In this chapter we will explain the notion of accrued IPOR and the model we will use to predict it.
Accrued IPOR at time $t$ is the annualized rate resulting from compounding IPOR historical rates for the following 28 days after $t$. As an equation, we define it as:
$$ AccR = (\prod_{i>t}^{i\leq t+28} (1 + r_i*dt_i) - 1) \cdot \frac{365}{28} $$
Where $r_i$ is the IPOR rate at time $i$, $dt_i$ is the time interval since the publication of the previous fixed rate ($r_{t-1}$).
Below is the Accrued IPOR for USDT for 2022 and most of 2023.
Given the Accrued IPOR, it is a trivial calculation to find that its value is the rate that represents the fair value of a IRS.
<aside> 💡 The Accrued IPOR is the theoretical rate of a fair IRS. But its value is unknown at the time the contract is offered.
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Only if we had a way to estimate the Accrued IPOR.
What we do next is to build a collection of models that will estimate the Accrued IPOR to the best of present knowledge.
We will use a very particular model to predict the quotes for IPOR IRS. Here are the main components:
<aside> 💡 (1). We will select a feature to classify between different market conditions (e.g., high volatility, low volatility, medium volatility, etc…)
(2). We will select some features to explain the Accrued IPOR at any given time.
(3). We will group IPOR rates given the feature on step (1).
(4). For each group from step (3), we will fit hyperplanes using the features from step (2) to explain the Accrued IPOR.
(5). We add a number of safe guards for risk management. We will go in detail later, but for example, we hard-cap receive fix contracts to never be higher than unreasonable values.
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See below a snapshot of a Base Spread model for Receive Fix for IPOR-USDT:
Below is a video of how the features and planes are changing over time based on the IPOR rate: