Market Risk

1. Introduction

VAR+ is designed for value-at-risk analysis of market risk, i.e. risks caused by the exposure of financial positions to fluctuations in interest rates, exchange rates, stock prices and commodity prices.

The system meets and exceeds the recommendations for internal models set out in January 1996 by the Basel Committee on Banking Supervision, and will meet the forthcoming Basel Committee Market Risk Guidelines to be implemented from the end of 2006.

The user can choose either Monte Carlo simulation or historical simulation for determining the risk exposure. In addition to the simulated value-at-risk levels of any portfolio, VAR+ provides the user with the complete distribution of his portfolio’s change of value. Also a variety of user-defined scenarios are available for stress testing. Full back-testing and performance measurement facilities are available on VAR+.

Currently, VAR+ is capable of measuring risks of positions consisting of around 100 types of instruments, including many complicated derivatives instruments.

2. Overview of VAR analysis

2.1 Two basic concepts in market risk measurement

  • Value-at-Risk analysis
  • Stress testing

Value-at-Risk (VAR) measures market risk under fairly normal market conditions. VAR models utilize statistical estimates derived from historical price data to predict future events. When using the history to predict the future, we have to assume that the future shows similar type of behavior as the past, an example being correlations. However, time after time, it is useful to challenge this assumption, i.e. to focus on stress testing by using history independent scenarios.

2.2 VAR+ methodology

VAR analysis is a probabilistic tool where risk measurement is based on the distribution of mark-to-market values of assets. VAR gives the possibility to compare different investment operations since all portfolios and markets are reported under a uniform measure, that being the value-at-risk as a monetary value. Another advantage of the model is the possibility to see the true portfolio effect, which is generated by the fact that the movements of market variables are correlated at various levels. A third advantage is that the risk measure has an intuitively clear content: “We calculate the possible values of a portfolio for tomorrow and we mark the point where 99% of all possible values have better outcome than the remaining 1%. Now we compare that point to the expected value of the portfolio. The amount of loss defined with this procedure is the 1% VAR level”. VAR+ can be tailored to provide VAR figures at requested levels.

VAR+ provides two ways to analyze the portfolios: first, historical data can be used to generate the future. This means that the user will run historical simulation. Second, a random number generator may be used to produce values for market variables with the assumption that prices of market risk generating factors follow either diffusion processes, geometric Brownian motion processes, mean reversion processes, or Poisson processes. This method is referred to as Monte Carlo simulation. (For more, please, see section 3.)

VAR+ captures the non-linearity feature of certain instruments, such as options. Compared to delta- or delta-gamma approximation methods, VAR+ utilizes the full valuation method, which provides the highest accuracy, as all the instruments are priced by true pricing formulas.

2.3 Model structure

The input data for the simulation model of VAR+ consists of current market rates and historical estimates, which are used to produce the simulated prices. The current market rates include spot and forward rates of a series of currencies, interest rates, stock indices and/or commodities, as well as current zero coupon yield curves. Volatilities and correlations of the market variables are estimated from historical time series.

VAR+ model calculates the distribution of portfolio values over a predefined time period (simulation step). For different reporting purposes and applications, the simulation step can be flexibly changed.

During the analysis, VAR+ first imports in the market data on FX rates, stock prices, yield curves, and commodities prices and futures curves. This data is accompanied with an underlying statistical model to produce simulations of future values of the market variables. The second phase is to import in the portfolio contents and to price portfolios based on the simulated market prices. The market risk can be measured as a price change from today’s known values to tomorrow’s simulated values, or it can be measured as the deviation of tomorrow’s values from their mean, depending on the specifications of the system.

It is necessary to run the simulation of market variables first and thereafter the pricing of portfolios may be carried out. The system values each generic portfolio separately, so it is easy to see the contribution of each such portfolio individually. (A generic portfolio contains market instruments while an aggregate portfolio contains a combination of portfolios).

The VAR values and the performance of the portfolios are reported both numerically and graphically. The reporting can show individual portfolios or their combinations; the reporting structure can be formed freely and on the desired currency base. It is also easy to add several reporting structures, an example being the individual reports on any branch office of a bank and the total risk taken by all the branch offices together.

The graph of the report displays a bar chart of the distribution of simulated portfolio values, where we have set zero to match the mean value of the simulation.

The essential information given in the bar chart is its shape. If it is close to normal distribution, the analyzed portfolio does not contain strategies that may provide ‘unusual’ surprises; if the distribution has ‘fat tails’ or is skewed in shape, the portfolio is likely to contain large risks. For management reporting, the main focus is usually on a single VAR level, for example VAR 1% level. If the shape of the distribution is close to normal, we know that the VAR 1% level fully reflects portfolio risk; on the other hand, if the distribution has a long ‘tail’ to the left, it indicates that the portfolio returns are highly non-normal and should obtain more attention. The curve drawn next to the bar charts is called the VAR curve. By choosing desired confidence level from y-axis the curve maps this level into the corresponding VAR figure in the x-axis. The calculations and reporting can be made in any currency, as selected by the user.

The report also displays the volatility of the portfolio in base currency, largest loss and gain obtained in the simulation, and VAR levels at 1%, 5%, 95% and 99% levels. It also shows the net open position, which is equal to the amount of currency received or paid if the position would be closed immediately. The last row shows the number of simulation rounds used to provide the report.

VAR+ includes a number of special functionalities, which allow the user to meet individual reporting requirements, such as scenario reports, factor sensitivities (i.e. convexity and duration), distribution and comparison tables, measures of kurtosis and skewness, performance measurement, back-testing etc.

2.4 Yield Curve Dynamics and Spread Risk

VAR+ has highly configurable yield curve dynamics. Each yield curve has an associated simulation model with one, two or three risk factors. Usually three factors explain most of the variability of yield curve movements. VAR+ also supports a bucket model with four or more risk factors. This gives additional accuracy and allows the yield curve dynamics to be modeled separately for money markets and bond markets.

Every market may have several yield curves in VAR+ model, typically at least one zero-risk (government) yield curve. Building on the government yield curve, spread curves can be added, each with its own dynamics. VAR+ can thus fully account for the spread risk of portfolios with counterparties of varying creditworthiness.

3. Simulation with VAR+

3.1 Monte-Carlo Simulation

Monte Carlo simulation is a stochastic procedure, which generates random numbers that are modified to have the distributions according to the input data. Monte Carlo simulation is computationally intensive, but it is the only accurate way for determining the true values of derivative instruments and other non-linear instruments.

Market variables are described with their expected values (i.e. forward prices) and volatilities. The interdependency of market variables is described with a correlation matrix. The model takes a set of possible values for each of the market variables during each simulation round and uses these values to calculate the corresponding prices for all positions. The method guarantees that the distribution of the simulated values of risk factors matches the expected values, volatilitites and correlations of the input data. With 10 to 20 thousand simulation rounds, the model provides reliable information about the portfolio’s distribution.

3.2 Historical Simulation

Historical simulation uses historical daily data. Full valuation method is applied to each instrument and for each day in the historical data set.

VAR+ offers both simulation methods; the choice of the method depends completely on the user’s decision.

Following, we provide a comparison table:

Monte Carlo Simulation Historical Simulation
Strengths Strengths
  1. Covers instruments with non-linear features, such as options
  2. Provides reliable estimates of true values
  3. Allows yield curve models to be applied
  4. Supports full distribution analysis
  1. Fast
  2. Can cover options
  3. Covers fat tails
Weaknesses Weaknesses
  1. Takes time
  2. Fat tails require special attention
  1. VAR levels are inefficient
  2. Results are completely
    determined by a finite
    state space of history


4. Instrument Library in VAR+

VAR+ covers four groups of instruments:

  1. Currencies
  2. cash and forward positions
  3. foreign exchange options: European, American, barrier, double barrier, average rate, binary and other exotic options, options on foreign exchange futures
  4. foreign exchange stop loss or take profit orders
  5. Bonds
  6. fixed rate, floating rate, callable, puttable and convertible bonds
  7. bond futures, options on bonds and bond futures
  8. Money markets
  9. FRAs, eurodeposit futures, options on futures, binary options, swaptions
  10. caps, floors and collars
  11. Stock and commodities markets
  12. cash positions on stocks and commodities
  13. index options and forwards
  14. options (European, American, Asian, barrier, double barrier, binary, quantos) and forwards on stocks
  15. warrants

VAR+ Instrument Library already has valuation formulas for some 100 instrument types including dozens of exotic options. It is also possible to add new instruments to the list.

5. Basel Committee proposal and CAD II

The Basel Committee published its Recommendations for market risk measurement in the banking sector in 1996. This document lays down a number of qualitative and quantitative requirements to control the risks involved in the daily operations of banking institutions. Among others, Basel Committee provisions demand that in banks relying on internal models approach a daily 99% VAR level are to be measured and the full-valuation method to be used to cover the nonlinearities. In addition, full correlation matrix and long data series are recommended. Stress testing and backtesting provisions are extensively dealt with.

These recommendations were effectively rephrased and slightly extended in the draft documents of the Basel Committee on the New Basel Capital Accord, published first in 2001. While the work of the Committee continues to be in progress until 2003, it has been announced that the new Basel Capital Adequacy requirements will take effect from the end of the year 2006.

In a similar fashion, the European Parliament and Council of the European Union have laid out directives, known as Capital Adequacy Directives (CAD). CAD II is the most recent set of provisions on accurate internal systems for daily risk control and appropriate measures for trading limits. The regulations require that credit institutions must comply with the EU directives.

VAR+ meets and exceeds all known and known to be forthcoming principles and requirements of the Basel Committee for Internal Models Approach in market risk measurement, modeling and reporting.

6. System Architecture

VAR+ introduces CDFT Modular Risk Architecture, which provides a set of risk management modules that integrate seamlessly and create a full suite of risk management applications.

VAR+ consists of Simulation Engine, Statistics Engine and Valuation Library. The Simulation Engine handles stochastic mathematics, random numbers, simulation model and other core elements of risk simulation. The Statistics Engine deals with simulated distributions and descriptive statistics. Valuation Library contains accurate pricing formulas for some one hundred types of different instruments, including dozens of exotic options. The engines are implemented with C++ using high performance mathematical libraries.

The graphical user interface in VAR+ is implemented with Microsoft Access.

CDFT Modular Risk Architecture aims for interoperability and currently the computations can be run on Windows NT/2000/XP and different flavors of UNIX systems. Third part systems can access Risk Modules through CORBA interface as well as DCOM interface.

VAR+ is available both for a single workstation and for a calculation server with multiple clients. The clients can access VAR+ server directly or through Terminal Service Server, which allows for a truly global access to all the functionalities of a VAR+ system.

When there is a large number of clients, very big simulation models or near real-time performance requirements, VAR+ simulation engine supports distributed parallel computing. The best results in the scalability can be achieved in symmetric multiprocessor environments.

VAR+ also interfaces with DATA+ and its Estimation Engine to retrieve up-to-date market data and parameter estimates. DATA+ is full-featured risk management database for collecting and processing market data. DATA+ integrates with financial information providers and estimates zero-coupon yield curves as well as stochastic process parameters.

7. Applications, Performance, Interfacing, Implementation and Maintenance

Obtaining a system for the measurement of Value-at-Risk brings at hand a tool for determining a risk taking policy and risk monitoring and control. The possibility for stress testing enables the risk management to detect the effects of major market moves. Marking to market portfolios on daily or even on intra-day basis and analyzing the distribution of risk provides information for capital allocation. VAR+ has the feature of reporting also on the risk contribution of each of the generic portfolios. Such information is useful for the management when making decisions concerning capital reallocation and strategic corporate planning. It is also useful in measuring performance and return/risk efficiency, which are vital information for funds management and asset allocation.

VAR+, while it is not meant to be a front office trading system, allows two-way pricing in its newest versions (starting from VAR+ 5.0). The pricing libraries of the system have been chosen, designed and tested while giving attention to both accuracy and calculation speed. On these grounds the system can be used for pricing options or calculating Greeks (such as Delta, Gamma, Theta or Vega). Due to its modular structure VAR+ can also use external pricing libraries, such as the ones used in the front office trading operations.

VAR+ can be offered as a whole package applicable to the bank's all trading systems or it can be applied in limited parts of the operations, i.e. analyzing only certain foreign exchange, interest rates, equity or commodities positions by Monte Carlo simulation.

In terms of quality, mathematical accuracy and the resulting level of confidence, VAR+ has established a sound track record. With improvements in the speed of VAR+ engine, with its scalable architecture, and with the recent speed of hardware development, the computation intensity relating to Monte Carlo simulation is not a problem. Near-real-time solutions are possible and fully realistic in most demanding applications, facilitating frequent intra-day risk monitoring and position planning.

Regarding user interfaces and data input, the systems have been linked with several different treasury systems used by various clients without any major difficulties arising during installation and implementation, which have been on schedule.

CDFT's experience has shown that once installed in suitable hardware and software environment, VAR+ requires a relatively low maintenance effort, which usually can be handled via telephone, e-mail or the Internet.

8. Additional Modules

8.1 Backtesting and Performance Measurement Modules

Separate back-testing and performance measurement modules enable the user to assess the feasibility of the simulated VaR levels and the relative risk-return efficiency in different operations of the treasury. Back-testing is performed following the guidelines of the Basel Committee of BIS for the banking sector. In this procedure the daily P/L changes are compared to the daily 1% VaR numbers, and the number of daily losses exceeding the VaR forecasts is tested.

9. Note

Depending on the client’s needs VAR+ market risk and ACES+ credit risk applications or elements thereof can be combined and/or complemented to form a comprehensive risk management system. Alternatively, parts thereof can also be used to support either in-house developed risk management systems or other systems available in the market.

For all our products, full demonstrations along with case studies are available on an individually tailored basis. For more information please contact:

CD Financial Technology
Mikonkatu 8

Tel: +358 9 612 3322

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