arXiv · arXiv · 2010
This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipović, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional Lévy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to m…
Thorsten Schmidt, Jerzy Zabczyk
arXiv · arXiv · 2010
We show that stochastic recovery always leads to counter-intuitive behaviors in the risk measures of a CDO tranche - namely, continuity on default and positive credit spread risk cannot be ensured simultaneously. We then propose a simple recovery variance regularization method to control the magnitude of negative credit spread risk while preserving the continuity on default.
Emmanuel Schertzer, Yadong Li, Umer Khan
arXiv · arXiv · 2009
This paper introduces a new semi-parametric approach to the pricing and risk management of bespoke CDO tranches, with a particular attention to bespokes that need to be mapped onto more than one reference portfolio. The only user input in our framework is a multi-factor model (a "prior" model hereafter) for index portfolios, such as CDX.NA.IG or iTraxx Europe, that are chosen as benchmark securities for the pricing o…
Igor Halperin
arXiv · arXiv · 2021
In this paper we perform a rigorous mathematical analysis of the word2vec model, especially when it is equipped with the Skip-gram learning scheme. Our goal is to explain how embeddings, that are now widely used in NLP (Natural Language Processing), are influenced by the distribution of terms in the documents of the considered corpus. We use a mathematical formulation to shed light on how the decision to use such a m…
Mengda Li, Charles-Albert Lehalle
arXiv · arXiv · 2010
This paper describes a consistent and arbitrage-free pricing methodology for bespoke CDO tranches. The proposed method is a multi-factor extension to the (Li 2009) model, and it is free of the known flaws in the current standard pricing method of base correlation mapping. This method assigns a distinct market factor to each liquid credit index and models the correlation between these market factors explicitly. A low-…
Yadong Li
arXiv · arXiv · 2009
We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. En passant, we also illustrate the implied copula, a method that can consistently account …
Damiano Brigo, Andrea Pallavicini, Roberto Torresetti
arXiv · arXiv · 2009
We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO's. In this paper, we consider a heterogeneous pool of names. Our main tool is a large-deviations analysis which allows us to precisely study the behavior of a large amount of idiosyncratic randomness. Our calculations allow a fairly general treatment of correlation.
Richard B. Sowers
arXiv · arXiv · 2009
We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO's. In this paper, we consider a simplified model which will allow us to introduce some of the concepts and calculations.
Richard B. Sowers
arXiv · arXiv · 2020
Recently, a number of structured funds have emerged as public-private partnerships with the intent of promoting investment in renewable energy in emerging markets. These funds seek to attract institutional investors by tranching the asset pool and issuing senior notes with a high credit quality. Financing of renewable energy (RE) projects is achieved via two channels: small RE projects are financed indirectly through…
N. Packham
arXiv · arXiv · 2026
Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $Δt \to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LV…
Nils Bundi
arXiv · arXiv · 2013
We show how to restructure the counterparty risk faced by the originator of a securitization or covered bond arising from an interest rate hedging swap assisted by a "one-way" collateral agreement. This risk emerges when the swap is negotiated between the special purpose vehicle and a third party that covers itself through a back-to-back swap with the originator. We show that the counterparty risk of the originator m…
Lorenzo Giada, Claudio Nordio
arXiv · arXiv · 2026
Bankruptcy is a low-frequency but high-impact corporate event, making early risk identification important for creditors, investors, regulators, and risk managers. Traditional bankruptcy-prediction models rely primarily on accounting ratios, but these measures may reflect financial deterioration only after it appears in reported financial statements. Narrative disclosures in annual 10-K filings may therefore provide i…
Zhen Zhang, Moxuan Zheng, Tongchen Zhang, Luyun Lin, Yiqing Wang
arXiv · arXiv · 2024
We investigate the efficacy of large language models (LLMs) in sentiment analysis of U.S. financial news and their potential in predicting stock market returns. We analyze a dataset comprising 965,375 news articles that span from January 1, 2010, to June 30, 2023; we focus on the performance of various LLMs, including BERT, OPT, FINBERT, and the traditional Loughran-McDonald dictionary model, which has been a dominan…
Kemal Kirtac, Guido Germano
arXiv · arXiv · 2010
The goal of this paper is to specify dynamic term structure models with discrete tenor structure for credit portfolios in a top-down setting driven by time-inhomogeneous Lévy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs and options on STCDOs. A calibration to iTraxx data with an extended Kalman f…
Ernst Eberlein, Zorana Grbac, Thorsten Schmidt
arXiv · arXiv · 2009
We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and index swaptions. Using properties of affine models, we derive closed formulas for the pricing of index CDS, CDO tranches and Nth-to-default. For index swaptions, we give an exact pric…
Louis Paulot