Introduction
When developing an autonomous system to quote asset prices on the blockchain one must be careful about risk management and controls in general. These notes define IPOR's automated market maker mechanism, its pricing system, risk management rules and payoff calculation (for IPOR Index, see link)
This white paper defines and gives examples of derivative contracts on interest rates called interest rate swaps. Our main concern is the pricing of these products in general, and most importantly, how to define a proxy calculation that is cheap enough to run on-chain.
The main innovation proposed in these notes is how to implement a sophisticated and intensive computation to price fairly and manage risk, while able to be run cheaply on the blockchain.
The IPOR Automated Market Maker (AMM) The IPOR Automated Market Maker (AMM) is a smart-contract that provides spread quotes on specific IPOR rates.
<aside> 💡 Key features of IPOR AMM are as follows:
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Although the IPOR AMM has many characteristics of other constant function market makers (for example Uniswap [2], and in depth in Wang [3]), the main difference is that the IPOR AMM does not set the price of the underlying asset, the IPOR AMM sets a spread on the underlying asset.
With the intent to shine light to the intuition behind the pricing formula (but taking the risk of over simplifying the mechanism behind the quoting), we can simplify IPOR swap contract pricing by the following formula:
<aside> âž• A quote for a $leg \in \{\text{Pay Fix, ReceiveFix}\}$ at time $t$ offered by the IPOR AMM has the following (simplified) form:
$\qquad Quote_{leg}(t) = IPOR(t) + SPREAD_{leg}(t)$
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The function behind the spread is affected by different market conditions (like volatility, IPOR rate changes, trends and sudden jumps). For example, one should expect the spreads to widen during periods of higher volatility when compared with periods of lower volatility.
Below is an example of the IPOR DAI, where the quotes for pay and receive fix rates can be seen (see section below for the definition of paying and receiving rates).
In the plot above we can see that the pay fix and receive fix quotes have different behaviors at different market conditions, including negative spreads at certain moments.
In summary, and to reemphasize, an important characteristic of the IPOR AMM is that it quotes a spread on IPOR rates, it does not set the IPOR rates.
In the remaining sections we will formally define interest rates swaps and the pricing of IPOR swaps.
A swap contract is a deal between two parties to exchange two streams of payments between one another. At predefined time intervals one party pays to the other the cashflow originated from their stream of payments. An interest rate swap is a swap between two interest rates, often one being a fix rate and the other being a floating rate (the IPOR rate in our case). In practice, only the net value is paid to one of the parties.
Each payoff on an interest rate swap is given by the following formula: