Historical simulation in finance's
value at risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by ...
(VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the
cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x.
Ev ...
(CDF) of assets returns over time. Unlike
parametric VaR models, historical simulation does not assume a particular distribution of the asset returns. Also, it is relatively easy to implement. However, there are a couple of shortcomings of historical simulation. Historical simulation applies equal weight to all returns of the whole period; this is inconsistent with the diminishing predictability of data that are further away from the present.
Weighted historical simulation
Weighted historical simulation applies decreasing weights to returns that are further away from the present, which overcomes the inconsistency of historical simulation with diminishing predictability of data that are further away from the present. However, weighted historical simulation still assumes
independent and identically distributed random variables
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is us ...
(IID) asset returns.
Filtered historical simulation
Filtered historical simulation tries to capture volatility which is one of the causes for violation of IID.
See also
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Monte Carlo methods in finance Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the dist ...
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Quasi-Monte Carlo methods in finance
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Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio o ...
References
Giovanni Barone-Adesi and Kostas Giannopoulos (1996)
A simplified approach to the conditional estimation of Values-at-Risk
Giovanni Barone-Adesi, Frederick Bourgoin, Kostas Giannopoulos (1998
Do Not Look Back
Giovanni Barone-Adesi, Kostas Giannopoulos & Les Vosper (1999)
VaR without correlations for portfolios of derivative securities
External links
Filtered Historical Simulation
{{Financial risk
Financial risk modeling
Monte Carlo methods in finance