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Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Mar…
USDC and USDT are the dominant stablecoins pegged to \$1 with a total market capitalization of over \$300B and rising. Stablecoins make dollar value globally accessible with secure transfer and settlement. Yet in practice, these stablecoins experience periods of stress and de-pegging from their \$1 target, posing significant systemic risks. The behavior of market participants during these stress events and the collec…
In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token. Our approach employs multi-level nested Ornstein-Uhlenbeck (OU) processes, for which we derive key properties and develop calibration and filtering techniques. Then, we design an …
We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity aris…
We consider a liquidity provider's (LP's) exposure to stablecoin and liquid staking derivative (LSD) depegs on Curve's StableSwap pools. We construct a suite of metrics designed to detect potential asset depegs based on price and trading data. Using our metrics, we fine-tune a Bayesian Online Changepoint Detection (BOCD) algorithm to alert LPs of potential depegs before or as they occur. We train and test our changep…
This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order approximation and provide the bounds for the error. We provide exact RS delta, approximated RS delta as well as mean variance hedging strategies for this specific model and compare thei…
Fiat-pegged stablecoins are by nature exposed to spillover effects during market turmoil in Traditional Finance (TradFi). We observe a difference in TradFi market shocks impact between various stablecoins, in particular, USD Coin (USDC) and Tether USDT (USDT), the former with a higher reporting frequency and transparency than the latter. We investigate this, using top USDC and USDT liquidity pools in Uniswap, by adap…
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang, we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these…
I introduce an agent-based model of a Perpetual Futures market with heterogeneous agents trading via a central limit order book. Perpetual Futures (henceforth Perps) are financial derivatives introduced by the economist Robert Shiller, designed to peg their price to that of the underlying Spot market. This paper extends the limit order book model of Chiarella et al. (2002) by taking their agent and orderbook paramete…
Silkswap is an automated market maker model designed for efficient stablecoin trading with minimal price impact. The original purpose of Silkswap is to facilitate the trading of fiat-pegged stablecoins with the stablecoin Silk, but it can be applied to any pair of stablecoins. The Silkswap invariant is a hybrid function that generates an asymmetric price impact curve. We present the derivation of the Silkswap model a…
We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep the exchange rate from breaking the prescribed barriers, the central bank is generating permanent price impact and thereby accumulating inventory in the foreign currency. Historical examples of failed target zones illustrate that this inven…
Synthetic assets are decentralized finance (DeFi) analogues of derivatives in the traditional finance (TradFi) world - financial arrangements which derive value from and are directly pegged to fluctuations in the value of an underlying asset (ex: futures and options). Synthetic assets occupy a unique niche, serving to facilitate currency exchange, giving traders a means to speculate on the value of crypto assets with…
Algorithmic stablecoins promise decentralized monetary stability by maintaining a target peg through programmatic reserve management. Yet, their reserve controllers remain vulnerable to regime-blind optimization, calibrating risk parameters on fair-weather data while ignoring tail events that precipitate cascading failures. The March 2020 Black Thursday collapse, wherein MakerDAO's collateral auctions yielded $8.3M i…
Stablecoins have emerged as a significant component of global financial infrastructure, with aggregate market capitalization surpassing USD250 billion in 2025. Their increasing integration into payment and settlement systems has simultaneously introduced novel channels of systemic exposure, particularly liquidity risk during periods of market stress. This study develops a hybrid monetary architecture that embeds fiat…
Stablecoins promise par convertibility, yet issuers must balance immediate liquidity against yield on reserves to keep the peg credible. We study this treasury problem as a continuous-time control task with two instruments: reallocating reserves between cash and short-duration government bills, and setting a spread fee for either minting or burning the coin. Mint and redemption flows follow mutually exciting processe…
With market capitalization exceeding USD250 billion by mid-2025, stablecoins have evolved from a crypto-focused innovation into a vital component of the global monetary structure. This paper identifies the characteristics of stablecoins from an analytical perspective and investigates the role of stablecoins in forming a hybrid monetary ecosystem where public (fiat, CBDC) and private (USDC, USDT, DAI) monies coexist. …
A stablecoin is a token that targets a peg, usually $1 — a money-market claim or an algorithmic hope, depending on the reserves.
The PEG ratio is P/E divided by expected earnings growth — a back-of-the-envelope adjustment of the multiple for growth.
Argentina’s 2001–02 collapse ended the convertibility 1:1 peg with default, corralito, and a violent real devaluation — a political-economy crisis of an overvalued peg.
The 1997–98 Asian crisis was a sequence of peg breaks, bank runs, and sudden stops starting in Thailand — short-dollar corporate debt plus weak bank regulation meeting a reversal of carry.
Sweden, Finland, and Norway’s early-1990s banking crises followed financial liberalization, a real-estate boom, and a peg-defense rate shock — a clean ‘credit boom gone wrong’ that ended in nationalization and bad banks.
On 15 January 2015 the SNB abandoned the 1.20 EUR/CHF floor in minutes — a peg break that wiped FX brokers and carry books that had treated the floor as a free option.
Mexico’s 1994–95 tequila crisis was a devaluation-and-tesobono run after political shocks and a crawling peg that had become incredible — the first big 1990s EM capital-account crisis.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
Argentina’s 2001–02 collapse ended the convertibility 1:1 peg with default, corralito, and a violent real devaluation — a political-economy crisis of an overvalued peg.
The 1997–98 Asian crisis was a sequence of peg breaks, bank runs, and sudden stops starting in Thailand — short-dollar corporate debt plus weak bank regulation meeting a reversal of carry.
A peg is a policy that holds the exchange rate to a target or band — a promise that spends reserves and rates when the market disagrees.
Currency Reserves Adequacy — Whether EM authorities can defend pegs or smooth disorderly depreciations.
Sweden, Finland, and Norway’s early-1990s banking crises followed financial liberalization, a real-estate boom, and a peg-defense rate shock — a clean ‘credit boom gone wrong’ that ended in nationalization and bad banks.
The PEG ratio is P/E divided by expected earnings growth — a back-of-the-envelope adjustment of the multiple for growth.
A stablecoin is a token that targets a peg, usually $1 — a money-market claim or an algorithmic hope, depending on the reserves.
On 15 January 2015 the SNB abandoned the 1.20 EUR/CHF floor in minutes — a peg break that wiped FX brokers and carry books that had treated the floor as a free option.
Mexico’s 1994–95 tequila crisis was a devaluation-and-tesobono run after political shocks and a crawling peg that had become incredible — the first big 1990s EM capital-account crisis.