Using Monte Carlo Smulation to Calculate Fat-tailed VaR
Date Issued
2006
Date
2006
Author(s)
Chen, Che-Kuan
DOI
zh-TW
Abstract
The risk management technique known as VaR(Value-at-Risk) has recently become an important tool for measuring the market risk of financial and commodity derivative instruments, and other financial instruments. VaR models measure the loss of a portfolio or an asset that will be exceeded with a specified probability over a specified time horizon. Moreover, the issues of the credit risk has been getting more and more important recently, so what we concern about now is to measure not only the market risk but also the credit risk effectively.
In this thesis, we also apply VaR for measuring the credit risk due to its simple property. However, the distribution of the value of a portfolio involved with the credit risk is fat-tailed i.e. the occurrences of the extreme values are more often than normal distribution, so we can’t calculate VaR under the normal distribution. Hence, we refer to a technical report proposed by Nomura in 2005 to establish a method to calculate VaR of a portfolio which is involved with the market risk and credit risk. We use the Monte Carlo simulation to estimate the distribution of the value of a portfolio in order to calculate VaR of the portfolio. We call VaR calculated by the method in this thesis as “FTV” for fat-tailed VaR because of the fat-tailed property of the portfolio. Furthermore, we also apply FTV to construct the efficient frontier.
There are some features of FTV we construct here. First, we consider the effects of the market risk and credit risk at the same time. Second, there is no specified statistical distribution used to fit the distribution of the value of a portfolio in our method, so we don’t overestimate or underestimate the risk from the inappropriate choice of distribution models. Finally, we can apply FTV to many areas, such as the risk management, optimization of the portfolio and asset allocation.
Subjects
市場風險
信用風險
蒙地卡羅模擬法
厚尾風險值
效率前緣
market risk, credit risk
fat tail, fat-tailed VaR
Monte Carlo simulation
efficient frontier
Type
thesis
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