Thread by @tarunchitra

One mechanism for improving capital efficiency in CFMM trading is borrowing against LP shares (e.g. @AaveAave, @AlphaFinanceLab, @MakerDAO, @SushiSwap)

How safe is it compared to normal lending?

New 📝💧 from @htkao, @GuilleAngeris, @alexhevans y moi

stanford.edu/~guillean/pape…

We first show how to compare Loan-to-Value (LTV) / collateral factors between borrowing A with B as a collateral vs. borrowing A against an A/B LP pool share

Turns out, with dynamically adjusted LTVs you can make LP share lending *more* safe than lending of the underlying

👉🏾 Lending + CFMM protocols like @SushiSwap’s Kashi can provide way better efficiency if they dynamically adjust LTVs in response to price changes and fee accruals

I found this insanely counterintuitive until I wrote the equations — LP shares can be amazing collateral w/ care

Another cool thing: we describe generalized LTVs which show that traditional lending in Aave/Compound can be viewed as a subset of CFMM lending

This suggests that the space of structured products spanned by borrowing against CFMMs is quite massive — does it include all payoffs?

We generalize our previous result on replicating market makers and show that *any* bounded convex payoff can be replicated by borrowing against an LP share with a particular curve

The precise bound depends on the choice generalized LTV — important for @AlphaFinanceLab users

Why? Effectively the convexity of their exposure is determined by the LP share value function except when they’re close to liquidation (Gamma violently changes sign near liquidation) — we quantify the amount this happens for generic portfolio value functions which keeps you safe

But what’s the risk held by these CFMM lenders?

While you need to do more in-depth fee & slippage simulation analysis for a true assessment (see: @gauntletnetwork), we describe an idealized, no-arbitrage way to hedge the risk held by a CFMM lender using barrier/exotic options

What does this mean?

Each loan that a lending protocol issues is *almost* a covered call exposure:
1. Holds collateral
2. Sold options to the borrower to repurchase collateral
3. Sold options to the liquidator for buy defaulted loans

But it’s not *quite* a covered call

Why?
1. @AaveAave and @compoundfinance define liquidatable and default states which are triggered when the price touches a certain limit (vanilla call options don’t do this)

2. Liquidators get paid an incentive — their execution price is different than that of a call

So what can we do?

In 2011, @arbitragegoth taught me about the *dirtiest* sounding product in FX finance: “one-touch digital options”

These are binary options triggered by the price touching a particular level — which is exactly the type of option a borrower in a protocol has!

One-touches are notoriously hard to price — they are path-dependent, making normal stochastic calculus methods hard to use

Luckily, Carr and El Karoui invented some tricks — namely Put-Call symmetry — to price these options

Also change of numéraire (Shreve II, Ch9) is used

What’s the upshot of such a hedge?
1. Represent protocol exposure as basket of options
2. Protocol can dynamically buy portfolio insurance to cover/hedge these risks

Insurance funds like @AaveAave safety module and @compoundfinance staking chain are DeFi’s first attempts at (2)

Can we do better than this when protecting users and protocols in DeFi?

Yes! But more on that in the coming weeks 🔮🔮🔮