Papers, wiki, Option Blackboard, encyclopedia, and cards.
We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance.…
Abstract Following the “flash crash” on May 6, 2010, warning signals for impending market stress have been in high demand, yet only the VPIN metric of Easley, López de Prado, and O’Hara (ELO) has claimed success. In addition, ELO find the metric useful in predicting short-term volatility. VPIN involves decomposing volume into active buys and sells. We utilize quotes and trade data to construct an accurate trade class…
Prediction markets are starting to look less like crowd polls and more like electronic markets. The central question is therefore no longer only whether these markets forecast well, but what happens when institutional liquidity enters: do spreads tighten, does price discovery improve, and do those gains actually reach the traders who are slowest to react when information arrives? This paper offers a research design f…
Predicting the intraday stock jumps is a significant but challenging problem in finance. Due to the instantaneity and imperceptibility characteristics of intraday stock jumps, relevant studies on their predictability remain limited. This paper proposes a data-driven approach to predict intraday stock jumps using the information embedded in liquidity measures and technical indicators. Specifically, a trading day is di…
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(ρ(λX))_{λ\ge 0}$, where $ρ$ is a convex risk measure and $X$ a random variable, and we call such a curve a \emph{liquidity risk profile}. The shape of a liquidity risk profile is intimately linked with the tail behavi…
Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a `liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption is that - due to changes on market liquidity conditions - one operates along an `operational time' to which the P&L process of liquidating a market portfolio i…
In this three-part series of papers, we argue that the conventional spread measures are not well defined for credit-risky bonds and introduce a set of credit term structures which correct for the biases associated with the strippable cash flow valuation assumption. We demonstrate that the resulting estimates are significantly more robust and remain meaningful even when applied to deeply distressed bonds. We also sugg…
Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liqu…
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers the asset-liability management of the liquidity gap risk (or asset-liability…
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second dimension focuses on asset liquidity risk (or market liquidity) modeling, and the third dimension considers asset-liability liquidity risk management (or asset-liability matching). The…
Systemic liquidity risk, defined by the IMF as "the risk of simultaneous liquidity difficulties at multiple financial institutions", is a key topic in macroprudential policy and financial stress analysis. Specialized models to simulate funding liquidity risk and contagion are available but they require not only banks' bilateral exposures data but also balance sheet data with sufficient granularity, which are hardly a…
Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatil…
Public blockchains can make many trading venues simultaneously visible and mechanically reachable, yet an order still has to pay to activate each additional venue: technological connectivity need not translate into economically integrated execution. Automated-market-maker (AMM) pools make this gap directly measurable, because exact pre-trade venue states, transaction-level routing costs, and realized venue use can be…
Three quantitative predictions have been advanced for the square-root law (SRL) of market impact, $I/σ_D = c\,(Q/V_D)^δ$ with $δ\approx 0.5$: GGPS ($δ=β-1$), FGLW ($δ=α-1$), and LOB walking ($δ=1/(1+γ)$). Using a minimal limit-order-book model populated by heterogeneous interacting agents and calibrated against the Tokyo Stock Exchange benchmark ($\langleδ\rangle = 0.489$~\citep{satoStrictUniversalitySquareRoot2025})…
We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve he…
We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical properties: persistent signed order flow, rough trading volume and volatility, and power-law market impact. In our framework, all these quantities are pinne…
Liquidity withdrawal is a critical indicator of market fragility. In this project, I test a framework for forecasting liquidity withdrawal at the individual-stock level, ranging from less liquid stocks to highly liquid large-cap tickers, and evaluate the relative performance of competing model classes in predicting short-horizon order book stress. We introduce the Liquidity Withdrawal Index (LWI) -- defined as the ra…