27 February 2019

The Lightning Network Reference Rate & Bitcoins Derivative Pricing

Patrick Heusser

Patrick Heusser

CEO at Crypto Finance (Brokerage) AG

About the author

Authors: Maximilian Boelstler (Research Assistant), Lewin Boehnke PhD (Head of Research), Patrick Heusser (Senior Trader)

Download The Lightning Network Reference Rate (LNRR) & Bitcoins Derivative Pricing Research Report PDF


“People far too often associate derivative markets with mere speculation, but there are very legitimate businesses that need derivatives to protect themselves against risk.”

         – Fred Ehrsam, Co-Founder of Coinbase


Bitcoin derivatives are relatively new, especially when compared to traditional derivative products. While doing research for our last paper on Bitcoin’s Lightning Network, we detected that there is a possibility of earning interest without counterparty risk. We put our heads together to ponder this interesting idea, which raised the question of how derivatives on Bitcoin are actually priced since no base rate is available. We conducted a quantitative analysis by calculating the implied interest rates of Bitcoin futures with different maturities. The results revealed that there are some similarities with the borrowing and lending rates that are used in the digital asset ecosystem. An additional thought experiment about the pricing of Bitcoin futures using the Lightning Network Reference Rate showed that this rate might serve as Bitcoin’s base rate and thus increase transparency in the pricing process.

As already pointed out above in the quote by Fred Ehrsam, the co-founder of the digital currency exchange company Coinbase, derivatives do not only serve a speculative purpose. A derivative is a contract, which derives its value from the performance of an underlying. In traditional banking, this kind of product is widely used for hedging purposes, resulting in a situation where the market capitalisation of derivatives is around 8 times greater than the equity market capitalisation, and around 2 times greater than the debt market capitalisation.

Forward and futures contracts represent a subset of these financial instruments, allowing market participants to offset or assume the risk of a price change of an asset over time. On December 10, 2017, the Cboe Futures Exchange, LLC (CFE) launched the first regulated Bitcoin Futures under the ticker symbol “XBT”. According to their factsheet, “XBT futures are U.S. dollar-denominated, cash-settled futures contracts that are based on the auction price of bitcoin on the Gemini Exchange”.

In the meantime, several futures for Bitcoin and even Ethereum are available. Cboe and the CME Group predominantly offer futures contracts for institutional investors, whereas Deribit, BitMEX, and Crypto Facilities (CF) also provide a selection for private investors. Interestingly, all platforms determine futures prices that are quite similar, despite the fact that no risk-free interest rate or base rate for Bitcoin is available. If we classify Bitcoin as a commodity, such as the US Commodity Futures Trading Commission does – they have also declared virtual currencies as commodities – the question arises as what implied interest rate curves are being used for the pricing?

Taking into consideration that the Lightning Network[1] is continuously growing and becoming more stable, the possibility of earning risk-free interest on Bitcoin deposits might be addressed in the wake of Bitcoin’s derivative pricing. For analysing this idea and its potential impact, this paper is structured as follows: first, we will address the analogies between the interest rates in traditional markets and the Lightning Network Reference Rate (LNRR) in the digital asset market in order to establish a general understanding. We will then look at the current pricing of Bitcoin Futures to provide both an overview and a comparison of the implied interest rates used. Finally, we will conduct a thought experiment to determine the impact on the Bitcoin Futures using the LNRR – carried out under specific assumptions.

The Lightning Network Reference Rate  and Traditional Interest Rates

In traditional banking, we believe in interest rates determined by the treasury curve, the LIBOR curve, and the OIS curve – whereas the last one is commonly used for determining the fair market value of a collateralised investment or the pricing of derivatives. A visualisation of the OIS curves of the USD and the EUR (EONIA[2]), retrieved from Bloomberg on February 8, 2019, can be found in Fig. 1. As can be observed in Fig. 1, rates may differ significantly from one country or economic area to another. Overall, the determination approach is based on a closed and non-transparent network of participants

Figure 1: Comparison of USD OIS Curve and EUR OIS Curve
Source: Bloomberg (February 8, 2019)

An interest rate is generally defined as “the amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets. Interest rates are typically noted on an annual basis, known as the annual percentage rate (APR)”. Central banks use interest rates also as a control instrument of their monetary policy. For instance, the decreasing of the interest rate could increase the demand for loans, thus increasing the purchases, and, ultimately, stimulating the associated economic growth. Because an interest rate might be such a powerful instrument, a central institution takes charge of its determination. E.g., the ECB in Europe and the FED in the US.

In wake of the Lightning Network, the idea emerged of the “technological” determination of interest rates – a peer-to-peer based interest rate for Bitcoin. As mentioned in our last report, one property of the Lightning Network is the “free choice” of the transaction path. Since every default setting of a Lightning application generally selects the cheapest path due to the routing algorithm employed, the channels, which are not in line with the fees of the great majority, will never be actively used. The market chases efficiency.

Even though the LNRR might not be used as a control instrument to accelerate/decelerate economic growth, a participant-based interest rate does allow the determination to be based on demand and supply in a more transparent manner. This rate also allows investors to measure their opportunity cost of Bitcoin. Thinking one step further, the risk-free LNRR might have an impact on the price determination of Bitcoin derivatives as the opportunity cost of Bitcoin becomes measurable.

Within this context, most readers will now start thinking about the risk-return relationship of traditional assets, and what is more, the question of why we actually consider the LNRR as “risk-free”.

Here’s a counter question: have you ever thought about the risk-return relationship of digital assets?

The Risk-Return Relationship of Digital Assets

In traditional markets, financial risk is defined as the variance or standard deviation of an asset’s returns. Debt instruments such as government or corporate bonds serve rather as low interest and secure investment vehicles compared to equity investments, e.g. the shares of a stock. Leveraged investments in non-established or almost bankrupt companies are associated with even more risk and therefore considered as high-risk investments, e.g. venture capital or private equity (funds), c.f. Fig. 2.

It is possible to determine many sub-classifications within each investment category leading to some products perhaps overlapping within the risk-return relationship. For example, junk bonds are characterised by higher risks as there is a higher probability of a payment default; in exchange, they usually bear higher interest rates than common corporate bonds.

Figure 2: Risk-Return Relationship (TM)
Source: Own Illustration

The general rule states: the higher the risk, the higher the expected return.

The concept of risk and return could even be applied to the digital asset ecosystem (c.f. Fig. 3). Let us consider the Lightning Network as risk-free because there is no related counterparty risk. An analogy could be drawn by investing in a US Government Bond or a US Government Bill – we will have a more detailed discussion about the term “risk-free” in the following section.

Several exchanges offer collateralised and uncollateralised borrowing and lending of cryptocurrencies. For instance, retail customers of Bitfinex may borrow and lend (without any collateral) either FIAT or cryptocurrencies in exchange for an interest rate that is between 8.5% and 9.5% p.a., depending on the term (by the beginning of January). There are also collateralised, institutional solutions as offered by the open exchange platform Lendingblock. The company provides a platform for the instant matching of borrowers and lenders allowing them to exchange digital assets in the double-digit millions for 12% p.a. (also state of the beginning of January).

Figure 3: Risk-Return Relationship (DAE)
Source: Own Illustration

Then, there are the initial coin offerings (ICOs),[3] which played a crucial role during the last years. According to, funds in the amount of approximately USD 14bn were raised by ICOs in 2017 and 2018. On average, this new funding approach has a by far larger variance than lending and borrowing – at least according to our most recent experiences. With the implementation of security token offerings (STOs), a more defined investment vehicle within the digital ecosystem should follow. We are therefore including them in the overview of the digital asset ecosystem.

From a risk-return perspective, the concept of a STO can be compared with a (regulated) IPO in the traditional financial world. In general, we would classify a STO between the uncollateralised lending and investing in ICOs within the ecosystem, measured by the expected risk and return. However, this is just an assumption that needs to be validated, as there is no representative data available.

But can the LNRR really be considered risk-free?

Doing an investment and receiving a positive return is commonly associated with risks. In wake of the financial crisis in 2008, particularly the counterparty risk (of derivatives) played a significant role. As a short reminder, counterparty risk describes the risk to each party of a contract that the counterparty will not live up to its contractual obligations.

In the report “Getting to grips with counterparty risk”, the consulting firm McKinsey created an overview of risks that might arise by doing an investment, matching the general risk categories of an investment with the corresponding capital market products offered. The matching has the advantage that not only the risks of a specific investment vehicle but also the deal type will be considered, i.e. how the product is traded (exchange traded, OTC, etc.). Depending on the trade type, risks may vary.

However, for our purposes, we adapted the initial overview, which exhibits the following four general risks: credit, market, operational, and liquidity risk. In order to conduct a proper analysis of the term “risk-free”, and why Lightning does not bear the common risks of a financial product, we applied these categories and compared an uncollateralised debt product (e.g. a traditional government bond with ten years to maturity), a collateralised debt product (e.g. a mortgage) and an investment in the Lightning Network. This enables us to compare traditional investment vehicles that are likely considered to be risk-free with the LNRR by applying the framework proposed by McKinsey (see Fig. 4).

The most discussed threat in regards to the risk-return relationship is the credit risk that could be sub-classified within the issuer and counterparty risk. In terms of a government bond (uncollateralised debt), there is every credit risk associated, since the bond is issued by a bank, and, moreover, a counterparty is involved – in this specific case a state. The situation is quite similar for a mortgage (collateralised debt), however, the debt is at least secured if the counterparty defaults. Additionally, both investments bear a settlement risk.

Figure 4: Risk Evaluation of Different Investment Vehicles – What is really “risk-free”? Source: Own Illustration according to McKinsey (2010, p.2)

Funds, which are locked in the Lightning Network, are not faced with any credit risk in general because the network is “using the Bitcoin scripting op-codes to enable the transfer of funds without risk of counterparty theft, especially with long-term miner risk mitigations.” This means that no counterparty could default or any issues might arise in relation with the settlement process.

However, market and operational risks are still included in all investment vehicles:

– Uncollateralised debt, e.g. government bond (state default, operational failure possible)

– Collateralised debt, e.g. mortgage (depreciation of collateral, operational failure possible)

– LNRR (flash crash risk and protocol risk, operational failure possible)

In terms of the liquidity risk, a government bond would definitely be the most liquid choice – especially in comparison to a mortgage. By comparing the LNRR, we have a kind of liquidity risk due to the timelock of the smart contract (generally, we are talking about 144 blocks being equal to one day). According to the original Lightning Whitepaper by Dryja and Poon, “it is [therefore] preferable to use a small payment per HTLC” since “if the payment does not reach its destination and one of the participants along the path is uncooperative, it is possible that the sender must wait until the expiry before receiving a refund.” Otherwise, this can be also seen as “the time-value of fees pays for consuming time (e.g. 3 days) and is conceptually equivalent to a gold lease rate without custodial risk; it is the time-value for using up the access to money for a very short duration.”

However, in every respect we could determine that the term risk-free is definitely misleading. Even the investment vehicles that in traditional terms are recognised as risk-free, bear several risks. The Lightning Network, controversially, and the resulting LNRR is associated with less risks if the necessary knowledge is available to deal with the operational risks. Nevertheless, it is surely not wrong to consider the LNRR as risk-free if your unit of account is Bitcoin.

Current Pricing of Bitcoin Futures

There are two types of Bitcoin Futures offered by several exchanges: futures contracts and perpetual swaps. In both cases, we traditionally have a currency’s base rate for its price determination. As there is no base rate in the cryptocurrency market, there is also no yield curve or any kind of interest rate for Bitcoin. However, if you take a closer look on the pricing of Bitcoin Futures, you could observe that an interest rate is applied. Because perpetual swaps are mainly spot driven contracts (the price cannot really deviate from the spot price as the derivatives market is outperforming the cash market), this analysis will focus on the futures contracts.

According to the CME Group, a futures contract needs to be “distinct from a forward contract in two important ways: first, a futures contract is a legally binding agreement to buy or sell a standardised asset on a specific date or during a specific month. Second, this transaction is facilitated through a futures exchange. The exchange also guarantees that the contract will be honoured, eliminating counterparty risk. Every exchange-traded futures contract is centrally cleared. This means that when a futures contract is bought or sold, the exchange becomes the buyer to every seller and the seller to every buyer. This greatly reduces the credit risk associated with the default of a single buyer or seller. The exchange thereby eliminates counterparty risk and, unlike a forward contract market, provides anonymity to futures market participants.”

However, the guarantee is only offered by regulated exchanges such as Cboe or CME. Even though Bitmex uses the so-called auto deleveraging, social losses are theoretical possible. The same applies to Deribit. To sum up, there is no guarantee that the counterparty risk is eliminated.

Figure 5: Futures Contracts on Bitcoin with various Maturities, dated on January 10, 2019

The overview (Fig. 5) on the previous page shows the futures contract prices from five exchange platforms offering Bitcoin Futures with various maturities, dated on January 10, 2019. Just as a reminder: whereas the more regulated exchanges, CME and Cboe, are solely offering services for institutional investors, the platforms Deribit, CF, and Bitmex also offer futures for retail investors. Moreover, LedgerX provides options that will be not subject to our analysis.

On first glance, it becomes obvious that the futures prices decline with the contract length. The moment we took this snapshot, the Bitcoin spot price was around USD 4,019. A futures contract that expires around 170 days later (June 25, 2019) was traded at around USD 3,915. Therefore, we made our first hypothesis: the implied interest rate curve or forward curve of Bitcoin, respectively, should be in backwardation.

Taking a further look at the futures prices around four weeks later, dated on February 11, 2019, another image is reflected. Although prices decline, one might recognise quickly that they do not decline as strongly as four weeks prior. Depending on the exchange, the term futures are almost flat (c.f. Fig. 6).

Figure 6: Futures Contracts on Bitcoin with various Maturities, dated on February 11, 2019

In order to get a better overview of how prices developed during this time please find attached a snapshot, extracted from Tradingview. Here you can see how the Bitcoin price developed (red) and how the XBT March 2019 futures price moved during these four weeks (see Fig.7). You can see a real shift concerning the relation between the spot and the futures price: the gap between the spot price and the March futures prices became even smaller; for a short time, the futures contract was actually trading higher than the spot. The blue line reflects this relationship more precisely, and the difference is expressed in USD (secondary y-axis).

Figure 7: Bitcoin Price Development from January 10, 2019 – February 11, 2019
Source: Tradingview

It is for this reason that our second hypothesis is that the implied interest rates also decreased.

Calculation of Implied Interest Rates

In order to support that hypothesis, we calculated the funding rates or the implied interest rates, respectively, for the several contract lengths – and for both dates we took the data. For the calculation, the following future price formula was employed:

FBTC, the futures contract’s price with time to maturity ( ) and as  the corresponding Bitcoin spot rate were extracted from the platform’s homepage on January 10, 2019. For  the USD Libor rate with the corresponding (and adapted[4]) time to maturity was used. An overview of the results can be found in Fig. 8.

This data shows that the implied interest rates vary between 3.6% and 3.9% for the futures contracts expiring the next month, and between 5.4% and 5.6% for the contracts expiring in a half year. This equals a yield of around 9.5% – 14%, if there would be a futures product available with a term period of one year[5]. A visualisation of the corresponding implied interest rate curves from January 10, 2019 can be also found in Fig. 8. Moreover, the USD Libor curve was inserted for comparison purposes.


Figure 8: Implied Interest Rates (January 10, 2019)

Please take now a second look on Fig. 9 below that shows the implied interest rate from February 11, 2019.

Figure 9: Implied Interest Rates (February 11, 2019)

The numbers show that the implied rates decrease around 2.4% and 2.7% for the futures contract expiring the next month, and between 3.4% and 3.8% for the contract with a period of a half year. This equals a yield of around 4.8% – 6.2% if there would be a futures product available with a term period of one year [6]. To sum up, the yields of the futures dropped around 5% p.a. within these four weeks, resulting in an interest rate curve that is considerably flatter than the one by the beginning of January.

If we compare these rates with borrowing and lending rates offered in the cryptocurrency space, we see a strong correlation. However, the unknown component is still the skew in this context. Nevertheless, it seems that these rates are mainly driven by supply and demand as there is no reference rate available. This should definitely not mean that futures in traditional markets are not driven by supply and demand, however, not in this scope.

Moreover, our sanity check verified that there was no arbitrage opportunity, at least not by the beginning of January, if:

1. Someone borrows money at a 2.5% p.a. interest rate and goes long on BTCs;

2. Or borrows the BTCs for 10%, and,

3. Simultaneously shorts BTC Futures (with an implied rate of approx. 12.5% p.a.)

Figure 10: Arbitrage Triangle

In conclusion, the assumption might be made that borrowing and lending rates are employed for the pricing of Bitcoin derivatives. By taking into consideration the borrowing and lending rates of February 11, this assumption could be strengthened. Nevertheless, we will conduct a more detailed quantitative analysis to finally verify this observations in a subsequent report, which will be based on the historic data available.

The Impact of the LNRR on Bitcoin’s Derivative Pricing

There is not so much transparency available in the recent pricing of Bitcoin Futures. Within a few weeks, the prices of Bitcoin Futures and the corresponding implied interest rates could change considerably. Accordingly, the prices of the traded futures become affected in the opposite direction. Nevertheless, the analysis has revealed that there might be a strong correlation between the borrowing and lending rates and the implied interest rates employed in Bitcoin’s derivative pricing.

By taking into account that the base rate of a currency also does not change as quickly as the implied rates employed in the recent pricing of Bitcoin Futures, we considered to introduce a potential base rate for Bitcoin: the LNRR. Therefore, here is another short thought experiment: What would happen if the LNRR could be used for Bitcoin’s derivative pricing?

In order to evaluate the potential impact of the LNRR on Bitcoin’s derivative pricing, we need to begin by making a few assumptions:

– It is possible to receive a LNRR of 0.4% p.a. with a rising trend, a second estimation is already around 1.5% p.a. (probably these are the most impressive rates that you can currently find and earn with the Lightning Network. However, there is definitely the possibility of earning interest for providing the liquidity)

– The LNRR is considered a risk-free rate for Bitcoin as concluded in the previous section

– Bitcoin is considered as a commodity

Firstly, the LNRR is lower than the LIBOR, the collateralised and the uncollateralised lending rates of BTCs. Taking into account that the LNRR could be considered risk-free, these numbers make sense from a risk-return perspective.

Secondly, we have determined that recently the futures are not priced on a base rate, but instead mainly driven by demand and supply through the mechanism of the trading platforms – to be validated in our upcoming report. This will definitely not change in the near future, which in turn is also due to the fact that there is still the option to leverage the future positions. However, with more trading volume and liquidity in the Lightning Network, the LNRR might become more attractive and, therefore, a specific yield curve for Bitcoin might be established. This should not lead to the situation where there is only one correct yield (measured by LNRR). However, it might help establish a kind of yield curve basis for Bitcoin. Keep in mind that in traditional markets, we also have various yield curves.

Thirdly, the LNRR as a kind of base rate could establish more transparency in the entire derivatives market and the associated pricing. Through the establishment of a further “yield curve” that can be used for comparative purposes, the resulting pricing would become more fundamental and reasonable. In the long term, the market might therefore become more efficient. Moreover, a new business model for OTC desks and brokers could emerge – risk-free lending of Bitcoin in exchange for the LNRR, a “Lightning Bank”?

Limitations of Employing the LNRR

Even though we have seen a considerable increase in the number of Lightning nodes, the number of payment channels, and the network’s capacity during the last months, one has to keep in mind that we are still in the early development stage. This means that the price-finding process for routing fees is not yet completed. Additionally, there are several open issues in wake of the centralisation of the network, liquidity balances, state of available routes, and live nodes.

The initial Lightning paper also addresses the following risk factors that might arise in the context of Lightning:

– Improper Timelocks

– Forced Expiration Spam

– Coin Theft via Cracking

– Data Loss

– Forgetting to Broadcast the Transaction in Time

– Colluding Miner Attacks

The person or company providing the node, however, might mitigate most of these risks. Therefore, we would classify almost all of them as “operational” risks – with the exception of miner collusion. After talking to our systems engineering, we estimate an annual fix costs of approximately CHF 320 for running one Lightning node including a bitcoind Full Node in an appropriate manner. On top of that, monitoring costs of around CHF 5,000 should be considered (rough estimation), but might be spread over the amount of active nodes; the more nodes are run the less monitoring costs. In any case, channel monitoring is inevitable.

Considering these costs, it is not surprising that Lightning nodes are currently mainly provided because of experimental and ideological reasons.


After dealing with some analogies between traditional financial markets and the digital ecosystem, the analysis has shown that the LNRR could be considered justifiably as risk-free. The current pricing exhibits that there is an implied interest rate used which has a strong correlation with the borrowing and lending rates. Since the rates could increase or decrease in a relative short timeframe, the hypothesis was made that the rates and therefore the futures prices are mainly driven by supply and demand. This will be tested in a more quantitative analysis based on historical data in a subsequent report.

In terms of using the LNRR as a base rate for Bitcoin, we were able to demonstrate that the usage of the LNRR would make sense from a risk-return perspective. In addition to that, more transparency concerning the pricing of Bitcoin derivatives could be established and the market efficiency might be increased.

Nevertheless, it is highly important to note that this thought experiment was conducted under several assumptions. As long as the Lightning Network is still in its early development stage, meaning that the network is not yet stable, the exhibited LNRRs are definitely not really representative and thus unusable for definitive pricing.

Download The Lightning Reference Rate (LNRR) & Bitcoins Derivative Pricing Research Report PDF


[1] In our last research paper about Bitcoin’s Lightning Network, we discussed the basics of the Lightning Network and the related emergence of innovative business models. We described the establishing of a peer-to-peer based, risk-free interest rate for a single-asset Lightning Network and proposed the opportunity to earn money by routing lightning payments.

[2] EONIA is the effective overnight reference rate for the euro, computed as a weighted average of all overnight-unsecured lending transactions in the interbank market from a panel of 28 banks. The OIS for the USD is similarly determined.

[3] For more information concerning ICOs, please take a closer look on our latest research report “ERC20 Token Swaps – the Redemption”.

[4] Using the term structure from 7 to 180 days, sourced by Bloomberg, and adapted for the corresponding time frame.

[5] Calculated by using the extrapolation method based on the average confidence interval of 95%

[6] Calculated by using the extrapolation method based on the average confidence interval of 95%

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