Value at Risk dan Tail Value at Risk dari Peubah Acak Besarnya Kerugian yang Menyebar Alpha Power Pareto

Ruhiyat Ruhiyat; Berlian Setiawaty; Muwafiqo Zamzami Dhuha

doi:10.34312/jjom.v5i1.16586

Value at Risk dan Tail Value at Risk dari Peubah Acak Besarnya Kerugian yang Menyebar Alpha Power Pareto

Ruhiyat Ruhiyat, Berlian Setiawaty, Muwafiqo Zamzami Dhuha

Abstract

Value at Risk (VaR) and Tail Value at Risk (TVaR) are two measures that are commonly used to quantify the risk associated with a loss severity distribution. In this paper, both values are calculated analytically and estimated using a Monte Carlo simulation when the loss severity random variable has an alpha power Pareto distribution. This distribution is the result of alpha power transformation on a Pareto distribution. The random numbers used in the Monte Carlo simulation are generated from the alpha power Pareto distribution using the inverse transformation technique. In the special case used, the estimated VaR and TVaR values obtained from the Monte Carlo simulation for some security levels used are close to the actual VaR and TVaR values as long as the number of random numbers generated in the Monte Carlo simulation is sufficiently large.

Keywords

Alpha Power Pareto Distribution; Monte Carlo Simulation; Tail Value at Risk; Value at Risk

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DOI: https://doi.org/10.34312/jjom.v5i1.16586