The evaluation of American compound option prices under stochastic volatility and stochastic interest rates

IF 0.8 4区 经济学 Q4 BUSINESS, FINANCE Journal of Computational Finance Pub Date : 2013-09-01 DOI:10.21314/JCF.2013.264
C. Chiarella, Boda Kang
{"title":"The evaluation of American compound option prices under stochastic volatility and stochastic interest rates","authors":"C. Chiarella, Boda Kang","doi":"10.21314/JCF.2013.264","DOIUrl":null,"url":null,"abstract":"A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate driven by Cox–Ingersoll–Ross processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free-boundary PDE problem, which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the projected successive over-relaxation method.","PeriodicalId":51731,"journal":{"name":"Journal of Computational Finance","volume":"17 1","pages":"71-92"},"PeriodicalIF":0.8000,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Finance","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.21314/JCF.2013.264","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 25

Abstract

A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston’s stochastic volatility and with stochastic interest rate driven by Cox–Ingersoll–Ross processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free-boundary PDE problem, which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the projected successive over-relaxation method.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
随机波动率和随机利率下的美式复合期权价格评价
复合期权(母期权)赋予持有者购买(做多)或卖出(做空)标的期权(子期权)的权利,而不是义务。本文研究了在Cox-Ingersoll-Ross过程驱动下,基础动力服从Heston随机波动率和随机利率的美式复合期权定价问题。我们使用偏微分方程(PDE)方法来获得数值解。通过稀疏网格法求解两道自由边界PDE问题,与基于最小二乘蒙特卡罗模拟结合投影逐次过松弛法的基准解的结果相比,发现该问题的求解是准确和高效的。
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 去求助
来源期刊
CiteScore
0.90
自引率
0.00%
发文量
8
期刊介绍: The Journal of Computational Finance is an international peer-reviewed journal dedicated to advancing knowledge in the area of financial mathematics. The journal is focused on the measurement, management and analysis of financial risk, and provides detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments. The journal welcomes papers dealing with innovative computational techniques in the following areas: Numerical solutions of pricing equations: finite differences, finite elements, and spectral techniques in one and multiple dimensions. Simulation approaches in pricing and risk management: advances in Monte Carlo and quasi-Monte Carlo methodologies; new strategies for market factors simulation. Optimization techniques in hedging and risk management. Fundamental numerical analysis relevant to finance: effect of boundary treatments on accuracy; new discretization of time-series analysis. Developments in free-boundary problems in finance: alternative ways and numerical implications in American option pricing.
期刊最新文献
Genus Aconitum (Ranunculaceae) in the Ukrainian Carpathians and adjacent territories. Toward a unified implementation of regression Monte Carlo algorithms Neural stochastic differential equations for conditional time series generation using the Signature-Wasserstein-1 metric Robust pricing and hedging via neural stochastic differential equations Estimating risks of European option books using neural stochastic differential equation market models
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1