SearcharxivSearch

arXiv subjects

Nils Bundi

Publications and source records attributed to Nils Bundi.

2 recordsLinked to original sources

Pricing the DeFi Tail: Do Protocols or Depositors Price Operational Risk?

Similar to banks, DeFi protocols expose depositors to operational risk (USD 9.45 billion across 1,075 events since 2020). Unlike banks, they are not required to hold capital against it. A protocol may maintain a buffer voluntarily. Absent one, the risk falls on the depositor, who should then demand a risk premium in the supply yield. I quantify the underlying tail on one benchmark, a per-sector Basel loss-distribution approach fitted to a new operational risk event dataset, and test both margins against it. Tails in the four core sectors are no heavier than the Moscadelli banking band $[0.85, 1.39]$. Bridge, Derivatives, and the residual Other sector exhibit cyber-loss-level tails ($\hat\xi \approx 1.6$), with point estimates past the infinite-mean boundary. The Lending tail implies a $\mathrm{VaR}_{99.9}$ capital buffer of 18% of TVL and of the ten largest Lending venues, the four holding a buffer cover on average 5% of it. Under market discipline, depositors should demand a higher yield in compensation where a venue does not maintain a buffer. I find that venues without a buffer pay a higher premium than those with (a 125-bps gap in medians): evidence the market discriminates in the right direction. However, the premium falls far short of an adequately priced tail. This unpriced tail falls disproportionately on the retail depositor, who sees only the posted rate but lacks the information and skills to price it. Because these products are not bank-regulated, I recommend disclosure over capital mandates: protocols, and any service providers that front access to it, should publish standardized losses, existing capital buffers and tail coverage.

q-fin.RM

Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices

Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $\Delta t \to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LVR rate splits into a diffusion channel carrying the known multiplier $F(\gamma/(\sigma\sqrt{\Delta t}))$ and a jump channel $\lambda V \cdot G(\gamma;m,\delta^2)$ carrying no $\Delta t$, the two interacting only through an explicitly bounded remainder. The block schedule therefore governs only one channel. For symmetric jump laws the jump channel is moreover an exact lower bound, $\ell(\Delta t) \ge \lambda V G > 0$, so the rate does not vanish as $\Delta t \to 0$, and descends slowly, as $\sqrt{\Delta t}$. At Ethereum's calibrated 12-second slot the rate is 471 bp/yr against a floor of 125, so only three quarters of LP loss is schedule-addressable. At Solana's 400 ms slot the jump channel already dominates. Netting the rate against per-block consensus cost, the LP-side optimal block time is invariant in pool size and in every jump parameter $(\lambda,m,\delta)$: jumps shift the level of LP loss but not the planner's marginal tradeoff. Volatility, the fee tier, and consensus cost set the optimum, near 8 s. However, LVR is only one input to block-time welfare, so this bounds the LP-side contribution rather than settling the design question.

q-fin.MF