A Structural Approach to Default Modelling with Pure Jump Processes

Jean-Philippe Aguilar, N. Pesci, V. James
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Abstract

ABSTRACT We present a general framework for the estimation of corporate default based on a firm’s capital structure, when its assets are assumed to follow a pure jump Lévy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short-term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included.
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使用纯跳转过程进行默认建模的结构化方法
本文提出了一个基于公司资本结构的公司违约估计的一般框架,假设其资产遵循纯跳跃lsamvy过程;这种设置为扩散(对数正态)模型中定义的通常默认指标提供了自然扩展,并允许捕获极端市场事件,如资产价格的突然下跌,这与违约发生密切相关。在此框架内,我们引入了几个纯跳跃过程,仅具有负跳跃,并推导出实用的股票价格封闭公式,这使我们能够使用基于矩的算法从真实市场数据校准参数,并估计相关的默认指标。这些模型的一个显著特征是信用风险向较短期限的再分配:这是对扩散模型的一个有趣改进,众所周知,扩散模型低估了短期违约概率。我们还提供了一个具有正跳跃和负跳跃的模型的扩展,并讨论了结果的定性和定量特征。为了方便读者,还包括了模型实现的实用工具和GitHub链接。
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来源期刊
Applied Mathematical Finance
Applied Mathematical Finance Economics, Econometrics and Finance-Finance
CiteScore
2.30
自引率
0.00%
发文量
6
期刊介绍: The journal encourages the confident use of applied mathematics and mathematical modelling in finance. The journal publishes papers on the following: •modelling of financial and economic primitives (interest rates, asset prices etc); •modelling market behaviour; •modelling market imperfections; •pricing of financial derivative securities; •hedging strategies; •numerical methods; •financial engineering.
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