*This post is for general information purposes only. It does not constitute investment advice or a recommendation or solicitation to buy or sell any investment, or to issue or trade derivatives, and should not be used in the evaluation of the merits of making any financial or investment decision.*

**TL; DR**

- The x5 leveraged token is designed as an intuitive way to take on leveraged exposure to anything, as long as it has a price feed on Ethereum.
- Starting with ETHx5 and BTCx5, backed by USDC collateral. More instruments to come.
- All CompliFi derivatives come in long-short pairs, and the protocol redistributes a fixed amount of collateral between them to generate returns. More on how this works for the x5 below.
- We explain the distinction between nominal value (derivative’s claim on collateral) and its market price, and how we can value the x5 token by comparing it to a well-known options strategy.

# CompliFi Basics

Before we dive in, here is a reminder of the key features of CompliFi. For a more detailed explanation, please have a looks at our documentation, white papers and other blog posts.

CompliFi is designed as a combination of a derivative issuance protocol with an AMM. The basic flow is as follows. LPs send collateral (currently USDC, but can be any ERC20) to the protocol, which mints their chosen derivative and places it straight into the appropriate AMM pool. Traders can then buy and sell derivatives as they would any other token on Uniswap.

All CompliFi derivatives are minted in pairs – two tokens akin to the long and the short positions. A portfolio that contains both in equal amounts is riskless relative to the collateral, and can be redeemed at any time, even prior to settlement.

Individually, the long and the short position tokens change value as the protocol redistributes the fixed amount of collateral between them depending on what happens to the derivatives underlying variable (e.g. price of ETH).

CompliFi derivatives have a finite maturity. At present, all derivatives fluctuate with the market for a period of four weeks. After that, the derivatives are settled and can be swapped back for the collateral by their ultimate holder at any time.

# The x5 Token in Simple Terms

The x5 token was designed as an intuitive way to get leveraged exposure to any chosen asset with an on-chain price feed. All tokens start off with a nominal value (aka claim on collateral) of 1 USDC. Over the course of its life, the token’s nominal value rises or falls at 5 times the rate of the underlying asset over the same period, but within the corridor of 0–2 USDC.

Let’s consider ETHx5 as an example. The corresponding long-short token pair is ETHx5 Up and ETHx5 Down. The “Up” token multiplies the percentage change in ETH price by 5, and the“Down” token by -5. In other words, a 1% increase in the price of ETH would result in the nominal value of ETHx5 Up rising by 5%, at the expense of a corresponding decline in ETHx5 Down. If ETH falls by 1%, the situation is reversed.

When ETH price hits + or -20%, one of the tokens will have a nominal value of 2 USDC and the other zero. These are the nominal value ceiling and floor — nominal value of an x5 token can never go higher than 2 USDC, or below zero (i.e. you would never receive a margin call).

If you hold a token that’s maxed out on nominal value, but want to maintain exposure to the upside, you could swap it for the same one from a later series (i.e. with a later settlement date). You would thus be crystallising your return on the maxed out token and using the profits to acquire fresh exposure.

# Market Value of the x5 Token

So far, we have been talking about the nominal value of the derivative, defined as the amount of collateral you would receive if settlement occurred right now. Let’s suppose again that you are sitting on a winning token with a 2 USDC nominal value, but you are a week away from settlement. Its value cannot rise any higher, but it could go lower if markets change direction. As a result, you would struggle to find a rational buyer for your position at 2 USDC. However, you would likely find it much easier to sell it at a discount, giving the buyer some nominal value upside to look forward to. This rationale is what gives rise to the difference between a derivative’s nominal value and its market price. Calculating the size of that difference is where things get a little technical.

Ultimately, the market always decides what the value of an asset should be, and each investor may well have their own approach to valuing a derivative. Below, we will give a brief overview of the methodology that CompliFi AMM uses to price the x5 tokens in every block prior to executing any trades.

To begin with, we have observed that the payoff functions of the x5 Up and Down tokens (i.e. nominal value given a change in underlying variable) are identical to some fairly common options strategies – Bull Call Spread and Bear Put Spread, respectively – applied to a hypothetical asset with a price of 5+5*(% change in price of underlying asset). Both of these options strategies have been extensively studied, and much of their intuition carries over to the x5 token. We strongly encourage the reader to take advantage of the wealth of relevant educational materials available on the web.

This is great news, since identical payoff functions mean identical market values. Both of the option strategies comprise a pair of European options — instruments that are quite well understood, and which we could value using the Black Scholes formula with appropriate inputs. Of these inputs, the only tricky one is the volatility parameter of our hypothetical asset with the price of 5+5*(% change in price of underlying asset). However, with volatility defined as the standard deviation of log returns, and we encourage the reader to verify that for any given ETH (or other) price process and any increment within it, the log return values for ETH are identical to those of our hypothetical asset. In other words, our hypothetical asset has the same volatility as ETH.

In summary, valuing the x5 leveraged token boils down to valuing a portfolio of two European options on an asset with a known volatility parameter. Here is what it looks like on a chart for ETHx5 Up (ETHx5 Down follows the same pattern in the opposite direction).

A few important points to note here. First, as derivatives approach settlement, their market value converges to nominal value. In simple terms, if you are a minute away from maturity, it is quite unlikely that the final nominal value (i.e. what you get paid at settlement) will be very different from what it is now, and the market reflects that.

Second, at 0% change in ETH, the ETHx5 Up is priced below nominal value (correspondingly ETHx5 Down is priced above). This is not a mistake, but a property of this derivative. Like the Bull Call Spread and the Bear Put Spread, the x5 would normally be considered “near-zero vega” (vega being the sensitivity of price to volatility of the underlying variable). At volatility levels commonly seen in conventional financial markets, this gap between market price and nominal value would be a rounding error. In the crypto market however, the “near-zero” part starts to matter, and this gap will likely be a regular occurrence for ETHx5 and BTCx5.

Lastly, when nominal value reaches its lower or upper bound, at 0 and 2 respectively, the market price does not. Say you are a week away from maturity and the price of ETH declined by 20% since the start of the Live period. Your nominal value stands at zero, but it only takes a small recovery in ETH to get you back into positive territory, and a whole week for that to happen. It makes sense for an asset like that to have a market value>0.

**As ever, please remember that decentralised derivatives are an early experimental product. Even if you have a solid fundamental understanding of financial engineering (which you absolutely should have to even consider committing capital to such instruments), you may still lose money for any number of reasons. As a rule of thumb, please assume that you will lose all of the capital you put in.**