Building Genuine Yield Curve

Demystifying Interest Rates Composability for Large-Scale Derivatives’ Applications

Masa | Secured Finance
Published in
7 min readSep 19, 2022



The previous article explained several components of developing capital markets for cryptocurrency and digital assets. The yield curve is briefly introduced as a continuous plot of interest rates. In this article, we’ll dive deeper into connecting interest rates to build the yield curve, discuss composability and scalability, and then explore the opportunities for derivatives’ applications. This is the fifth article of the DeFi blog series presented by Secured Finance.

Disclaimer: This is not financial advice. All information, assumptions, and scenarios are created and simplified for educational purposes.

Photo by Joel Filipe on Unsplash

What is an Interest Rate?

An interest rate is a premium that a lender charges a borrower and is expressed as an annualized percentage of the principal — the amount loaned. Theoretically, there are many ways to model and understand the interest rate (such as the Fisher Effect), but in business practice, it can be decomposed into three factors.

Interest Rate = Risk-free Rate + Risk Premium + Expected Inflation Rate

An interest rate here is often called ‘Nominal Interest Rate’ to contrast with ‘Real Interest Rate’, which excludes the inflation factor (i.e., Real Interest Rate = Risk-free Rate + Risk Premium).

A risk-free rate is the theoretical rate of return of an investment with zero risk. The government bond yield is often practically used; however, a genuinely risk-free rate does not exist.

A risk premium contains complex factors such as credit risk, liquidity risk, and country risk, among others, expressed in percentages to cover the damage.

  • Credit risk: Premium is calculated from probability and expected loss to cover the counterparty’s default.
  • Liquidity risk: Additional cost is paid to find the counterparty in the market to trade at the desired timing.
  • Country risk: Economic, social, and political changes affect the government obligator’s likelihood of default.

In DeFi, we earn lending rates and staking rewards in the form of tokens. The yields are nominal interest rates, usually high because of the token’s pre-designed high-inflation rate and the market’s liquidity risk premium. The AMM-based interest rates are regulated by the pool’s algorithm, such as a supply-demand ratio in the lending pool; therefore, the liquidity risk premiums vary among pools.

Onshore and Offshore Rates

It’s worth noting that interest rates can differ, even with the same currency and maturity, depending on the market conditions, such as onshore and offshore markets. Onshore markets are more regulated by local jurisdictions, and capital control restrictions are put in place compared to offshore markets. Since the interest rate structures differ, we cannot directly connect onshore and offshore rates.


The Chinese RMB lending rates differ from onshore (Shanghai Interbank Offered Rate [SHIBOR]) and offshore (Hong Kong Interbank Offered Rate [HIBOR] — note that offshore RMB is different from HKD). The offshore market plays an essential role in cross-border settlements and internationalizing the currency, thus nurtured by clearing banks in China (More: RMB Internationalization Report).

In 2020, the interest rate of the offshore market was overall higher than that of the onshore market, with the HIBOR 0.39% higher than the SHIBOR on average.
— 2021 RMB Internationalization Report

Eurodollar Market

The US Dollar interest rates on deposits and loans made in the domestic (onshore) money market differ from rates on apparently equivalent deposits and loans in the Eurodollar (offshore) market. (See: What is Eurodollar)

Financial institutions and corporations prefer the Eurodollar market due to its greater flexibility from fewer restrictions, less capital control, and more profitability from narrower margins between the deposit and lending rates. As you can see below, the differentials persist, so we cannot mix or connect different kinds of rates to build the yield curve.

U.S. rates and Eurodollar rates
Source: Interest Rates in the US and Eurodollar Markets Working Paper № 145 (Giddy, Duffey, & Min, 1977)

The essence of the Eurodollar market is external financial intermediation: financial institutions (Eurobanks) outside the regulatory reach of the United States compete for dollar-denominated deposits and dollar-denominated loans.
— Giddy, Duffey, & Min, 1977

Interbank Market Development with the Eurocurrency

The first Eurodollar was created in the 1950s by British banks. After World War II and during the Cold War, the quantity of US dollar banknotes outside the United States increased significantly (source). The Eurodollar demand surged in Europe from the financial pressure in the Suez Crisis in 1957, followed by the US’s series of capital control and interest rates ceiling by Regulation Q. As the Eurodollar and Eurocurrency market kept growing, British bankers began referring to the lending rates in this market in the 1960s. Later, British Bankers Association started publishing London Interbank Offered Rate (LIBOR) (see more for LIBOR history).

Since the World Bank’s first currency swap in 1981, the OTC derivatives market has become the largest financial market. LIBOR, determined by the offshore market rates, became the defacto-standard for the OTC swaps. LIBOR, a universal benchmark rate, played an essential role in the OTC derivatives market, snowballing its scale to over $600 trillion.

LIBOR Scandal and Decentralized Finance

LIBOR became the most crucial interest rate; however, it was prone to manipulation because it was administered by only a small group of banks, which caused the LIBOR scandal. Eventually, its publications were stopped. This incident revealed the problem of the centralization of power. We may develop a better system with a more transparent, decentralized, and autonomous financial protocol. We should study LIBOR and Eurocurrency markets' long-term and tremendous contribution to building the new financial era through decentralized finance technology.

Yield Curve as One Market

Interest rates introduce the concept of the Time Value of Money, which reveals the impact of time on calculating the money’s worth. Then we can see the Term Structure of Interest Rates by grouping loans and bonds with the same or similar risk and plotting those yields (on the Y-axis) along with different maturities (on the X-axis). We call it the Yield Curve, which gives rich information about the markets and overall economy. Thanks to the Yield Curve, we’ve built large-scale OTC derivative markets.

Connecting Yields

There are two conditions to connecting interest rates. The first is ensuring the same risk profile. Why don’t we connect yields between different markets? Generally, we cannot mix different types or quality of interest rates; for example, we don’t mix government bond yields and corporate equity dividend yields. It makes it difficult to analyze the risk premium of the interest rate.

Despite the extensive arbitrage between the U.S. and Eurodollar markets, interest rate differentials between the two markets persist.
— Dufey et al., 1977

In DeFi, we don’t connect yields between different pools (ex. 3-month pool and 6-month pool). Similar to onshore and offshore markets, DeFi rate differences persist because of different algorithms on pool usage. That’s why we see various DeFi rates with the same currency and maturity.

The second condition is ensuring No-Arbitrage Pricing (Arbitrage-Free Pricing). We want to interpolate rates to estimate a fair interest rate on the yield curve. For example, we want to know the 1.5y rate from 1y and 2y rates. If no-arbitrage pricing works, we can estimate the forward 6m rates (1.0y — 1.5y and 1.5y — 2.0y). These rates provide deep insights into future rate prediction (Forward Rates). In this case, we can understand how the market participants expect the future 6m rates to go up or down.

Composability and Scalability for Derivatives

Arbitrage-free condition enables us to treat the yield curve as one market to bring composability to interest rates markets. We can calculate the forward rate at any point with any maturity on the curve. For example, we can compose a custom-made forward loan where a borrower thinks the interest rate may go up and wants to lock the rate now, to borrow money 1 year later for 1 year. Traditionally, the lender, the counterparty, is a structuring/swap desk at an investment bank that can decompose the forward loan into two standard loans (1 year and 2 years) via no-arbitrage pricing and hedge with the plain vanilla market.

Forward Loan Structuring with Two Standard Loans

With the composability, we can create any complex future cashflows and calculate a fair value with no-arbitrage pricing. Furthermore, we can make an OTC swap transaction by exchanging two different cashflows with the same present value. This means the swap is priced at zero and allows payment netting to reduce collateral requirements. (Note: DeFi uses the term ‘swap’ differently. It usually refers to a single spot exchange.)

In many cases, there’s no initial capital required. Thanks to netting, leverage can be provided as long as counterparty risk is covered. Also, because the swap price is zero, it is an off-balance transaction for corporates, so we have more flexibility in designing future cashflows and hedging market risks. That’s how we have achieved massive trillion-dollar scalability in OTC swaps and derivatives over 40 years. There’s no doubt we will grow in the same way with digital assets in decentralized finance.


We reviewed the characteristics of the interest rate and how the interbank market evolved with LIBOR, the universal benchmark rate. Then, we learned the term structure of interest rates and how to connect them to build the yield curve as one market. Certain conditions must be met to ensure the composability of transactions to achieve massively scalable derivative markets. The yield curve is the final missing piece to bringing full-scale institutional finance into digital assets. Secured Finance is building an interbank-grade and scalable-derivatives market protocol.

Next Articles

  • Intro to the Forward FX market
  • How to hedge volatility risk on Cryptocurrency
  • A practical guide for structured products in business practice
  • How structured products are made and why they are useful
  • A handbook of Secured Finance derivative solutions

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Giddy, I.H., Dufey, G. & Min, S. Interest rates in the U. S. and eurodollar markets. Weltwirtschaftliches Archiv 115, 51–67 (1979).



Masa | Secured Finance
Secured Finance

Secured Finance Founder | Fixed Income DeFi | Former Head of Derivatives Structuring | Computer Scientist | Task Force Member for Cabinet Secretariat Japan