Value-at-Risk computation by Fourier inversion with explicit error bounds

Siven, Johannes Vitalis; Lins, Jeffrey Todd; Szymkowiak-Have, Anna

doi:10.1016/j.frl.2008.12.002

Cited by 12 publications

(6 citation statements)

References 6 publications

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“…Bali, Mo, and Tang (2008) adopted the skewed generalized t ‐distribution with a time‐varying parameter for VaR estimation. Others using either parametric models with tail driven dynamics or non‐parametric techniques in the computation of VaR include Sun, Rachev, and Fabozzi (2009), Siven, Lins, and Szymkowiak‐Have (2009), Huang (2009), and Taamouti (2009).…”

Section: Var Methodologiesmentioning

confidence: 99%

An optimization process in Value‐at‐Risk estimation

Huang

2010

Rev Financ Econ

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A new method is proposed to estimate Value-at-Risk (VaR) by Monte Carlo simulation with optimal backtesting results. The Monte Carlo simulation is adjusted through an iterative process to accommodate recent shocks, thereby taking into account the latest market conditions. Empirical validation covering the current financial crisis shows that VaR estimation via the optimization process is relatively reliable and consistent, and generally outperforms the VaR generated by a simple Monte Carlo simulation. This is particularly true in cases when the out-of-sample evaluation sample spans a lengthy period, as the traditional method tends to underestimate the number of extreme shocks.

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Section: Var Methodologiesmentioning

confidence: 99%

An optimization process in Value‐at‐Risk estimation

Huang

2010

Rev Financ Econ

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“…Considering the difference between multivariate normal distribution and multivariate t distribution in the description of market risk factors, Albanese and Campolieti (2006) proposed the probability density function for calculating the change of option portfolio value and the Monte Carlo simulation method for estimating the multivariate VaR at a given confidence level and explored the relationship between a normal distribution and a fat tail distribution. Like Glasserman (2004), Siven et al (2009) deduced the closed expression of moment generating function in the case of multivariate t distribution and compared Fourier-Inversion method with Monte Carlo simulation method. The results showed that the Fourier-inversion method was much quicker than Monte Carlo simulation method and that Fourier-Inversion was a good way to calculate option VaR.…”

Section: Figurementioning

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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“…see El-Jahel et al (1999). The Delta-Gamma method has been developed in terms of a Cornish-Fisher expansion in Jaschke (2002); in Glasserman et al ( 2001) Delta-Gamma is used to provide more efficient Monte Carlo simulated estimates of VaR; in Siven et al (2009) Delta-Gamma is used along with Fourier inversions to calculate VaR.…”

Section: Option Risk Measurementmentioning

confidence: 99%

Efficient option risk measurement with reduced model risk

Mitra

2017

Insurance: Mathematics and Economics

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Options require risk measurement that is also computationally efficient as it is important to derivatives risk management. There are currently few methods that are specifically adapted for efficient option risk measurement. Moreover, current methods rely on series approximations and incur significant model risks, which inhibit their applicability for risk management. In this paper we propose a new approach to computationally efficient option risk measurement, using the idea of a replicating portfolio and coherent risk measurement. We find our approach to option risk measurement provides fast computation by practically eliminating nonlinear computational operations. We reduce model risk by eliminating calibration and implementation risks by using mostly observable data, we remove internal model risk for complex option portfolios by not admitting arbitrage opportunities, we are also able to incorporate liquidity or model misspecification risks. Additionally, our method enables tractable and convex optimisation of portfolios containing multiple options. We conduct numerical experiments to test our new approach and they validate it over a range of option pricing parameters.

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Value-at-Risk computation by Fourier inversion with explicit error bounds

Cited by 12 publications

References 6 publications

An optimization process in Value‐at‐Risk estimation

An optimization process in Value‐at‐Risk estimation

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Efficient option risk measurement with reduced model risk

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