A Family of Density Expansions for Lévy-Type Processes

Matthew J. Lorig, S. Pagliarani, A. Pascucci
{"title":"A Family of Density Expansions for Lévy-Type Processes","authors":"Matthew J. Lorig, S. Pagliarani, A. Pascucci","doi":"10.2139/ssrn.2245118","DOIUrl":null,"url":null,"abstract":"We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci, and Riga (2013), we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and defaultable bond prices. For the density expansion, we also provide error bounds for the truncated asymptotic series. Our method is numerically efficient; approximate transition densities and European option prices are computed via Fourier transforms; approximate bond prices are computed as finite series. Additionally, as in Pagliarani et al. (2013), for models with Gaussian-type jumps, approximate option prices can be computed in closed form. Sample Mathematica code is provided.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"28","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2245118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 28

Abstract

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci, and Riga (2013), we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and defaultable bond prices. For the density expansion, we also provide error bounds for the truncated asymptotic series. Our method is numerically efficient; approximate transition densities and European option prices are computed via Fourier transforms; approximate bond prices are computed as finite series. Additionally, as in Pagliarani et al. (2013), for models with Gaussian-type jumps, approximate option prices can be computed in closed form. Sample Mathematica code is provided.
一类lvac型过程的密度展开式
我们考虑一种违约资产,其风险中性定价动态由违约的指数列维型鞅描述。这类模型允许局部波动、局部违约强度和局部依赖的Levy度量。推广并扩展了Pagliarani、Pascucci和Riga(2013)的新型伴随展开技术,我们得到了标的转移密度以及欧式期权价格和违约债券价格的渐近展开式族。对于密度展开,我们也给出了截断渐近级数的误差界。我们的方法在数值上是有效的;通过傅里叶变换计算近似过渡密度和欧式期权价格;近似债券价格以有限级数计算。此外,如Pagliarani等人(2013)所述,对于具有高斯型跳跃的模型,近似期权价格可以以封闭形式计算。提供了Mathematica示例代码。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信