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We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Indu…
In theory, the sum of squares of log returns sampled at high frequency estimates their variance. When market microstructure noise is present but unaccounted for, however, we show that the optimal sampling frequency is finite and derives its closed-form expression. But even with optimal sampling, using say 5-min returns when transactions are recorded every second, a vast amount of data is discarded, in contradiction t…
Empirical correlation matrices estimated from financial return time series are contaminated by statistical noise arising from finite sample size, obscuring genuine interactions among assets. We apply spectral decomposition to separate the empirical correlation matrix into a structured component associated with eigenvalues exceeding the Marchenko-Pastur bounds and a random component representing statistical noise. Usi…
Applying historical data from the USD LIBOR transition period, we estimate a joint model for SOFR, Fed Funds, and Eurodollar futures rates as well as spot USD LIBOR and term repo rates. The framework endogenously models basis spreads between each of the benchmark rates and allows for the decomposition of spreads. Modelling the LIBOR-OIS spread as credit and funding-liquidity roll-over risk, we find that the spike in …
In this paper, we analyze the diversity of term structure functions (e.g., yield curves, swap curves, credit curves) constructed in a process which complies with some admissible properties: arbitrage-freeness, ability to fit market quotes and a certain degree of smooth- ness. When present values of building instruments are expressed as linear combinations of some primary quantities such as zero-coupon bonds, discount…
We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to con…
We review the main changes in the interbank market after the financial crisis started in August 2007. In particular, we focus on the fixed income market and we analyse the most relevant empirical evidences regarding the divergence of the existing basis between interbank rates with different tenor, such as Libor and OIS. We also discuss a qualitative explanation of these effects based on the consideration of credit an…
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…
Put-call parity is a terminal-payoff identity; quoted residuals against traded futures are near zero. Yet enforcing parity is path-dependent, exposing arbitrageurs to daily settlement, margin, and finite capital. Using minute-level NBBO data on S&P 500 and Russell 2000 options, I extract option-implied discount factors, compare them with the OIS curve, and construct an annualized carry gap. A reduced-form specificati…
This study introduces a new technique to recover the implicit discount factor in the derivative market using only European put and call prices: this discount is grounded in actual transactions in active markets. Moreover, this study identifies the implied cost of funding, over OIS, of major market players. Does a liquid equity market allow arbitrage? The key idea is that the (unique) forward contract -- built using t…
In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and…
We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine pr…
Artificial transaction generation remains an important source of potential market manipulation on cryptocurrency exchanges, as it may distort reported liquidity and reduce market transparency. This study proposes a diagnostic framework for detecting unusual trading patterns based on complexity and statistical-structure measures derived from high-frequency trade-level data. The analysis considers log-returns, trading …
Agent skills, structured packages of procedural knowledge and executable resources that agents dynamically load at inference time, have become a reliable mechanism for augmenting LLM agents. Yet inference-time skill augmentation is fundamentally limited: retrieval noise introduces irrelevant guidance, injected skill content imposes substantial token overhead, and the model never truly acquires the knowledge it merely…
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rate…
Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of …
Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-Itô-OI model, we assume that the option-implied volatility can influence the security's future volatility, and the option-implied volatility is tre…
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.
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.
OIS Swap (Rates).
Bid Ask Bounce (Liquidity).
OIS Discounting (Rates).
OIS Curve 1M (Rates).
OIS Curve 3M (Rates).
OIS Curve 6M (Rates).
OIS Curve 1Y (Rates).
OIS Curve 2Y (Rates).
OIS Curve 5Y (Rates).
OIS Curve 7Y (Rates).
OIS Curve 10Y (Rates).
OIS Curve 20Y (Rates).
OIS Curve 30Y (Rates).
OIS Curve front (Rates).
OIS Curve belly (Rates).
OIS Curve long-end — Interest-rate policy, curve, or STIR concept for rates desks.
OIS Curve ultra-long — Interest-rate policy, curve, or STIR concept for rates desks.
OIS Curve Fed (Rates).
OIS Curve ECB (Rates).
OIS Curve BoE (Rates).
OIS Curve BoJ (Rates).
OIS Curve PBoC (Rates).
OIS Curve RBA (Rates).
OIS Curve BoC (Rates).
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.
OIS Curve 10Y (Rates).
OIS Curve 1M (Rates).
OIS Curve 1Y (Rates).
OIS Curve 20Y (Rates).
OIS Curve 2Y (Rates).
OIS Curve 30Y (Rates).
OIS Curve 3M (Rates).
OIS Curve 5Y (Rates).
OIS Curve 6M (Rates).
OIS Curve 7Y (Rates).
OIS Curve belly (Rates).
OIS Curve BoC (Rates).
OIS Curve BoE (Rates).
OIS Curve BoJ (Rates).
OIS Curve ECB (Rates).
OIS Curve Fed (Rates).
OIS Curve front (Rates).
OIS Curve long-end — Interest-rate policy, curve, or STIR concept for rates desks.
OIS Curve PBoC (Rates).
OIS Curve RBA (Rates).
OIS Curve ultra-long — Interest-rate policy, curve, or STIR concept for rates desks.
OIS Discounting (Rates).