arXiv · arXiv · 2012
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. At rollov…
Gechun Liang, Eva Lütkebohmert, Wei Wei
arXiv · arXiv · 2016
We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes for…
Damiano Brigo, Cristin Buescu, Marek Rutkowski
arXiv · arXiv q-fin · 2025
Financial markets often appear chaotic, yet ranges are rarely accidental. They emerge from structured interactions between market context and capital conditions. The four-hour timeframe provides a critical lens for observing this equilibrium zone where institutional positioning, leveraged exposure, and liquidity management converge. Funding mechanisms, especially in perpetual futures, act as disciplinary forces that …
Habib Badawi, Mohamed Hani, Taufikin Taufikin
arXiv · arXiv q-fin · 2015
An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional cash margin to the lender which needs to be financed at her unsecured debt rate. This paper incorporates funding asymmetry (borrowed cash and invested cash earning different intere…
Wujiang Lou
OpenAlex · Review of Financial Studies · 2008 · cites 5059
We provide a model that links an asset's market liquidity (i.e., the ease with which it is traded) and traders' funding liquidity (i.e., the ease with which they can obtain funding). Traders provide market liquidity, and their ability to do so depends on their availability of funding. Conversely, traders' funding, i.e., their capital and margin requirements, depends on the assets' market liquidity. We show that, unde…
Markus K. Brunnermeier, Lasse Heje Pedersen
arXiv · arXiv · 2026
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…
Christian P. Fries
arXiv · arXiv · 2011
We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral modeling, Gap Risk, Re-hypothecation, Wrong Way Risk, Basel III, inclusion of Funding costs, First t…
Damiano Brigo
arXiv · arXiv · 2017
We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, i.e., one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semi-linear BSDEs and PDEs, and thus it is necessary to solve the equations numerically. However, once it can be gua…
Junbeom Lee, Chao Zhou
arXiv · arXiv · 2016
Credit and liquidity risks represent main channels of financial contagion for interbank lending markets. On one hand, banks face potential losses whenever their counterparties are under distress and thus unable to fulfill their obligations. On the other hand, solvency constraints may force banks to recover lost fundings by selling their illiquid assets, resulting in effective losses in the presence of fire sales - th…
Giulio Cimini, Matteo Serri
arXiv · arXiv · 2014
We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA, DVA, LVA and FVA) are introduced…
Damiano Brigo, Qing Liu, Andrea Pallavicini, David Sloth
arXiv · arXiv · 2014
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collatera…
Damiano Brigo, Andrea Pallavicini
arXiv · arXiv · 2013
Funding is a cost to trading desks that they see as an input. Current FVA-related literature reflects this by also taking funding costs as an input, usually constant, and always risk-neutral. However, this funding curve is the output from a Treasury point of view. Treasury must consider Regulatory-required liquidity buffers, and both risk-neutral (Q) and physical measures (P). We describe the Treasury funding problem…
Chris Kenyon, Andrew Green
arXiv · arXiv · 2012
The main result of this paper is a collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debit valuation adjustments (CVA, DVA) along with margining and funding costs, all in a consistent way. Funding risk breaks the bilateral nature of the valuation formula. We find that the equation has a recursive form, making the introduction of a purely…
Andrea Pallavicini, Daniele Perini, Damiano Brigo
OpenAlex · Munich Personal RePEc Archive (Ludwig Maximilian University of Munich) · 2011 · cites 235
The financial crisis and the ensuing recession have caused a sharp deterioration in public finances across advanced economies, raising investor concerns about sovereign risk. The concerns have so far mainly affected the euro area, where some countries have seen their credit ratings downgraded during 2009−11 and their funding costs rise sharply. Other countries have also been affected, but to a much lesser extent. Gre…
Fabio Panetta, Ricardo Correa, Michael Davies, Antonio Di Cesare, José-Manuel Marques
arXiv · arXiv · 2023
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…
Claudio Fontana, Simone Pavarana, Wolfgang J. Runggaldier
arXiv · arXiv · 2021
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…
Thierry Roncalli
arXiv · arXiv · 2021
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…
Thierry Roncalli, Amina Cherief, Fatma Karray-Meziou, Margaux Regnault
arXiv · arXiv · 2021
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…
Thierry Roncalli, Fatma Karray-Meziou, François Pan, Margaux Regnault