Perpetual convertible bonds in jump-diffusion models

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2005-01-01 DOI:10.1524/STND.2005.23.1.15

P. Gapeev, C. Kühn

引用次数: 37

Abstract

Summary A convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give an explicit solution to the corresponding optimal stopping game in the context of a reduced form model driven by a Brownian motion and a compound Poisson process with exponential jumps. It turns out that the occurrence of jumps leads to optimal stopping strategies whose structure differs from the results for continuous models.

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跳跃扩散模型中的永续可转换债券

可转换(可赎回)债券是一种证券，持有人可以转换成一定数量的相关股份。此外，发行人可以收回债券，支付一些赔偿，或迫使持有人立即转换债券。在布朗运动驱动的简化模型和具有指数跳变的复合泊松过程中，给出了相应的最优停止对策的显式解。结果表明，跳跃的出现导致了最优停止策略，其结构与连续模型的结果不同。

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

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.