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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…
Persistent shifts in term-structure dynamics undermine the stability of single-regime models in long samples. We develop an arbitrage-free regime-switching generalized CIR (RS-GCIR) model that jointly prices the Chinese government bond (CGB) curve and corporate bond curves. To capture the systematic transmission from interest-rate conditions to credit spreads, we structure the model into two blocks and price corporat…
ABSTRACT We examine the role of price discovery in the U.S. Treasury market through the empirical relationship between orderflow, liquidity, and the yield curve. We find that orderflow imbalances (excess buying or selling pressure) account for up to 26% of the day‐to‐day variation in yields on days without major macroeconomic announcements. The effect of orderflow on yields is permanent and strongest when liquidity i…
This whitepaper introduces an innovative mechanism for pricing perpetual contracts and quoting fees to traders based on current market conditions. The approach employs liquidity curves and on-chain oracles to establish a new adaptive pricing framework that considers various factors, ensuring pricing stability and predictability. The framework utilizes parabolic and sigmoid functions to quote prices and fees, accounti…
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…
The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than attempting to fit spreads -- and as we discuss here, the Z-spread is unsuitable -- we fit parametrised survival curves. By deriving a valuation formula for a risky bond, we explain and …
We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamen…
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modelling, integrating the origination of different term structures with such effects. Under a number of ass…
This text grew out of a historical introduction initially written for a study of interest rates in cryptocurrency markets. The difficulty of defining a term structure for a currency without a conventional bond market led naturally to a more fundamental question: under what historical conditions does a yield curve become observable at all? Credit existed long before modern money, and interest-bearing loans are documen…
The term structure of interest rates (yield curve) is a critical facet of financial analytics, impacting various investment and risk management decisions. It is used by the central bank to conduct and monitor its monetary policy. That instrument reflects the anticipation of inflation and the risk by investors. The rates reported on yield curve are the cornerstone of valuation of all assets. To provide such tool for B…
The Nelson-Siegel framework is employed to model the term structure of commodity futures prices. Exploiting the information embedded in the level, slope and curvature parameters, we develop novel investment strategies that assume short-term continuation of recent parallel, slope or butterfly movements of futures curves. Systematic strategies based on the change in the slope generate significant profits that are unrel…
In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. doll…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of…
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time descr…
We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market after the credit-crunch crisis started in summer 2007, standard single-curve no-arbitrage relations…
This paper re-examines the empirical Phillips curve (PC) model and its usefulness in the context of medium-term inflation forecasting. A latent variable Phillips curve hypothesis is formulated and tested using 3,968 randomly generated factor combinations. Evidence from US core PCE inflation between Q1 1983 and Q1 2025 suggests that latent variable PC models reliably outperform traditional PC models six to eight quart…
In traditional financial markets, yield curves are widely available for countries (and, by extension, currencies), financial institutions, and large corporates. These curves are used to calibrate stochastic interest rate models, discount future cash flows, and price financial products. Yield curves, however, can be readily computed only because of the current size and structure of bond markets. In cryptocurrency mark…
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.