DEFAULTABLE TERM STRUCTURES DRIVEN BY SEMIMARTINGALES

IF 0.5 Q4 BUSINESS, FINANCE

International Journal of Theoretical and Applied Finance Pub Date : 2021-03-02 DOI:10.1142/s0219024921500321

Sandrine Gumbel, Thorsten Schmidt

引用次数: 0

Abstract

In this paper, we consider a market with a term structure of credit risky bonds in the single-name case. We aim at minimal assumptions extending existing results in this direction: first, the random field of forward rates is driven by a general semimartingale. Second, the Heath–Jarrow–Morton (HJM) approach is extended with an additional component capturing those future jumps in the term structure which are visible from the current time. Third, the associated recovery scheme is as general as possible, it is only assumed to be nonincreasing. In this general setting, we derive generalized drift conditions which characterize when a given measure is a local martingale measure, thus yielding no asymptotic free lunch with vanishing risk (NAFLVR), the right notion for this large financial market to be free of arbitrage.

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由半鞅驱动的可违约期限结构

在本文中，我们考虑了在单一名称情况下具有信用风险债券期限结构的市场。我们的目标是在这个方向上扩展现有结果的最小假设：首先，前向速率的随机场是由一般半鞅驱动的。其次，Heath–Jarrow–Morton（HJM）方法得到了扩展，增加了一个组件来捕捉从当前时间可见的术语结构中的未来跳跃。第三，相关的恢复方案尽可能通用，只是假设它不会增加。在这种一般情况下，我们导出了广义漂移条件，其特征是给定测度是局部鞅测度，因此不产生具有消失风险的渐近自由午餐（NAFLVR），这是这个大型金融市场不存在套利的正确概念。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Theoretical and Applied Finance BUSINESS, FINANCE-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.