In this section, we will extend the IPOR curve from 4 weeks to 8 and 12 weeks. First, we will review the challenges of extending the curve. Then, we will propose the estimation of a 12-week yield curve using the conditional expectation of future rates.
The initial yield curve, IPOR, is defined up to 4 weeks. Extending this curve to longer tenors, like 8 and 12 weeks, introduces uncertainties due to longer tenors often needing more liquid instruments, which might make it challenging to find reliable market prices. Longer horizons increase the unpredictability due to potential economic, regulatory, political, cyber security, and global events. Extended horizons often rely more on model predictions, which come with inherent assumptions and risks.
What will the accrued interest rates be two/three months from now?
To answer this, we need a framework to estimate forward rates, which represents the market’s expectations of future short-term rates.
The reader less familiar with interest rates might be surprised that in traditional finance, one can reasonably get a workable solution for this question. But of course, when it comes to DeFi interest rates, the challenges are numerous.
For perspective, let us go through a few vanilla examples of how the Bootstrap method can be used to find future rates today in traditional finance.
The Bootstrap method connects the dots with an interpolation method. For example, imagine we have a 1-year zero-coupon government bond at a 7% rate and a 3-year zero-coupon government bond at 4%. How much should the 2-year rate be?
<aside> 💡 Yield Curve Construction in Global Markets
Collect market prices for Risk-Free Rates (RFRs) from actively traded securities (the black crosses in the plot). In major markets, the short end of the curve (typically up to 1-2 years), we use money certificates of deposit and STIR (Short-Term Interest Rate) futures. In emerging markets, implied interest rates can be backed out from the forward FX market, where we decompose the Spot FX rates and interest rate differentials between the two currencies involved.
The curve is constructed by deriving discount factors and forward rates from market prices of sequential instruments using bootstrapping. We apply market conventions to each input instrument to convert market prices to forward rates, thereby establishing our pivot points.
An interpolation method is used - both during the curve construction and afterward - to estimate rates between known tenor pivot points. The interpolation method choice often involves balancing smoothness, monotonicity, and curve accuracy. Standard interpolation methods include cubic spline, monotone convex, Hermite, and tensor spline. The end-user of the curve that has a portfolio of option products typically requires smoother curves, while linear derivatives like interest rate swaps prioritize precision.
(optional) Convert the constructed yield curve into a zero curve, where the transitioning from a constructed yield curve to a zero curve offers computational advantages. The zero curve's simplicity enhances scenario analyses, particularly when handling multiple concurrent curves. While this technique has its merits, it's distinct from constructs such as the crack spread curve in oil trading or single-name credit default spread curves in credit trading.
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The image below highlights the steps often taken in traditional finance.
Yield curve bootstrap example. The magenta curve is unknown and needs to be estimated given existing instruments on Traditional Finance. The blue curve is assumed to be given from existing instruments in the market. The bootstrap possibilities are exaggerated for clarity.
In traditional finance, beyond valuation, the curve plays a pivotal role in hedging portfolios and comprehensive risk management, often enabling detailed perturbation and scenario analyses. Moving forward, we'll delve into the unique dynamics of the DeFi market. While it presents certain challenges due to its nascent state and fewer actively traded market prices, it also opens avenues for innovation and adaptation of traditional methods.
When it comes to DeFi, trying to reproduce the yield curve construction from traditional finance is challenging in its first step:
The fixed-income markets in DeFi are not a complete market