Blockchain and DeFi ESADE 2024

Blockchain and Decentralized Finance:
A 2024 Primer for ESADE

Presenter: Andreas Park

Some Technological Innovations throughout History

Financial Infrastructure

Decentralized trading using automated market makers (AMM)

AMM pricing is mechanical:

determined by the amounts of deposits
most common:
- constant product
- #USDC $\times$ #ETH = const

No effect on the marginal price

Most common form of AMM liquidity rule is Constant Product Pricing
$L(a,c)=a\cdot c~\Rightarrow~a\cdot c= (a-q)\cdot (c+\Delta c).$
Total cost of trading $q$ $\Delta c=\frac{cq}{a-q}.$
Price per unit $p(q)=\frac{c}{a-q}.$

The Pricing Function

Most common form of AMM liquidity rule is Constant Product Pricing
$L(a,c)=a\cdot c~\Rightarrow~a\cdot c= (a-q)\cdot (c+\Delta c).$
Total cost of trading $q$ $\Delta c=\frac{cq}{a-q}.$
Price per unit $p(q)=\frac{c}{a-q}.$
Average spread paid $\frac{p(q)}{p(0)}-1=\frac{q}{a-q}.$

liquidity provider makes asset and cash deposit
more deposits flatten price curve
- may attract more volume
- but larger "positional" dollar loss when prices move

larger liquidity deposits $a$ $\Rightarrow$
- lower costs (price impact) for liquidity demanders

fractional collateral $\to$ collateralization factor $=$ 150%

\begin{array}{rcl} &&\textsf{maximal amount of DAI in \$}\\\\ &=&\frac{\textsf{\$ equivalent of ETH in escrow}}{\textsf{collateralization factor}}\\\\ &=&\frac{1,500}{150\%}=\$1,000 \end{array}

\begin{array}{rcl} &&\textsf{maximal amount of DAI in \$}\\\\ &=&\frac{\textsf{\$ equivalent of ETH in escrow}}{\textsf{collateralization factor}}\\\\ &=&\frac{1,500}{150\%}=\$1,000 \end{array}

total collateral = $1,500

maximum loan = $1000

overcollateralization = $500

actual loan (example) = $500

buffer = $500

The User's Perspective for a DAI Loan

ETH $\searrow$ $150

value of ETH collateral = $600

maximum loan = $600/150%=$400

total collateral = $600

maximum loan = $400

required overcollateralization = $200

actual loan (example) = $500

buffer = -$100

for reference: former value of collateral

$\Rightarrow$ triggering of liquidation auction by "keeper"

sell 3.33 ETH=$500=500 DAI

repay $500=500 DAI loan

retain incentive

return remainding ETH to vault owner

tokens are a re-imagination of value, ownership, use, rewards
tokens live on a single infrastructure and can interact with other tokens
tokens are immediately transferable & immediately usable in DeFi
token can be programmed to have many features and have many different uses

tokens can assign ownership to "things" that could not be owned before
tokens are often important for the functioning and incentives of platforms

What's a crypto-token and what's special about it?

a blockchain is a protocol in which
- users have direct control and responsibility over their assets
- users can create codes at will
- $\rightarrow$ any user can create tokens and applications

Case 2: price(1 SC) $<$ 1 FU $\to$ SC cheap

DISCUSSION

backing/collateral is the value of the LUNA/Terra Network
- $\to$ must have value(Terra) $\ge\sum$ SC
when you issue new LUNA tokens
- shift value from current to new owners
- create inflation $\to$ price(Luna) $\searrow$

POTENTIAL PROBLEMS

value(Terra) $<\sum$ SC
- could be pre-drop SC
when SC<FU, LUNA token holders
- know price(LUNA) will drop
- $\to$ pre-emptive selling
- more LUNA issued
- $\to$ more inflation
- $\to$ more price drops
- $\to$ DEATH SPIRAL!!!

So far there has never been an algorithmic stablecoin that did not collapse.
Disclaimer: I am not aware of a mathematical proof that an algo stablecoin cannot work.