History of Filtered Historical Simulation

the web site of the authentic Filtered Historical Simulation (FHS)

the web site of the authentic Filtered Historical Simulation (FHS)

Back in the middle of 1990’s, when every risk manager was struggling to estimate correlations matrices across thousands of risk factors to compute their VaR’s in their newly build in-house systems, Giovanni Barone-Adesi and Kostas Giannopoulos published an article (F&OW 1996) on how to compute VaR without using correlations. They argued that the variance-covariance matrix is necessary only in calculating the optimal portfolio holdings. In risk management, when the investment decisions are already made by others, the use of the correlation matrix in calculation is both unnecessary and prone to pitfalls.

- In fact the estimation of VaR from the correlation matrix requires the knowledge of the probability distribution of each series. It is extremely unlikely that the actual distribution of the returns conforms to any known distribution. For most of the assets, the tails of the actual (empirical) distribution will exceed the 2.33 standard deviations predicted by the most commonly used, the normal one. VaR measures based on arbitrary distributional assumptions could be extremely unreliable, especially if a great variety of assets is assumed to follow distributions of the same type.
- Unless certain conditions are satisfied when estimating the correlation matrix, there is no assurance that the resulting matrix is invertible.

The bypass of the correlation matrix, but without ignoring the co-dependencies of security returns, was the cornerstone in developing the Filtered Historical Simulation. In two following up articles, in Risk magazine (1998) and the Journal of Futures Markets in (1999) the FHS methodology was developed. The first article was an application on a synthetic portfolio, the latter on a portfolio consisting of a futures and options on futures.

The first draft of the 1999 paper was made available in early 1997. At that time the London Clearing House started a feasibility study on the clearing of OTC products. The idea of FHS was very promising in modelling the daily yield curves of major currencies needed in the clearing of SWAPS. An in-house research project was started by LCH, with Barone-Adesi and Giannopoulos, to develop a prototype software and carry out extensive backtesting of the FHS. The backtesting lasted about two years and the summarised results were published at a journal article (2002).

Over the following years the basic idea of the FHS in generating price and volatility scenarios, has been widely used in industry and academia.

Giovanni Barone-Adesi, Robert Engle and Loriano Mancini (2008) proposed a new method to compute option prices based on GARCH models. In an incomplete market framework, they allowed for the volatility of asset return to differ from the implied volatility of options, explaining several anomalies in the financial literature.

Kostas Giannopoulos and Radu Tunaru (2005) proved that the FHS risk measures are spectral and coherent and they provided the statistical error formula that allows to calculate the error of the expected shortfall as estimated by the FHS.

Kostas Giannopoulos (2008) showed how to use FHS to in pricing multivariate contingent claims.

During the last decade the FHS has become a theme of articles written by many other authors. It has also been the subject of investigation for Masters dissertations and PhD thesis.

Barone-Adesi Giovanni, Robert Engle^{1} and Loriano Mancini (2008), “GARCH options in incomplete markets”, *Review of Financial Studies*, 21, 1223 – 1258

Kostas Giannopoulos (2008), “Nonparametric, conditional pricing of higher order multivariate contingent claims”, *The Journal of Banking and Finance, ***32**, 9, *1907-1915*.

Kostas Giannopoulos and Radu Tunaru, (2005), “Coherent risk measures under filtered historical simulation”, *The* *Journal of **Banking and Finance, *

Barone-Adesi Giovanni, Kostas Giannopoulos and Les Vosper (2002), “Backtesting derivative portfolios with filtered historical simulation”, *European Financial Management*, **8**, 1, 31-58

Giovanni Barone-Adesi, Kostas Giannopoulos (2001), “Non-parametric VaR techniques; myths and realities”, *Economic Notes, 30,* July, 167-181

Giovanni Barone-Adesi, Kostas Giannopoulos and Les Vosper (1999), “VaR without correlations for non-linear portfolios”, *Journal of Futures Markets*, **19**, August, 583-602.

Giovanni Barone-Adesi, Frederick Bourgoin and Kostas Giannopoulos (1998) “Don’t look back” , * Risk, ***11**, August, 100-104

Giovanni Barone-Adesi and Kostas Giannopoulos, (1996) “A simplified approach to the conditional estimation of Value-at-Risk”, *Futures and Options World*, October, 68-72.

^{1} Winner Nobel prize in Economics, 2003.

©2014-2017 Giovanni Barone-Adesi & Kostas Giannopoulos

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