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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…
We establish innovative liquidity premium measures, and construct liquidity-adjusted return and volatility to model assets with extreme liquidity, represented by a portfolio of selected crypto assets, and upon which we develop a set of liquidity-adjusted ARMA-GARCH/EGARCH models. We demonstrate that these models produce superior predictability at extreme liquidity to their traditional counterparts. We provide empiric…
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…
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…
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…
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.
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.
Twin Deficits — Combined fiscal and current-account deficits pressuring currency and term premium.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
Term premium is the extra compensation investors demand for holding longer-term bonds instead of rolling short-term debt, reflecting duration risk, uncertainty, and market structure.
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.
Forward Guidance — How central bank language shapes term premium and front-end rate expectations before actual policy moves.
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.
Term premium is the extra compensation investors demand for holding longer-term bonds instead of rolling short-term debt, reflecting duration risk, uncertainty, and market structure.
Twin Deficits — Combined fiscal and current-account deficits pressuring currency and term premium.