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This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on fa…
We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve price accuracy and reduce spread, but after some point additional liquidity begins to deteriorate price. The model allows to connect the bid-ask spread and high-low bars to measurable…
Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find that the spread return is lack of long-rang…
We study the problem of forecasting and optimally trading day-ahead versus real-time (DART) price spreads in U.S. wholesale electricity markets. Building on the framework of Galarneau-Vincent et al., we extend spike prediction from a single zone to a multi-zone setting and treat both positive and negative DART spikes within a unified statistical model. To translate directional signals into economically meaningful pos…
In this study, we applied a stochastic spread pairs trading strategy on the Indian commodity market. The complete set of commodities were taken whose spot price was available for the period of January 1st 2010 to December 31st 2018 including energy, metals and the agricultural commodity sector. Spot data was taken from the MCX pooled spot prices for 17 commodities. The data was split into training period (January 1st…
Using micro-level data, we construct a credit spread index with considerable predictive power for future economic activity. We decompose the credit spread into a component that captures firm-specific information on expected defaults and a residual component–– the excess bond premium. Shocks to the excess bond premium that are orthogonal to the current state of the economy lead to declines in economic activity and ass…
ABSTRACT Using dealer's quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are highly cross‐correlated, and principal components analysis implies they are mostly driven by a single common factor. Although …
ABSTRACT Most structural models of default preclude the firm from altering its capital structure. In practice, firms adjust outstanding debt levels in response to changes in firm value, thus generating mean‐reverting leverage ratios. We propose a structural model of default with stochastic interest rates that captures this mean reversion. Our model generates credit spreads that are larger for low‐leverage firms, and …
ABSTRACT This article examines the optimal capital structure of a firm that can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's (1994a) closed‐form results to a much richer class of possible debt structures and permit study of the optimal maturity of debt as …
Abstract Two intermediary-based factors—a corporate bond dealer inventory measure and a broad intermediary distress measure—explain more than 40$\%$ of the puzzling common variation in credit spread changes beyond canonical structural factors. A simple intermediary-based model with partial market segmentation accounts for intermediary factors’ explanatory power and delivers three further implications with empirical s…
This paper extends an option-theoretic approach to estimate liquidity spreads for corporate bonds. Inspired by Longstaff's equity market framework and subsequent work by Koziol and Sauerbier on risk-free zero-coupon bonds, the model views liquidity as a look-back option. The model accounts for the interplay of risk-free rate volatility and credit risk. A numerical analysis highlights the impact of these factors on th…
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 …
In this paper, we propose a methodology based on piece-wise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dy…
Several studies have established the predictive power of the yield curve in terms of real economic activity. In this paper we use data for a variety of E.U. countries: both EMU (Germany, France, Italy) and non-EMU members (Sweden and the U.K.). The data used range from 1991:Q1 to 2009:Q1. For each country, we extract the long run trend and the cyclical component of real economic activity, while the corresponding inte…
Over the last decade, the foreign exchange derivatives market has witnessed a collapse of covered interest parity (CIP). Not only does this collapse give rise to large deviations from CIP, it has unlocked a stream of exploitable arbitrage opportunities across currencies. In this paper, we introduce two new factors – inflation differential and relative economic performance – as potential drivers of deviations from CIP…
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a…
Lead-lag relationships, integral to market dynamics, offer valuable insights into the trading behavior of high-frequency traders (HFTs) and the flow of information at a granular level. This paper investigates the lead-lag relationships between stock index futures contracts of different maturities in the Chinese financial futures market (CFFEX). Using high-frequency (tick-by-tick) data, we analyze how price movements …
A growing number of contributions in the literature have identified a puzzle in the European carbon allowance (EUA) market. Specifically, a persistent cost-of-carry spread (C-spread) over the risk-free rate has been observed. We are the first to explain the anomalous C-spread with the credit spread of the corporates involved in the emission trading scheme. We obtain statistical evidence that the C-spread is cointegra…
Too big to fail is the expectation that a firm’s collapse would force a public rescue — a subsidy in funding spreads and a policy problem.
CDX HY Index tracks the cost of insuring a basket of North American high-yield corporate credit and serves as a sensitive gauge of credit risk appetite and stress.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
Default risk is the chance the issuer misses a contractual payment — the event credit spread is trying, noisily, to price.
High Yield OAS measures the spread of high-yield corporate bonds over risk-free Treasuries after adjusting for embedded options, serving as a key gauge of speculative credit stress.
Investment Grade OAS measures the spread of high-quality corporate bonds over Treasuries after adjusting for embedded options, helping track broad corporate credit conditions.
A junk bond is a high-yield, below-investment-grade credit — more equity-like default risk, still quoted in spread and price.
Refinery margin: long gasoline and distillate, short crude, in a stated ratio — energy RV rather than a WTI call.
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.
Long one commodity, short a related one — WTI/Brent, gold/silver, corn/wheat, gas/power — a relative-value family across complexes.
Long soymeal and soyoil versus short soybeans (or the reverse) — the processor’s margin as a futures spread.
Power minus the fuel needed to generate it (usually gas, sometimes coal) — the electricity generator’s margin as a spread.
Short-term interest-rate futures — SOFR, SONIA, Euribor strips — a specialist language of meeting-to-meeting path trades and pack/bundle spreads.
A butterfly is long one wing, short two bodies, long the other wing — a bet on a pin or on the curvature of the smile.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
Implied Realized Spread — Gap between implied and realized vol that defines carry for short-vol books.
Risk Reversal — Call-put spread package measuring directional skew in FX and equity options.
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
To lift the offer is to buy the posted ask — aggressive demand that pays the spread for immediacy.
On-the-run is the latest issued Treasury (or benchmark) in a maturity; off-the-runs are older issues. The on-the-run is richer and more liquid; the spread is a liquidity and specials object.
BTP-Bund spread measures the yield difference between Italian and German government bonds and is a key indicator of euro-area sovereign stress and fragmentation risk.
EMBI sovereign spread measures the yield premium on emerging-market sovereign debt over U.S. Treasuries and serves as a key gauge of EM credit risk and external financing stress.
Europe Periphery Spreads — BTP-Bund and similar spreads as euro-area fragmentation gauges.
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
Leveraged Loan Index — Floating-rate corporate credit sensitive to defaults, spreads, and CLO demand.
Option-Adjusted Spread — Spread adjusted for embedded prepayment options in callable bonds and MBS.
Rising Stars — High-yield upgrades into investment grade, often supporting spread tightening episodes.
Z Spread — Static spread over the government curve capturing credit and liquidity premium.
Commercial paper spreads track the cost of short-term corporate borrowing relative to safer benchmarks and help identify stress in corporate funding markets.
FRA-OIS spread measures the difference between interbank funding expectations and overnight indexed swap rates, often used as a gauge of banking and short-term funding stress.
LIBOR-OIS spread tracks the gap between unsecured bank funding rates and overnight indexed swap rates, historically serving as a benchmark for banking-system stress.
TED Spread measures the difference between interbank lending rates and short-term U.S. government bill yields, historically used as a gauge of credit and funding stress.
A Financial Conditions Index aggregates variables such as rates, credit spreads, equities, and the dollar to measure how supportive or restrictive the market environment is for growth and risk assets.
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.
Adverse selection is the expected loss a liquidity provider takes when the other side is informed — the Glosten–Milgrom reason spreads exist even with no inventory.
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
The bid-ask spread is the gap between the best bid and the best offer — the round-trip tax of crossing the book.
BTP-Bund spread measures the yield difference between Italian and German government bonds and is a key indicator of euro-area sovereign stress and fragmentation risk.
A butterfly is long one wing, short two bodies, long the other wing — a bet on a pin or on the curvature of the smile.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
Cointegration Pairs Trading — Mean-reversion on stationary spreads between related instruments.
Commercial paper spreads track the cost of short-term corporate borrowing relative to safer benchmarks and help identify stress in corporate funding markets.
Trade refined-product minus crude (crack) or nearby-versus-deferred calendars — commodity relative value, not a directional oil call.
Refinery margin: long gasoline and distillate, short crude, in a stated ratio — energy RV rather than a WTI call.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
CS01 is the dollar value of one basis point of credit spread — how much the book makes or loses if the name or index OAS/CDS widens by 1 bp.
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.
Default risk is the chance the issuer misses a contractual payment — the event credit spread is trying, noisily, to price.
Effective spread is twice the signed distance from the trade price to the prevailing midpoint, the realized cost of crossing versus posting.
EMBI sovereign spread measures the yield premium on emerging-market sovereign debt over U.S. Treasuries and serves as a key gauge of EM credit risk and external financing stress.
Europe Periphery Spreads — BTP-Bund and similar spreads as euro-area fragmentation gauges.
The risk that your trade logic is right but your realized fill, slippage, timing, or spread destroys the expected edge.
A Financial Conditions Index aggregates variables such as rates, credit spreads, equities, and the dollar to measure how supportive or restrictive the market environment is for growth and risk assets.
FRA-OIS spread measures the difference between interbank funding expectations and overnight indexed swap rates, often used as a gauge of banking and short-term funding stress.
A funding-stress monitor can warn before equity volatility reprices.
A liquidity premium monitor can separate default risk from liquidity-driven spread widening.
A card for handling fast markets, wide spreads, liquidity air pockets, and broken execution assumptions.
A card for tracking cross-currency basis, repo dislocations, and balance-sheet stress as early warning signals.