New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management

Sensitivity analysis is at the core of risk management for financial engineering; to calculate the sensitivity with respect to parameters in models with probability expectation, the most traditional approach applies the finite difference method, whereafter integration by parts formula was developed...

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Main Authors: Zheng Gu, Yue Liu, Aijun Yang, Kaodui Li
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/9510466
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author Zheng Gu
Yue Liu
Aijun Yang
Kaodui Li
author_facet Zheng Gu
Yue Liu
Aijun Yang
Kaodui Li
author_sort Zheng Gu
collection DOAJ
description Sensitivity analysis is at the core of risk management for financial engineering; to calculate the sensitivity with respect to parameters in models with probability expectation, the most traditional approach applies the finite difference method, whereafter integration by parts formula was developed based on the Brownian environment and applied in sensitivity analysis for better computational efficiency than that of finite difference. Establishing a similar version of integration by parts formula for the Markovian environment is the main focus and contribution of this paper. It is also shown by numerical simulation that our proposed methodology and approach outperform the traditional finite difference method for sensitivity computation. For empirical studies of sensitivity analysis on an NPV (net present value) model, we show the approaches of modeling, especially for parameter estimation of Markov chains given data of company loan states. Applying our newly established integration by parts formula, numerical simulation estimates the variations caused by the capital return rate and multiplier of overdue loan. Furthermore, managemental implications of these results are discussed for the effectiveness of modeling and the investment risk control.
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issn 2314-4785
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spelling doaj-art-141dc386ffa043cd89fe907338c887ea2025-02-03T01:20:12ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9510466New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk ManagementZheng Gu0Yue Liu1Aijun Yang2Kaodui Li3School of FinanceSchool of Finance and EconomicsCollege of Economics and ManagementSchool of Finance and EconomicsSensitivity analysis is at the core of risk management for financial engineering; to calculate the sensitivity with respect to parameters in models with probability expectation, the most traditional approach applies the finite difference method, whereafter integration by parts formula was developed based on the Brownian environment and applied in sensitivity analysis for better computational efficiency than that of finite difference. Establishing a similar version of integration by parts formula for the Markovian environment is the main focus and contribution of this paper. It is also shown by numerical simulation that our proposed methodology and approach outperform the traditional finite difference method for sensitivity computation. For empirical studies of sensitivity analysis on an NPV (net present value) model, we show the approaches of modeling, especially for parameter estimation of Markov chains given data of company loan states. Applying our newly established integration by parts formula, numerical simulation estimates the variations caused by the capital return rate and multiplier of overdue loan. Furthermore, managemental implications of these results are discussed for the effectiveness of modeling and the investment risk control.http://dx.doi.org/10.1155/2022/9510466
spellingShingle Zheng Gu
Yue Liu
Aijun Yang
Kaodui Li
New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
Journal of Mathematics
title New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
title_full New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
title_fullStr New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
title_full_unstemmed New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
title_short New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management
title_sort new method of sensitivity computation based on markov models with its application for risk management
url http://dx.doi.org/10.1155/2022/9510466
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AT yueliu newmethodofsensitivitycomputationbasedonmarkovmodelswithitsapplicationforriskmanagement
AT aijunyang newmethodofsensitivitycomputationbasedonmarkovmodelswithitsapplicationforriskmanagement
AT kaoduili newmethodofsensitivitycomputationbasedonmarkovmodelswithitsapplicationforriskmanagement