frac{Q}{X_T(0)} $$
In plain English: the USD Delta of a Deribit Future position is equal to the USD notional of the position divided by the entry price — which is simply the amount of BTC the position represented at the time of the trade.
This is a crucial insight for delta hedging. If you buy 100kUSD of BTC futures at 50kUSD, you have a delta of exactly 2BTC at inception. That delta is fixed at entry — it does not change as BTC moves which is the same behaviour seen on USD denominated Crypto Futures.
Options
Forward Settlement in Crypto
Deribit's options on BTC and ETH are forward-settled in the underlying cryptocurrency. This is another point of departure from options market conventions which typically require the option premium to be settled at inception. On Deribit, no capital changes hands at the time of the trade. Instead, the value of the position is tracked in the underlying cryptocurrency throughout the life of the option, and settlement happens in crypto at expiry or position closure. This approach is consistent with Deribit's broader philosophy of keeping everything in crypto terms but it introduces a subtlety in how you compute the USD value of an options position.
The USD Value of an Options Position
Let $V_{\text{USD}}(t)$ denote the current USD value of the option itself. Let $V_{\text{ETH}}(t_0)$ denote the value of the option in ETH at the time of the trade — this is the premium that will eventually be settled.
The USD P&L of holding the options position can be written as:
$$ P_{\text{USD}}(t) = V_{\text{USD}}(t) - V_{\text{ETH}}(t_0) \cdot X(t) $$
The first term, $V_{\text{USD}}(t)$, is simply the current mark-to-market value of the option in USD. The second term, $V_{\text{ETH}}(t_0) \cdot X(t)$, represents the dollar cost of the crypto you implicitly owe as premium, revalued at the current spot price. As spot rises, this liability grows in dollar terms, which is what the subtraction captures.
The Delta of an Options Position
Differentiating the P&L expression with respect to the spot price gives the delta:
$$ \frac{\partial P_{\text{USD}}}{\partial X} = \frac{\partial V_{\text{USD}}}{\partial X} - V_{\text{ETH}}(t_0) $$
The first term, $\frac{\partial V_{\text{USD}}}{\partial X}$, is the Delta of the USD-valued option expressed in ETH. The second term is a constant correction factor equal to the option premium expressed in ETH at the time of entry.
In summary: the USD delta of a Deribit Option position is the Delta of the USD-valued Option corrected by its ETH-denominated entry price.
This correction term is easy to overlook but important in practice. It means that the effective delta of your options position is slightly lower by a fixed amount which depends on how expensive the option was at entry. For long dated at-the-money options, this correction can be significant.
Summary
Deribit is a sophisticated exchange that has made a coherent and principled set of design choices: to keep the entire portfolio denominated in cryptocurrency, to use inverse contract structures for futures, and to forward-settle options in crypto. These choices serve a real constituency of crypto-native traders who think in crypto terms. For anyone coming from a more traditional derivatives background, these choices introduce complexity that must be understood before trading.
The key takeaways are:
- Deribit Futures are inverse contracts: quantity is in USD, P&L is in crypto, and the USD delta is fixed at the entry price.
- Deribit Options are forward-settled in Crypto: the USD delta of an options position is the USD denominated option delta minus the ETH-denominated entry price of the option.
- Capital held in Crypto adds USD exposure: Do not forget that the Crypto hodlings used as trading collateral for margins should be added to the total position delta.
These features make Deribit a true Crypto derivatives exchange which still provides the necessary tools for USD based traders to operate efficiently. Armed with the key knowledge presented here, derivatives traders can now approach trading on the exchange with a little more confidence.
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