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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…
In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control theoretic approach of Gombani & Runggaldier (2013) and…
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 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…
We develop a continuous-time structural dynamic model to determine the exact insolvency regions of banks arising from the non-linear interaction between liquidity and credit risk. While existing literature predominantly treats these risks in isolation or via reduced-form specifications, we explicitly model the feedback loop where funding shocks and regulatory constraints force balance-sheet adjustments that can lead …
This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury …
This paper proposes a reinforcement learning--based framework for cryptocurrency portfolio management using the Soft Actor--Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Traditional portfolio optimization methods often struggle to adapt to the highly volatile and nonlinear dynamics of cryptocurrency markets. To address this, we design an agent that learns continuous trading actions directly f…
We propose ARBITER, a risk-neutral neural operator for learning joint SPX-VIX term structures under no-arbitrage constraints. ARBITER maps market states to an operator that outputs implied volatility and variance curves while enforcing static arbitrage (calendar, vertical, butterfly), Lipschitz bounds, and monotonicity. The model couples operator learning with constrained decoders and is trained with extragradient-st…
We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full stability and ergodicity proofs for both linear and nonlinear Hawkes models, implements time-rescaling and goodness-of-fit diagnostics, and calibrates exponential and power-law kernels …
SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR term structure model that is well-suited for risk management and derivatives pricing within the incomplete markets paradigm. The model incorporates relevant macroeconomic factors tha…
Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade…
Overnight rates, such as the SOFR (Secured Overnight Financing Rate) in the US, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates due to monetary policy interventions and liquidity constraints. This corresponds to stochastic discontinuities (i.e., discontinuities occurring at ex-ante known points in…
With the improvement of computer performance and the development of GPU-accelerated technology, trading with machine learning algorithms has attracted the attention of many researchers and practitioners. In this research, we propose a novel portfolio management strategy based on the framework of Deep Deterministic Policy Gradient, a policy-based reinforcement learning framework, and compare its performance to that of…
The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use t…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to different distribution spread rates compared to standard models. In financial modelling this has been used to accommodate for random trade duration in the tick-by-tick price process. We …
Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath-Jarrow-Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lacking in the finance literature so far.
In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift…
Chain-of-thought prompting asks the model to emit intermediate reasoning steps before the answer, which reliably lifts arithmetic, symbolic, and multi-hop tasks.
LSTM is a gated RNN whose cell state can carry information across many steps, with input, forget, and output gates trained by gradient descent.
A VAE is a probabilistic autoencoder: the encoder outputs a distribution q(z|x), the decoder p(x|z), and training maximizes an ELBO with a KL term that keeps the latent well-behaved.
Balance Sheet Constraint Dealer — Dealer SLR/balance-sheet limits reducing intermediation.
Bank Capital Ratio — Loss-absorbing equity buffer determining lending capacity and dividend policy.
Net Stable Funding Ratio — Stable funding versus long-term assets — constrains maturity transformation.
Trade nearby versus deferred on the same curve — a pure term-structure book, the smallest-beta cousin of commodity RV.
Slow trend: lookbacks of roughly 6–12 months, low turnover, fewer whipsaws, later entries, and the bulk of classic CTA crisis convexity.
The workhorse speed: roughly 1–4 month lookbacks — enough signal to catch swings, enough noise to bleed in ranges.
A single platform that allocates risk across trend, carry, short-term, RV, and sometimes options — a house of sleeves, not a style-pure trend shop.
Holds for a few days to two weeks — higher turnover, tighter capacity, lower correlation to slow trend, and a different execution problem.
Short-term interest-rate futures — SOFR, SONIA, Euribor strips — a specialist language of meeting-to-meeting path trades and pack/bundle spreads.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
Realized Volatility — Historical return variation that determines PnL for delta-hedged option positions.
Term Structure of Volatility — How IV varies across expiries — front vs back month regimes.
VIX Futures Term Structure — Curve shape driving roll yield for vol ETNs and systematic short-vol carry.
VIX term structure tracks the shape of volatility futures across maturities and helps identify whether the market is pricing stable conditions or near-term stress.
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.
Don’t fight the Fed is the rule of thumb that a determined policy impulse (easing or tightening) will eventually dominate discretionary macro views.
Comparative advantage says a country (or desk) should specialize in the activity with the lowest opportunity cost, even if it is worse at everything in absolute terms.
US 10-Year Breakeven Inflation reflects the inflation rate implied by the gap between nominal Treasuries and TIPS, serving as a market-based gauge of long-term inflation expectations.
Original Sin EM Debt — Inability to borrow long-term in local currency, raising external vulnerability.
The 1973–74 OPEC embargo quadrupled oil prices, fused inflation with a growth shock (stagflation), and ended the last illusions of the post-war energy-cheap regime.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
Terms of Trade Shock — Relative export-import price shifts altering growth and currency paths.
Twin Deficits — Combined fiscal and current-account deficits pressuring currency and term premium.
BTFP usage tracks how much funding banks obtain through the Bank Term Funding Program, offering insight into balance-sheet stress and demand for official liquidity backstops.
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.
Money market fund assets track the amount of cash parked in short-term low-risk vehicles, providing insight into liquidity preference, deposit substitution, and defensive positioning.
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.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
Quantitative Tightening Pace — The speed of balance-sheet runoff and its impact on reserves, collateral markets, and term funding.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.
Itô’s lemma is the chain rule for stochastic calculus: a smooth function of an Itô process picks up a second-order dt term from (dW)² = dt.
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.
Balance Sheet Constraint Dealer — Dealer SLR/balance-sheet limits reducing intermediation.
Bank Capital Ratio — Loss-absorbing equity buffer determining lending capacity and dividend policy.
Bank Term Funding Program Legacy — Crisis facility allowing par advances against securities.
BTFP usage tracks how much funding banks obtain through the Bank Term Funding Program, offering insight into balance-sheet stress and demand for official liquidity backstops.
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.
Calendar Spread — Relative vol trade across expiries exploiting term structure dislocations.
Chain-of-thought prompting asks the model to emit intermediate reasoning steps before the answer, which reliably lifts arithmetic, symbolic, and multi-hop tasks.
Commercial paper spreads track the cost of short-term corporate borrowing relative to safer benchmarks and help identify stress in corporate funding markets.
Comparative advantage says a country (or desk) should specialize in the activity with the lowest opportunity cost, even if it is worse at everything in absolute terms.
Trade nearby versus deferred on the same curve — a pure term-structure book, the smallest-beta cousin of commodity RV.
Don’t fight the Fed is the rule of thumb that a determined policy impulse (easing or tightening) will eventually dominate discretionary macro views.
Trade the VIX curve — short steep contango, respect backwardation — a roll-yield book in vol futures.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
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.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Itô’s lemma is the chain rule for stochastic calculus: a smooth function of an Itô process picks up a second-order dt term from (dW)² = dt.
LSTM is a gated RNN whose cell state can carry information across many steps, with input, forget, and output gates trained by gradient descent.
Slow trend: lookbacks of roughly 6–12 months, low turnover, fewer whipsaws, later entries, and the bulk of classic CTA crisis convexity.
The workhorse speed: roughly 1–4 month lookbacks — enough signal to catch swings, enough noise to bleed in ranges.
Blend intermediate momentum, short-term reversal, and a volatility filter — a multi-horizon equity recipe.
Money market fund assets track the amount of cash parked in short-term low-risk vehicles, providing insight into liquidity preference, deposit substitution, and defensive positioning.
A single platform that allocates risk across trend, carry, short-term, RV, and sometimes options — a house of sleeves, not a style-pure trend shop.
Net Stable Funding Ratio — Stable funding versus long-term assets — constrains maturity transformation.