AMPL greatly simplifies the creation of on-chain derivatives through tranching. Traditionally complex financial operations are made safe, transparent, and simple.

describe $ampl --tranching

Λ_{t}

Tranching is the process of reorganizing the AMPL's supply volatility into two or more derivative assets with different volatility profiles.

AMPL's volatility, A_{i} can be separated into senior and junior tranches by tranching:

$\begin{array}{c}{A}_{\mathrm{i}}\end{array}\to \left[{\mathrm{Sr}}_{\mathrm{i}}& {\mathrm{Jr}}_{\mathrm{i}}\\ \right]$

[Sr, Jr]

AMPL

**The Sr Tranche**— is affected by volatility*last***The Jr Tranche**— is affected by volatility*first*

Holding both [Sr_{i}, Jr_{i}] is equivalent to holding AMPL because volatility is conserved. After a fixed period of time (defined at the time of tranching) both senior and junior tranches become raw AMPL and rebase normally.

AMPL tranching greatly simplifies the process of converting a medium risk asset into two derivative assets: one that is safe and one that's extra risky.

**Safe Asset**— The senior tranche (Sr_{i}) can be held as a safe asset because it is only affected by rebases after its matching junior (Jr_{i}) has been depleted**Risky Asset**— The Junior tranche (Jr_{i}) offers magnified volatility because all rebases accrue to it until it has been fully depleted

Much of traditional finance works by some variation of this, but the methods used are complex, opaque, and difficult to implement without administrative oversight. AMPL tranching (through Buttonwood Tranche) reduces this to a single operation.

The tranching operation A_{i} → [Sr_{i}, Jr_{i}] is like taking out a loan against your mortgage, only much simpler. When someone borrows against a property, they are effectively looking to hold onto its equity upside while extracting some fixed amount of money to use today. In exchange for this immediate money, interest will be assigned to the loan (or a discount will be assigned to the value of the house) by a bank and underwriter.

With AMPL tranching there's no need for a third party speculator. There's no risk of default or liquidation—and there's no need for laws or law-enforcement agencies to secure the contract because all future obligations are settled at the time of tranching.

Fixed term tranching, described above, is an extremely powerful financial building block. In fact you can use fixed-term AMPL tranches to create perpetual tranches that reorganize volatility indefinitely.

describe $ampl --tranching --perpetual

Λ_{t}

Perpetual Tranching is the process of reorganizing AMPL's supply volatility into two or more derivative assets with different volatility profiles —— indefinitely.

AMPL's volatility, A, can be separated into senior and junior tranches *perpetually*, by bundling multiple fixed-term tranches that are evenly offset by time.

$\left[\begin{array}{c}{A}_{0}\\ {A}_{1}\\ {A}_{2}\\ {A}_{3}\end{array}\right]\to \left[\begin{array}{cc}{\mathrm{Jr}}_{0}& {\mathrm{Sr}}_{0}\\ {\mathrm{Jr}}_{1}& {\mathrm{Sr}}_{1}\\ {\mathrm{Jr}}_{2}& {\mathrm{Sr}}_{2}\\ {\mathrm{Jr}}_{3}& {\mathrm{Sr}}_{3}\end{array}\right]\to \begin{array}{cccc}\left[{\mathrm{Jr}}_{0}& {\mathrm{Jr}}_{1}& {\mathrm{Jr}}_{2}& {\mathrm{Jr}}_{3}& \right]\\ \left[{\mathrm{Sr}}_{0}& {\mathrm{Sr}}_{1}& {\mathrm{Sr}}_{2}& {\mathrm{Sr}}_{3}& \right]\end{array}$

And then systematically rotating maturing tranches out (left), in exchange for fresh tranches in (right):

Perp Senior

Perp Junior

**The Perpetual Senior**— is a claim on a rotating basket of Sr tranches — and can be held as a safe asset.**The Perpetual Junior**— is a claim on a rotating basket of Jr tranches — and can be held for magnified AMPL exposure**Rotation**— is the process of swapping maturing tranches out in exchange for fresh tranches in. To learn more about this in detail see the spot docs.

Fixed-term tranching is great for temporarily reorganizing volatility, but fixed-term tranches aren't fungible across vintages because different vintages have experienced different market conditions over time. This makes them less perennially liquid. By bundling multiple vintages into rotating baskets of Sr_{i}'s and Jr_{i}'s we can solve for this problem in a simple and highly durable way.

As it turns out, the perpetual senior tranche described above makes for a much more durable, scalable, and decentralized low volatility asset than liquidation-market-based approaches today. It can be used as a peer to peer digital cash. To see a complete implementation of perpetual tranching visit www.spot.cash.

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