Constructing Crypto Yield Curves Beyond Perpetual Funding Rates

# How would you build a yield curve for a cryptocurrency with only a perpetual futures market?


# How would you build a yield curve for a cryptocurrency with only a perpetual futures market?












Assuming that hourly/daily funding rates are autocorrelated and revert to a long term mean, then perhaps the following would work:

Use the average of the last N day funding rate as as predictor of the next N day funding rate. Sample a few points and use that to build the curve.

Any other ideas?

## Answer by ThatDataGuy (score 1)

https://quant.stackexchange.com/a/73491

Building a yield curve is about trying to understand the market's perception of risk and it's relation with time.

Typically, you need sample funding rates at different tenors. Some fairly simple calcs are then used to create consistent rates that can be plotted. You shouldn't need any assumptions or predictors about how rates evolve over time.

In other words, building a yield curve is about describing the market's term structure at a point in time, not it's evolution.

## Answer by Hamish Gibson (score 0)

https://quant.stackexchange.com/a/77309

This is an interesting question, and definitely something which is currently unanswered in the Cryptocurrency ecosystem.

Let's go back to basics for a second and think about what a yield curve is. A yield curve is a graphical representation of interest that can be earned for different terms to maturity.

The curve itself is built using a range of debt instruments. From RFR Futures and FRAs on the short end, to bonds and swaps on the longer end of the curve. Other money market instruments are also used in construction of this curve. These debt instruments reference some kind of underyling benchmark or index, such as SONIA, and formerly LIBOR.

The fiddly part is that, to my knowledge, there doesn't exist a 'money market' per se for Cryptocurrency. This is an unintentionally by design, as we do not have a centralised monetary authority dictating interest rates for Cryptocurrency. Therefore, we have no concept of a risk-free rate or interest rate index for Bitcoin.

With that in mind though, we may as well try.

Back to OP's original point, I don't think that using the funding rates on perpetual futures serve much use. The funding rate is merely a mechanism used to ensure there is no basis between the Spot price and the Future price. The funding rate is not a deposit, it is what you earn (or pay) as a result of entering a perpetual futures contract. It is merely a vehicle to converge the Future price to the Spot price.

On the other hand though, there are debt instruments that exist on exchanges. Whilst highly unregulated, and subject to counterparty risk, exchanges such as Binance and Kucoin allow you to deposit Crypto assets and earn an income on them through lending mechanisms. The exchange handles the issuance of funds to margin traders, who have borrowed from lenders like you and I. You can 'lock' your funds in such a lending mechanism for different length tenors too. Some range from 7 days up to 28 days. Whilst this would be a stunted yield curve, it nevertheless allows you to examine interest rates over time for a given Cryptocurrency.

More promising, is the growing ecosystem of DeFi. Smart contracts have brought the most primitive and liquid instruments to a decentralised network, that being dollar-backed stablecoins in the form of ERC20 tokens. Smart contracts have evolved to create mechanisms that allow users to earn interest income on assets.

For example, DEXs. Users on a DEX do not trade on an orderbook, they trade against a pool of available funds for a particular pair in a liquidity pool. Users who lock away their funds in this pool earn a reward through a process called yield farming. These funds can be locked away for a range of tenors, with the rate increasing the longer the funds are locked away for. However, I'm sceptical of this method as the rewards are also a function of liquidity, imbalance in the pool, and users are open to impermanent loss.

The most obvious example would be ETH-staking. Users lock away their Ether to validate the network, earning rewards for validating blocks in the meantime. I would not be surprised to see if Futures on staking rewards begin to appear over the coming years as a hedge for validators.

Moreover, the creation of smart contracts offer a chance for users to enter a plethora of OTC Derivatives via a bilateral deal. The contract is transparent, visible, and highly customised. The issuance of funds is controlled by the code itself and cannot be tampered with once deployed. As all transactions are visible, and every derivative trade can be seen, data availability would be global. An issue I see here though is counterparty risk, suppose one party is massively out of the money and there aren't enough funds to pay the counterparty? What happens then?

These are merely my own ideas of how you could construct a yield curve. I'm more than interested to hear others.

## Answer by user68819 (score 0)

https://quant.stackexchange.com/a/77321

Haven't read the answers above..for a yield curve you need lend or borrow rates at different terms. In crypto their used to be term lending markets on some defi protocols like compound and aave.

The complexity here being that they had different levels and types of collateral for certain tokens. In a yield curve the credit or collaterlaistion of the loans or instruments should be harmonised, so that at least on that curve you are comparing similar credit instruments else you have a whole combination of different Premia which you are implicitly comparing.

## Answer by Anouer Bhy (score 0)

https://quant.stackexchange.com/a/81378

I attempted to construct the yield curve for BTC by assuming that spot prices are discounted futures. For example, Deribit uses futures to price options with the same maturity. Assuming the future price is a discounted spot price, we have the relationship:

$F = S e^{(r - q) \times T}$

Following FX conventions, $r$ represents the risk-free rate, such as the US Treasury rate, while $q$ corresponds to the BTC rate. By inverting this equation and interpolating the obtained data, one can construct a crypto yield curve.

If the data lacks explicit future prices (as is the case with exchanges like Binance), I extract the implied forward price that satisfies call-put parity from option prices and repeat the same process. I believe my method is valid, given a set of assumptions.

Empirically, using this method, I find the crypto yield to be negative across maturities. However, I am uncertain whether this outcome indicates a flaw in the method or reflects an intrinsic property of the crypto markets that results in such behavior.