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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…
Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bo…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review t…
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio, usually taken to be the S\&P 500. We insert size effect in the CAPM, capturing a real-life feature that on average, small stocks (measured by market capitalization) have higher risk and return than large stocks. Testing CAPM involves fitting linear regressions. Our goal is to ensure that regression residuals ar…
In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP's beliefs about asset prices and trader behav…
We give a detailed account of correlations between credit sector/quality and treasury curve factors, using the robust framework of the Barclays POINT Global Risk Model. Consistent with earlier studies, we find a strong negative correlation between sector spreads and rate shifts. However, we also observe that the correlations between spreads and Treasury twists reversed recently, which is likely attributable to the Fe…
Deep reinforcement learning (DRL) has been envisioned to have a competitive edge in quantitative finance. However, there is a steep development curve for quantitative traders to obtain an agent that automatically positions to win in the market, namely \textit{to decide where to trade, at what price} and \textit{what quantity}, due to the error-prone programming and arduous debugging. In this paper, we present the fir…
This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated …
We develop a fundamentally different stochastic dynamic programming model of trading costs. Built on a strong theoretical foundation, our model provides insights to market participants by splitting the overall move of the security price during the duration of an order into the Market Impact (price move caused by their actions) and Market Timing (price move caused by everyone else) components. We derive formulations o…
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…
In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maximum risk) and lower variance (minimum risk). By introducing a risk factor $w$ to conduct coupled modeling of the maximum …
Machine learning techniques are playing more and more important roles in finance market investment. However, finance quantitative modeling with conventional supervised learning approaches has a number of limitations. The development of deep reinforcement learning techniques is partially addressing these issues. Unfortunately, the steep learning curve and the difficulty in quick modeling and agile development are impe…
This paper addresses the question of how much to bid to maximize the profit when trading in two electricity markets: the hourly Day-Ahead Auction and the quarter-hourly Intraday Auction. For optimal coordinated bidding many price scenarios are examined, the own non-linear market impact is estimated by considering empirical supply and demand curves, and a number of trading strategies is used. Additionally, we provide …
In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important because it permits the scaling of investment size across trade opportunities in a principled and data-driven way. We showcase this insight with a prediction model and find clear ou…
We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of member…
The trade size $ω$ has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization $C$ is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in…
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The proposed method is based on a generalization of kriging models with linear equality constraints (market-…
Backwardation is a futures curve that falls with tenor — nearby richer than deferred, usually a tightness / convenience-yield story.
Commodity Carry — Return from rolling futures along the curve — core systematic commodity strategy.
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Contango is a futures curve that rises with tenor — deferred contracts richer than nearby, often a storage and rate story.
Crude Oil Contango — Upward-sloping futures curve implying storage economics and weak spot demand.
Trade nearby versus deferred on the same curve — a pure term-structure book, the smallest-beta cousin of commodity RV.
Market-neutral futures spreads — calendar, inter-commodity, or intra-curve — a CTA that tries not to own outright direction.
Steepeners, flatteners, and butterflies on the bond/STIR strip — duration-neutral-ish curve trades as a CTA RV sleeve.
A managed-futures book that is structurally long options or long VIX-curve convexity — pays carry, aims to print in jumps and persistent stress.
Trade the VIX curve as a first-class market — trend on VIX, carry on contango, and a respect for inversion — not just an equity hedge overlay.
VIX Futures Term Structure — Curve shape driving roll yield for vol ETNs and systematic short-vol carry.
A bear steepener is a curve move where long yields rise more than front yields (or fronts fall less) as the market prices more term premium, more deficit, or less faith in long-run restraint — and duration loses.
Behind the curve means policy (or a book) is too easy or too slow relative to incoming inflation, growth, or a Taylor-type benchmark — the market is already pricing a catch-up.
A bull flattener is the curve flattening as yields fall, usually because the front end rallies more than the long end into easier policy or a growth scare.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
Priced in means the event or path is already in the forwards, the curve, or the multiple — so the announcement is not new information unless it surprises that path.
NAIRU is the unemployment rate consistent with stable inflation — below it, wage/price pressure tends to rise; above it, inflation tends to cool.
Beveridge Curve — Vacancy-unemployment relationship signaling matching efficiency and structural labor shifts.
Phillips Curve — The relationship between labor market tightness and inflation dynamics, heavily debated in post-pandemic regimes.
Carry and Roll Down — Expected return from holding higher-yielding tenor as it rolls down a positively sloped curve.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
Z Spread — Static spread over the government curve capturing credit and liquidity premium.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.
Yield Curve Control — Official caps on benchmark yields and the distortions they create in RV and cross-market hedging.
PCA finds orthogonal directions of maximum variance in a covariance (or correlation) matrix — the yield-curve level/slope/butterfly and many equity ‘statistical factors’ are PCA.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
The 3M10Y Treasury curve compares 10-year Treasury yields with 3-month Treasury bill yields and is closely watched as a recession and policy-cycle indicator.
Eurodollar Futures Legacy — Legacy CME short-rate futures still relevant for curve history.
Trade the VIX curve — short steep contango, respect backwardation — a roll-yield book in vol futures.
Prefer commodity futures with more attractive skewness (or fade lottery-like positive skew) — a moment factor in the curve complex.
Long commodities in backwardation (positive roll yield) and short those in contango — harvest the curve, not the spot headline.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
The 3M10Y Treasury curve compares 10-year Treasury yields with 3-month Treasury bill yields and is closely watched as a recession and policy-cycle indicator.
Backwardation is a futures curve that falls with tenor — nearby richer than deferred, usually a tightness / convenience-yield story.
A bear steepener is a curve move where long yields rise more than front yields (or fronts fall less) as the market prices more term premium, more deficit, or less faith in long-run restraint — and duration loses.
Behind the curve means policy (or a book) is too easy or too slow relative to incoming inflation, growth, or a Taylor-type benchmark — the market is already pricing a catch-up.
Beveridge Curve — Vacancy-unemployment relationship signaling matching efficiency and structural labor shifts.
A bull flattener is the curve flattening as yields fall, usually because the front end rallies more than the long end into easier policy or a growth scare.
Carry and Roll Down — Expected return from holding higher-yielding tenor as it rolls down a positively sloped curve.
Commodity Carry — Return from rolling futures along the curve — core systematic commodity strategy.
Commodity Inventory Financing — Repo-like financing of physical stocks linking curve to rates.
Contango is a futures curve that rises with tenor — deferred contracts richer than nearby, often a storage and rate story.
Crude Oil Contango — Upward-sloping futures curve implying storage economics and weak spot demand.
Trade nearby versus deferred on the same curve — a pure term-structure book, the smallest-beta cousin of commodity RV.
Market-neutral futures spreads — calendar, inter-commodity, or intra-curve — a CTA that tries not to own outright direction.
DV01 is the dollar value of one basis point: how much the position’s mark changes if the yield (or the curve point you risk on) moves by 0.01%.
Eurodollar Futures Legacy — Legacy CME short-rate futures still relevant for curve history.
Trade the VIX curve — short steep contango, respect backwardation — a roll-yield book in vol futures.
Steepeners, flatteners, and butterflies on the bond/STIR strip — duration-neutral-ish curve trades as a CTA RV sleeve.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
A managed-futures book that is structurally long options or long VIX-curve convexity — pays carry, aims to print in jumps and persistent stress.
Phillips Curve — The relationship between labor market tightness and inflation dynamics, heavily debated in post-pandemic regimes.
Priced in means the event or path is already in the forwards, the curve, or the multiple — so the announcement is not new information unless it surprises that path.
PCA finds orthogonal directions of maximum variance in a covariance (or correlation) matrix — the yield-curve level/slope/butterfly and many equity ‘statistical factors’ are PCA.