arXiv · arXiv · 2013
The market practice of extrapolating different term structures from different instruments lacks a rigorous justification in terms of cash flows structure and market observables. In this paper, we integrate our previous consistent theory for pricing under credit, collateral and funding risks into term structure modelling, integrating the origination of different term structures with such effects. Under a number of ass…
Andrea Pallavicini, Damiano Brigo
arXiv · arXiv · 2013
Changes in collateralization have been implicated in significant default (or near-default) events during the financial crisis, most notably with AIG. We have developed a framework for quantifying this effect based on moving between Merton-type and Black-Cox-type structural default models. Our framework leads to a single equation that emcompasses the range of possibilities, including collateralization remargining freq…
Chris Kenyon, Andrew Green
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 · 2010
Bilateral CVA as currently implement has the counterintuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However, there are two significant omissions for practical implementation that come from the same source, i.e. positions not booked in us…
Chris Kenyon
arXiv · arXiv · 2017
Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable in the repo market, for derivatives netting sets are perpetual while repo tenors are typically in months. This arti…
Wujiang Lou
arXiv · arXiv · 2015
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of interest rates in a fully collateralized market. It gives a new form…
Masaaki Fujii, Akihiko Takahashi
arXiv · arXiv · 2026
Collateral allocation for uncleared derivatives is a legally constrained and operationally discrete optimization problem. Institutions must satisfy margin requirements while respecting CSA eligibility rules, valuation percentages, rounding, transfer thresholds, concentration limits, custody conditions, inventory, and VM, IM, or IA side constraints. This manuscript develops CR-HO-QAOA, a certified higher-order quantum…
Tao Jin, Stuart Florescu
arXiv · arXiv · 2026
We study permissionless spot--perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execution frictions. The paper delivers three results. First, it solves a static control problem for the collateral share and…
Anatoly Krestenko, Mikhail Butov, Rostislav Berezovskiy, Danila Bolotin
arXiv · arXiv · 2017
Haircutting non-cash collateral has become a key element of the post-crisis reform of the shadow banking system and OTC derivatives markets. This article develops a parametric haircut model by expanding haircut definitions beyond the traditional value-at-risk measure and employing a double-exponential jump-diffusion model for collateral market risk. Haircuts are solved to target credit risk measurements, including pr…
Wujiang Lou
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 · 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
arXiv · arXiv · 2012
In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties -- an investor and a counterparty. Moreover, we model the margin process as a functional of the credit ratings of the counterparty…
Tomasz R. Bielecki, Igor Cialenco, Ismail Iyigunler
arXiv · arXiv · 2011
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interest-rate swaps as underlying portfolio, and allow for mutual dependences betwe…
Damiano Brigo, Agostino Capponi, Andrea Pallavicini, Vasileios Papatheodorou
arXiv · arXiv · 2025
We address finance-native collateral optimization under ISDA Credit Support Annexes (CSAs), where integer lots, Schedule A haircuts, RA/MTA gating, and issuer/currency/class caps create rugged, legally bounded search spaces. We introduce a certifiable hybrid pipeline purpose-built for this domain: (i) an evidence-gated LLM that extracts CSA terms to a normalized JSON (abstain-by-default, span-cited); (ii) a quantum-i…
Tao Jin, Stuart Florescu, Heyu, Jin
arXiv · arXiv · 2024
The aim of this work is to propose an end-by-end modeling framework to evaluate the risk measures of a bank's portfolio of collateralized loans in an economy subject to the climate transition. The economy, organized in sectors, is driven by a multidimensional Ornstein-Uhlenbeck (OU) productivity process while the climate transition is declined thanks to continuous deterministic carbon price and intensities processes.…
Lionel Sopgoui
arXiv · arXiv · 2015
We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that…
Giacomo Bormetti, Damiano Brigo, Marco Francischello, Andrea Pallavicini
arXiv · arXiv · 2013
We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed on simple single asset classes to simple derivatives embedding the new or previously neglected type…
Damiano Brigo, Andrea Pallavicini
arXiv · arXiv · 2013
In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation (PDE) for the derivatives price, obtain and decompose its solution into the risk-free value of the d…
Lixin Wu