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Understanding the Application of Greeks Symbols to Tech and Finance in Crypto

Being at the intersection of technology and finance, crypto has inherited the illustrious vocabulary of wall street traders, computer scientists, and degens; of course, while putting its own unique spin on things.

The longer you stay involved in crypto, the more likely it is for you to encounter a model of conversation that has been heavily influenced by one of the oldest and (IMO) most influential societies in human history, the Greeks. 

Full of mythology that captivates our imaginations with majestic gods, mythical creatures, and stories of heroes overcoming extreme difficulties, the Greeks have passed down timeless wisdom that has made its way into the language of modern man.

As it pertains to legacy finance, symbols from the Greek alphabet have been used to express certain “meta-metrics” that relate to options. Options are exotic instruments that allow investors to gain abstract forms of exposure in their portfolio, namely as a right to purchase an asset without being obligated to execute the purchase of it.

As it relates to technology, those same Greek symbols have been used to describe stages of product development (this applies far beyond and before crypto). 

So let's take a look at some of these ancient symbols in our modern world.

Α — Alpha — α

This one has a few different meanings depending on the context within which it is used and the group that is using it. 

The most widespread use of the term “alpha” in crypto is to express the possession of superior knowledge about a market. Information that nobody else has realized/accessed gives you an edge in terms of how you play it. 

A simple example would be that while everybody is buying a token on some hype marketing campaign, you know that an unlock is scheduled to happen soon and you short it instead.

Alpha can also be used to describe the first stage of a product that is released to the public. Sometimes projects will say things like “private-alpha arriving soon” or “alpha access to the earliest community members now available” and the such. Ultimately, the alpha phase comes right after MVP and right before Beta (oh look another Greek letter).

The traditional financial definition of Alpha is the return on your investment that supersedes the return of benchmark indexes. If the S&P increased by 7% last year, but your portfolio increased by 9%, then your strategy has an alpha of 2%. 

β — Beta — β

This term is almost never used in the financial circles of crypto but is always prevalent in the technical sense.

“Beta” is used to describe a certain phase of a product's development that has already passed rigorous internal testing and controlled groups of public testing. The phase comes right after “Alpha” and before mainnet.

In relation to the financial side of things, “Beta” is just a fancy word used to express the innate volatility of a portfolio or individual security in relation to the general market. 

If the Beta of the S&P is 1.0 and your portfolio has a Beta of 1.5, then your portfolio is more volatile than the S&P. The Beta metric itself is neutral, it is just a read on divergence in fluctuations of price. So something that moves ~1% up/down per day is “stable” at 1.0 Beta, and something that moves ~10% per day is “volatile” at >1.0 Beta. 

As you might already begin to be able to deduce, the Beta marker of Bitcoin and other crypto’s are much higher than 1.0 because their prices move much faster and in bigger swings than traditional assets like the S&P.

Δ — Delta — δ

An airline company. Just kidding. 

Another term with multiple meanings based on context and group. Not very common in crypto, I have only ever heard “delta” actually be used by a few macro traders and select giga-brains in the space. Unlikely to find this just floating around the empty echo chambers of Twitter chats.

Delta is a term that is commonly found in the business world as a way to measure the potential returns available to them as a result of exposing some kind of market inefficiencies. It is a simple measure of the profit that can be generated via a specific business model.

Imagine you want to sell shampoo. The production costs you $2, you sell it for $20 per bottle, the total addressable market size is 1,000,000 buyers, and the purchase velocity is 1 bottle every 2 months. Under the perfect assumption that you capture 10% of the market (100,00 buyers) that buy your shampoo 6 times per year, means you will sell 600,000 products and your expected income will be $12,000,000 (100,000 x 20 x 6). Of that $12,000,000 your cost of goods it $1,200,000, leaving you with a profit of $10,800,000. That profit is the delta. You can now use that delta to carve out a marketing budget and accordingly plan other expenses such as hiring.

Within the context of options pricing, delta is a measure of the price's rate of change is relation to the rate of change in the underlying asset price. 

So if a stock is priced at $100 and an option if priced at $5 and when the stock rallies to $110 the option follows to $5.50. The rate of change for both is evenly 10%. However, the actual measurement gets slightly more complex when accounting for the time delay. If the Stock rally happens over the course of 24 hours, but the option price adjusts over the course of 48 hours, then the delta is slightly different. As a rule of thumb, a delta of 0 means that options move in tandem with their underlying assets. 1 or -1 means that there is some kind of large notable delay or gap in the options pricing.

Θ — Theta — θ 

The only time this term has come across any conversations in crypto has been regarding the crypto project that carries the name Theta Network (THETA).

In the world of options, theta measures the impact of time on an options price, more specifically the decay in value.

Options are priced in respect to their underlying assets, as well as, their time to expiry. The closer an expiration the sharper the price decay, the more theta the option has.

Let's look at a simple example with a Binary option. 

Say the price of $BTC is currently $25,000. If I buy a Binary option at $50 that expires in 30 days betting that the price of $BTC will be above $26,000. My maximum payout is $100 and my maximum loss is $50. For the first few days of being in that position, the price of the option will be correlated more tightly to the price of $BTC than it will with anything else. So if $BTC spikes to $26,000 my option immediately becomes more valuable. However, as the days go by and if $BTC doesn’t change in price, the option will begin to be less and less impacted by the spot price of $BTC and become more sensitive to the amount of time remaining for that option. All things being equal, assuming $BTC remains at $25,000, then the option I have will begin to lose value at an increasing rate. 
7 days out the price of the option might fall from $50 to $48.
6 days out it falls to $44
5 days out it falls to $38 
4 days out it falls to $31
3 days out it falls to $23
2 days out it falls to $12
1 day out it falls to $1

That acceleration in price depreciation relative to the time is called Theta.

Γ — Gamma — γ

I have personally never heard this be used anywhere at all, ever, in crypto.

In TradFi, gamma is a meta-meta metric, a second degree of deviation off from direct relation to the spot asset. (yes, that's two, metas). Gamma is a measurement that relies on another measurement in order to be calculated, namely the Delta.

Delta, within, in, and of itself, is already a measurement of the deviation in an asset price and its option. Gamma, measure the rate of change in the Delta, in relation to the underlying asset price.

The major use of gamma is to establish the neutrality or sensitivity of a portfolio’s hedge.

Ρ — Rho — ρ

Incredibly rare to come across in finance in general, Rho is a metric used in TradFi that represents the sensitivity of an Option’s price relative to interest rates. 

This terminology has only shown up in the intellectual wastelands of Whitepapers and scholarly discussions that are way over my head.

While this is not used in crypto, at least at the retail level, It shouldn’t be too difficult to apply this.

It would just basically measure the relationship between Bitcoin’s price action and the actions of interest rates. Specifically using the interest rates as the leading factor and seeing how Bitcoin options react.

So if interest rates go up, how do the $BTC options move? If for every 0.25% increase in interest rate, the $BTC option goes up by 5%, then we know Jerome Powell is sh*t out of luck and Elizabeth Warren is gonna have a seizure when she sees this. 

But in all reality, the RHO measurement of that kind of ratio would be some odd 0.05. 

*Quick note, RHO is peaking when measuring options with longer times to expiry. As the timeframe gets shorter, the RHO falls.

Ν — Vega — ν

Another metric that is a second degree of deviation away.

Vega measures the rate of change, specifically in the premium, of an options price as it relates to the volatility of the underlying asset.

Imagine $BTC is $50,000. An Option is $5,000, but is trading on second-hand markets for $7,500. The spread of $2,500 is the premium that will be measured by Vega. While the price of $BTC is floating around $50,000, with tiny fluctuations in price of $1,000 intra-day (2% of the spot price), the Vega will be floating around 0.01 to -0.01 because the options price will likely not change. If BTC begins getting volatile with sharper price movements and that premium begins to shrink to $1,500 then the Vega will adjust accordingly. Ex. $BTC price starts jumping $2,000 intraday (4% of the options spot price) then the Vega will become -0.1 (10x relative to the 2x in volatility due to the amplification by the premium devaluation).

Here we just covered seven of the more widely used Greek symbols, but there are a few more that I have never interacted with or heard of anybody else using (vomma, vera, zomma & ultima). If you know what they are, I’d love to learn from you.

This was intended to be as light-hearted and educational as possible. 

I hope you enjoyed it and were able to extrapolate a few nuggets of knowledge that will help you navigate your journey through the wild world of digital finances and Web3.

Live long and prosper 🥂