Historical Simulation Approach Research Articles

Lost in noise? Some thoughts on the use of machine learning in financial market risk measurement

Machine learning has permeated almost all areas in which inferences are drawn from financial data. Nevertheless, in financial market risk measurement most machine learning techniques struggle with some inherent difficulties: Financial time series are very noisy, not stationary and mostly considerably short. This paper contains an easy to implement sequential learning algorithm that overcomes some of these disadvantages. It is based on a Kalman filtering mechanism for quite general stochastic processes and provides a first step in the direction of separating parameter dynamics from the ubiquitous noise component. The core idea here is to use some stylised facts inherent to financial markets time series such as time varying measures of volatility. The new approach is tested using real market data in two different settings. First, a hypothetical portfolio containing credit spread and equity risk is analysed over a time frame containing the outbreak of the global pandemic in 2020 and the beginning of the Russian attack on Ukraine in 2022. Another analysis is focused on US$/EUR exchange rate during a time span containing the global financial crisis of 2008 and the subsequent European sovereign crisis. In all test calculations the proposed sequential learning algorithm performs better than the historical simulation approach used by many firms in the banking industry to meet regulatory capital requirements. Due to its simplicity this method has a high degree of explainability and interpretability which will decrease the inherent model risk. The paper concludes with a discussion of model risk for machine learning in financial institutions. Compared to classical model risk frameworks, the emphasis must be put on the more prominent role of data. The simple approach described in this paper shows that machine learning in financial market risk does not have to get lost in noise.

Quantifying Downside Risk in Euro Area Stock Markets: A Value at Risk Study

The present research paper aims to assess and quantify the downside risk of Euro Area stock markets using the Value at Risk (VaR) methodology over a substantial time frame spanning 26 years. The study employs daily closing price data from the main stock exchanges of Euro Area nations. Using the historical simulation method, VaR estimates are calculated for each country's stock index, providing valuable insights into market performance and risk levels during both normal and crisis periods. The non-parametric nature of the historical simulation approach is favored due to its flexibility in dealing with non-normal distribution data, making it suitable for this analysis. The findings reveal significant variations in downside risk among Euro Area countries. Certain nations consistently exhibit lower VaR estimates, indicating comparatively lower downside volatility and potential losses. These markets may prove attractive to risk-averse investors seeking stability during adverse market conditions. In contrast, some countries consistently demonstrate higher VaR estimates, signaling heightened downside risk, which may offer higher potential returns but may not align with risk-averse investors' preferences. During periods of crisis, certain Euro Area markets display a lower level of downside volatility, showcasing their resilience during turbulent times. This information can guide investors in constructing diversified portfolios that can withstand adverse market conditions. Additionally, policymakers can draw upon these findings to formulate targeted monetary policies to support financial markets during economic uncertainty. Overall, this study contributes valuable insights into downside risk and market performance in Euro Area stock markets, providing investors, policymakers, and financial participants with essential information to make informed decisions and navigate the complexities of global financial markets effectively.

Takahashi–Alexander Revisited: Modeling Private Equity Portfolio Outcomes Using Historical Simulations

In 2001, Dean Takahashi and Seth Alexander of the Yale University Investments Office developed a deterministic model for estimating future cash flows and valuations for the Yale endowment’s private equity portfolio. Their model, which is simple and intuitive, is still commonly used by investors to this day. However, the model possesses significant shortcomings, including its sensitivity to the assumptions necessary for the model to function and its failure to provide a range of possible portfolio outcomes. Both issues can result in investors developing overconfidence in forecasts, which can result in suboptimal—or even adverse—portfolio management decisions. To address these shortcomings, we propose a novel historical simulation approach that preserves the simplicity and intuition behind Takahashi and Alexander’s approach. However, our model, which leverages historical private equity cash flow data, requires no user assumptions and naturally provides a range of outcomes. We explore this model in some depth, highlighting the model’s power and flexibility across myriad use cases.

Measuring Market Risk of Commercial Banks Implementing VaR with Historical Simulation Approach

This paper attempts to picture the impact of the market risk of ten commercial banks located in Bangladesh with the help of a non-parametric model known as the Historical Simulation Approach over the course of eight years. These banks' daily stock prices were used as inputs and analyzed in Microsoft Excel by means of Percentile and LN function. The study revealed market risk exposure as third, second-and first-generation banks from the least to the highest. It also pointed out the ups and downs of these banks' share prices in the selected period. Further analysis showed the portfolio VaR estimation for different time intervals. JEL classification numbers: G32. Keywords: Value-at-risk, Historical Simulation, Market Risk, Confidence Interval.

AR-GARCH-EVT-Copula for securitised real estate: an approach to improving risk forecasts?

ABSTRACT This study presents a quantitative analysis of the so-called AR-GARCH-EVT-Copula model aimed at forecasting risk metrics for multi-asset portfolios, including securitised real estate positions. The model incorporates a non-linear dependence structure and time-varying volatility in asset returns. Accordingly, an empirical study using data from six major global markets is carried out. The approach is applied to forecast risk metrics, in comparison to classical methods like historical simulation and variance-covariance models. Forecasts are then compared with realised returns, to calculate hit sequences and conduct statistical interference on the respective models. It is empirically shown that, the AR-GARCH-EVT-Copula model provides a superior forecast concerning risk metrics. This is mainly due to the usage of copulas, allowing us to individually model the dependence structure of random variables. Back testing and test results confirm the superiority of our model in comparison with classic methods such as historical simulation and Variance-Covariance approach. The decomposition of the univariate and multivariate models of the target model reveal the necessity to allow for high order and thus long-lasting autoregressive modelling as well as asymmetric tail dependence and rotated copulae across different portfolios.

Coupled transmission and distribution simulations to assess distributed generation response to power system faults

The historical simulation approach of aggregating distributed generation (DG) with load for transmission simulations is proving inadequate at capturing these DG dynamics. Presented is a methodology that uses interfacing data sets to couple disparate simulations in an iterative manner. This methodology was implemented with a Positive Sequence Load Flow (PSLF) dynamic model of the Western Interconnection with 9 GW of DG. A transmission fault leading to a fault-induced delayed voltage recovery (FIDVR) is analyzed with this iterative coupled simulation method, with more than 120 substation voltage profiles extracted, representing more than 4 GW of DG, and simulated in OpenDSS to capture the ride-through dynamics. OpenDSS simulations of feeders populated with photovoltaic DG and associated time-dependent tripping and momentary cessation criteria based on the IEEE 1547 standard are performed. Coupled simulation results show significant differences in DG responses, as well as overall system responses, between single PSLF and the coupled simulations.

Measuring Value at Risk for Kijang Emas Investment using Historical Simulation Approach

Measuring Value at Risk for Kijang Emas Investment using Historical Simulation Approach

Pricing temperature derivatives with a filtered historical simulation approach

ABSTRACTIn this paper, we propose pricing temperature derivatives using a filtered historical simulation (FHS) approach that amalgamates model-based treatment of volatility and empirical innovation density. The FHS approach implicitly captures the risk premium with the entire risk-neutral model (except the innovation distribution), thereby providing significantly more flexibility than existing methods that use only one designated parameter to capture the risk premium. Additionally, instead of relying on the fitted innovation distribution, the FHS approach uses empirical innovations to capture excess skewness, excess kurtosis, and other non-standard features in the temperature data, all of which are important for the correct pricing of temperature derivatives. We apply the FHS approach to pricing derivatives written on the temperature of Chicago, and demonstrate that this approach yields better in-sample and out-of-sample pricing performance than the constant market price of risk method and the consumption-based method.

Measuring expected shortfall under semi-parametric expected shortfall approaches: a case study of selected Southern European/Mediterranean countries

We investigate the applicability of semi-parametric approaches for estimating expected shortfall. More precisely, we examine the applicability of several models based on the historical simulation (HS) approach: one based on untransformed historical data, and others based on transformed historical data. Our research shows that the HS models based on certain transformed historical data can reliably be used for the estimation of market risk in terms of the Basel III standards. This investigation was conducted on the capital markets of selected Southern European/Mediterranean countries and those of Serbia and Ireland. Our backtesting results were verified using Monte Carlo testing and the bootstrap method.

The Recovery Theorem With Application to Risk Management

The forward-looking nature of option prices provides an appealing way to extract risk measures. In this paper, we extract forecast densities from option prices that can be used in forecasting risk measures. More specifically, we extract a real-world return density forecast, implied from option prices, using the recovery theorem. In addition, we backtest and compare the predictive power of this real-world return density forecast with a risk-neutral return density forecast, implied from option prices, and a simple historical simulation approach. In an empirical study, using the South African FTSE/JSE Top 40 index, we found that the extracted real-world density forecasts, using the recovery theorem, yield satisfying forecasts of risk measures.

In search of robust methods for multi-currency portfolio construction by value at risk

The main purpose of this paper is to select the most appropriate technique predicting precisely the exchange rate risk from three main approaches, namely, the Historical Simulation approach, the Variance–Covariance approach and the Monte Carlo Simulation approach. Our main finding shows that the historical simulation approach with exponentially weighted moving average, which exhibits the lowest out-of-sample loss, is the most appropriate method for value at risk estimation with regard to a multi-currency portfolio construction in the Taiwan foreign exchange market. Moreover, results in backtesting lend support to the accuracy of our proposed strategies at the 99% confidence level.

Backtesting extreme value theory models of expected shortfall

We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts.

Time-Varying Semi-Nonparametric Distribution and Portfolio Performance

In this paper, we extend the semi-nonparametric (SNP) densities of Leon, Mencia and Sentana (2009) through time-varying (TV) volatility, skewness and kurtosis. We derive some parametric properties, the conditional expected shortfall, quantiles and partial moments. We obtain closed-form expressions of reward-to-risk measures under the TV-SNP density. An empirical study of portfolio selection based on equity screening under alternative performance measures for stocks from the S&P 100 index is carried out. We show that the Rachev ratio and skewness-kurtosis ratio both yield portfolios that dominate those obtained under the Sharpe ratio. These results are more significant for weekly rebalancing than for lower rebalancing frequency. We also find that portfolio performance is significantly sensitive to alternative weighting schemes. Besides, a study of tail dependence through copulas is implemented to provide robustness to our results. Finally, a comparative analysis with respect to the historical simulation approach is also provided.

A Filtered Historical Simulation Approach to Macroeconomic Scenario Analysis

This paper applies a filtered historical simulation (FHS) approach to macroeconomic scenario generation. The aim of the approach is to generate more plausible macroeconomic scenarios than other macroeconomic scenario models such as the global vector autoregression (GVAR) model. This paper shows how to handle the relation between macroeconomic statistics and financial market factors in a filtered historical simulation approach. The application fields of the approach are integrated risk management, stress testing, business planning and so on.

Market Risk and Volatility Weighted Historical Simulation after Basel III

Regulatory capital requirements for market risk, also known as the Fundamental Review of the Trading Book (FRTB), were disclosed by the Basel Committee on January 2016. This major overhaul of the Basel 2.5 framework challenges risk model specification and backtesting. Given the prevalence of historical simulation approach within large financial institutions, we focus on the Filtered (Volatility Weighted) Historical Simulation (VWHS) approach associated with a EWMA volatility filter. Volatility dynamics is then directed by a single parameter. We discuss how this decay parameter, chosen within a reasonable range, at banks’ discretion, impacts capital metrics, backtesting statistics, as prescribed by the Basel Committee, and fouls the regulatory benchmarking of internal risk models. We show a trade-off between the resilience of risk models to periods of turmoil and the magnitude of capital metrics. Under the new regulatory rules, this would favour plain historical simulation, as compared with filtered or volatility weighed historical simulation. Understanding why, might be helpful for regulated banks, regarding the management of their market risk models, and supervisors involved in internal model approval.

Measuring and Comparing the Value-at-Risk Using GARCH and CARsR Models for CSI 300 Index

This article is the first to provide a detailed method for range-based CARR model to estimate the VaR and its out-of-sample prediction. In this paper, we use GARCH and CARR volatility models to compare the VaR’s out-of-sample forecasting performance. Using the historical simulation method as benchmark for VaR estimation, we found that the historical simulation approach for VaR measurement is more conservative than GARCH and CARR methods. The mean violation rate for the CARR VaRs is lower than that of the GARCH VaRs. Meanwhile, the CARR VaR is able to deliver lower required capital levels without producing bigger violations. This paper argued that the CARR VaR valuation approach is suitable as an internal model method for financial institution in VaR forecasting.

How accurate are modern Value-at-Risk estimators derived from extreme value theory?

In this study, we compare the out-of-sample forecasting performance of several modern Value-at-Risk (VaR) estimators derived from extreme value theory (EVT). Specifically, in a multi-asset study covering 30 years of stock, bond, commodity and currency market data, we analyse the accuracy of the classic generalised Pareto peak over threshold approach and three recently proposed methods based on the Box–Cox transformation, L-moment estimation and the Johnson system of distributions. We find that, in their unconditional form, some of the estimators may be acceptable under current regulatory assessment rules but none of them can continuously pass more advanced tests of forecasting accuracy. In their conditional forms, forecasting power is significantly increased and the Box–Cox method proves to be the most promising estimator. However, it is also important to stress that the traditional historical simulation approach, which is currently the most frequently used VaR estimator in commercial banks, can not only keep up with the EVT-based methods but occasionally even outperforms them (depending on the setting: unconditional versus conditional). Thus, recent claims to generally replace this simple method by theoretically more advanced EVT-based methods may be premature.

PENERAPAN MODEL VAR DALAM PENGUKURAN RISIKO PENURUNAN OPERATIONAL REVENUE PADA INDUSTRI TELEKOMUNIKASI

The objective of this paper is to measure operational risk in the telecommunications company using Value at Risk (VAR) model. VaR methods used in this paper are historical simulation and variance-covariance approach. The results of this paper indicated that the average value of historical simulation is smaller than variance covariance. Both methods show valid results when tested using backtesting methods. This result shows that both methods can be used to calculate the amount of risk reduction in operational revenue.

Pricing Options with the Stochastic Volatility Regime Simulation for GARCH, HAR GARCH-VIX and VIX Models

This working paper uses as a starting point the filtered historical simulation (FHS) approach developed by Barone-Adesi et al. One builds a GJR-GARCH model and generates Monte-Carlo return/price paths with normalized returns. This introduces a severe drift-bias. The Stochastic Volatility Regime Simulation (SVRS) avoids the bias by sampling from the same volatility regime. As an alternative to GJR-GARCH an asymmetric HAR and a GARCH-VIX model is used. Path sampling is done in the same way. As a model free alternative a VIX based approach is additionally investigated. This alternative clearly beats the models during the pre and post-Brexit market turmoil. Barone-Adesi et al. transform the real-world into the risk-neutral measure. The current model stays in the real-measure. One simulates a realistic trading behavior by hedging the options along the Monte-Carlo paths. One can calibrate the model by adding external noise.

Testing VaR Accuracy for CDS Portfolios Using Historical Simulation and Delta-Normal Models

This paper studies the accuracy of the VaR using the Delta-Normal and Historical approaches in measuring the risk of CDS portfolios in three different zones, US, Europe and Asia, for the period March 2013-November 2015. The portfolios consist exclusively of CDS of high rated banks and financial institutions. We found that at the 95% confidence level both approaches were accurate using equal weights over 500 days. However, at the 99% level, the Delta-Normal method underestimated the VaR except for Aisa portfolio even with the use of exponential weights for different values of λ. The Historical Simulation approach was more accurate because it accounted for fat tails and therefore avoided nonstationarity. Both approaches failed in accurately measuring the VaR over 50 days.