Measuring the risk of a non-linear portfolio with fat-tailed risk factors through a probability conserving transformation

Date, Paresh; Bustreo, Roberto

doi:10.1093/imaman/dpu015

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…Wang and Huang (2016) endogenously formulated the best form of insurance contract to maximize the expected utility of insurance under VaR and CVaR constraints. Date and Bustreo (2016) studied how to approximate VaR and CVAR using new heuristic methods when the net return of portfolio investment may be a nonlinear function of non-Gaussian risk factors. Chen and Yang (2017) used CVaR as a risk measure to propose portfolio stochastic programming and stage wise portfolio stochastic programming based on the stock investment data.…”

Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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The literature on portfolio selection and risk measurement has considerably advanced in recent years. The aim of the present paper is to trace the development of the literature and identify areas that require further research. This paper provides a literature review of the characteristics of financial data, commonly used models of portfolio selection, and portfolio risk measurement. In the summary of the characteristics of financial data, we summarize the literature on fat tail and dependence characteristic of financial data. In the portfolio selection model part, we cover three models: mean-variance model, global minimum variance (GMV) model and factor model. In the portfolio risk measurement part, we first classify risk measurement methods into two categories: moment-based risk measurement and moment-based and quantile-based risk measurement. Moment-based risk measurement includes time-varying covariance matrix and shrinkage estimation, while moment-based and quantile-based risk measurement includes semi-variance, VaR and CVaR.

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Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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“…Delta Normal VaR (DN VaR) and Delta Gamma Normal VaR (DGN VaR) have been developed using the Taylor Polynomial concept to approximate the return value of the stocks underlying the call option (Sulistianingsih et al, 2019). DN VaR uses a first-order Taylor Polynomial, while DGN VaR uses a second-order Taylor Polynomial (Date & Bustreo, 2016). As the name suggests, risk measurement of options using DN VaR only incorporates the Delta Greeks in its formula, whereas DGN VaR incorporates both Delta and Gamma Greeks.…”

Section: A Introductionmentioning

confidence: 99%

The Application of Delta Gamma Normal Value at Risk to Measure the Risk in the Call Option of Stock

Astuti,

Sulistianingsih,

Martha

et al. 2024

JTAM

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Call options of stock have a nonlinear dependence on market risk factors, thus encouraging the development of a method capable of measuring the risk of call option of stock, namely the Delta Gamma Normal Value at Risk (DGN VaR) method. The DGN VaR method can provide a more accurate VaR estimate than Delta Normal VaR (DN VaR) because of the Delta and Gamma sensitivity measures in the formula. The DGN VaR method uses the second-order Taylor Polynomial approach to approximate the return of stock price underlying the call option. This research applies the DGN VaR method to analyze the risk of call options of Atlassian Corporation (TEAM) and MicroStrategy Incorporated (MSTR). Both companies operate in the technology sector and are among the top 100 largest software companies based on market capitalization for the analysis period September 21, 2022 to September 21, 2023. The analyzed options in this research consist of in-the-money and out-of-the-money options with several strike prices (K). For in-the-money options, the strike prices are $105, $110, and $115 for TEAM, and $150, $160, and $170 for MSTR, while for out-of-the-money options, the strike prices are $190, $195, and $200 for TEAM, and $330, $340, and $350 for MSTR with varying confidence levels of 80%, 90%, 95%, and 99%. Based on the results of the analysis, the DGN VaR for the analyzed in-the-money option has a greater value than the DGN VaR for the analyzed out-of-the-money option.

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“…Another important line of research is focused on relaxing the assumption that portfolio value changes linearly with changes in risk factors, which results in methods commonly called delta-gamma developed in (Britten-Jones and Schaefer, 1999;Duffie and Pan, 2001;Wilson, 1999). Offering a similar computational cost as the delta-gamma approach, Date and Bustreo (2016) propose a novel heuristic methods by mapping non-normal marginal distributions to normal distributions using a probability conserving transformation. Their approach is specially designed for portfolios exposed to non-linear functions of non-normal risk factors.…”

Section: Introductionmentioning

confidence: 99%