What's a "Delta"?

Although UXD is no longer backed solely by a "delta-neutral" position, the delta-neutral strategy has proven itself to be resilient across market cycles and will remain a key part of the UXD stablecoin.

But what is a "delta"?

Delta, as in the Greek letter δ\delta, is one of the most fundamental concepts in the field of financial derivatives. But what's a financial derivative?

Financial Derivatives

tl;dr: A financial derivative is a bet between two parties that references an underlying asset without having to own that asset.

Taking a step back, a financial derivative is a way of betting on the price of another thing (asset) without having to own that thing (asset). For example, if I bet you $10 that the price of Tesla stock will double next year, then we've just created a derivative contract between you and me. Neither of us needs to own Tesla stock in order to make this bet, but we are referencing another asset in our bet- Tesla stock. In other words, our bet derives its ultimate outcome from the referenced Tesla stock, hence the whole bet is named a derivative. At the end of 1 year, you and I check on the price of Tesla stock. If it's doubled, you give me $10 and if it hasn't, I give you $10.

More common derivatives may be familiar to users of stock trading apps, such as Call and Put Options. Options are derivatives on the referenced stock. When you enter into an options contract, someone else takes the opposite side of the bet and you both agree to settle your bet by referencing the value of the underlying stock.

The thing referenced by a derivative is called the "underlying" asset in financial terms.


tl;dr: A "delta" is the amount a derivative's price changes as the referenced underlying asset changes in price.

Now that we understand what a derivative is, we need to understand a bit about derivatives pricing. Derivatives themselves can also be traded and exchanged between people. What exactly does that mean?

Returning to the example from the previous section, suppose it's January 1st, 2022 and you and I bet that by January 1st, 2023 the price of Tesla stock will double. If it doubles, you give me $10, if it doesn't double, I give you $10.

Let's say 9 months pass by, and I want to exit this bet for whatever reason. You say "no, we had a deal" or "you signed a contract on a napkin", etc etc. I offer you a solution: what if my friend Bob takes my place in the bet, so that the bet will now be with him instead of me. You agree, because you don't really care who the bet is with as long as the bet still holds.

Now I call up Bob and ask him if he's interested in entering the bet instead of me. He says sure. Suppose, however, that in the 9 months since the bet started, Tesla stock price has gone up 95% and therefore has almost doubled. Bob realizes if he enters this bet he will probably win given how the stock has performed, so he may even be willing to pay me to enter this bet. I myself realize that there's a really good chance Bob makes $10, so I tell him he can enter the bet if he pays me $5. Bob agrees because he is pretty certain Tesla stock will go up more than the remaining 5% over the next 3 months.

So what has happened here? Bob paid me $5 to take my place in a $10 bet that Tesla stock doubles by January 1st, 2023. Tesla stock has gone up 95% already, so by paying me $5, Bob is essentially betting $15 ($5 paid + $10 potential loss) that Tesla will go up that last 5%, in order to make $10. From your perspective, nothing has changed. Your bet is now with Bob instead of me, but that's the only difference.

The $5 Bob has paid me is the derivative price. It represents the price someone would be willing to pay in order to enter the bet in my place. Actual pricing of derivatives, such as through Black-Scholes, is quite mathematically complex but the basic ideas are pretty simple. What factors would influence how much someone is willing to pay to enter the Tesla stock bet? For example:

  1. Time until the bet is over- If today is December 31st, 2022 and the price of Tesla stock is four times the price it was on January 1st, 2022 then it is very very likely that the price the following day will be at least two times the price it was at the beginning of the year, because it is unlikely the stock goes down more than 50% overnight. So, a rational derivatives price would be very very close to $10, say $9.95. On the other hand, if it's month 3 (9 months of the bet remaining) and the price is four times the price at the beginning of the year, it seems somewhat likely that the stock will be above the two times bet price by the end of the year. But, this extra 9 months introduces some uncertainty, changing the confidence of winning the bet from very very likely to somewhat likely, so a rational derivatives price would be somewhat close to $10, say $7. Note the price of the Tesla stock is the same in both cases, what has changed is the time until the bet is over, which changes the derivative price.

  2. Price of the referenced asset- Regardless of the time until the end of the bet, the derivatives price will depend on the price of Tesla stock at any given moment. Suppose it's 6 months into the bet (6 months remaining). If Tesla stock is up ten times in this 6 month period, I can be pretty confident that I will win the bet, so someone might be willing to pay me $9 to take on this bet. If Tesla stock was down 99% from the beginning of the year, it would be very unlikely that I will win the bet so someone wouldn't be willing to pay me anything. In fact, I'd have to pay someone almost $10 to take the risk. Note the time to the end of the bet is the same in both cases, what has changed is the price of Tesla stock.

  3. Volatility of the referenced asset- Volatility refers to the amount up or down an asset will typically move in a defined time period. For example, gold's volatility is usually pretty low, because the price fluctuates pretty slowly. Bitcoin's volatility is usually pretty high, because it can double or halve in short period of time. Suppose hypothetically that Tesla stock was a very very low volatility asset and in its entire history has only ever gone up or down 2% annually. The price never changes much. Then, a bet that Tesla will double is not very likely, because it doesn't usually change price that much. So, the derivatives price of this bet would be low. On the other hand, if hypothetically Tesla stock often moves by 10% per day, it seems much more possible that Tesla could double over a year. So, the derivatives price of this bet would be much higher.

To summarize, we've defined what it means for a derivative to have a price, and some of the basic variables that might influence that price. But getting back to the original question: what's a delta? A delta is the amount a derivatives price changes depending on the price of the underlying asset. For example, a delta of 1 means that for every $1 the underlying asset moves, the derivatives price changes by the same $1. A delta of 0.5 means that for every $1 the underlying asset moves, the derivatives price changes by $0.50. It's the second variable explained above, "2. Price of the referenced asset". Delta is one of the fundamental ways to think about how much a derivative is worth, through the lens of the price of the underlying asset, everything else equal.

Practical Uses of Delta, Delta-Neutral

tl;dr: A derivative is Delta-Neutral with respect to an asset if the derivative's price does not change when the asset's price changes.

Derivatives traders often talk about their exposure to an underlying asset in terms of "Delta". You might hear someone say they have "10 Delta" exposure to Bitcoin. This is a measure of their exposure to the price of Bitcoin. All else equal, having a 10 Delta exposure is essentially similar to owning 10 Bitcoin. Of course, there are different ways to get Delta exposure. You could simply buy 1 Bitcoin and hold it to get 1 Delta of exposure, or you could buy a call option on Bitcoin, which would have some implied Delta (say, of 0.75 Delta). The important point is that understanding your "Delta exposure" helps you understand how much the value of your portfolio should go up or down as the value of the underlying asset goes up or down. A position is said to be "Delta-Neutral" with respect to some asset if the value of the position does not depend on the value of that asset, i.e. 0 Delta exposure. An obvious example: if the value of my house doubles, this probably does not change the value of our bet on Tesla stock (other than through some correlation like the economy doing well), so our bet on Tesla stock has 0 Delta and is Delta-Neutral with respect to my home price.

Now that you understand what a "Delta" is, see our section on Delta-Neutral Position to understand why this concept is important to UXD.

For those of you comfortable with calculus, if we define PP to be the price of the derivative and SS to be the price of the underlying asset (the Tesla stock), then delta, δ\delta, is defined as δ=dPdS\delta = \frac{dP}{dS}, the mathematical derivative of PP with respect toSS.

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