Risk Valuation Management Financial Modeling - Assignment Example

Risk Valuation Management –Financial Modeling The main objective of risk valuation in commercial and financial sector is the probability based risk measurement referred to as Value-at-Risk or VaR. The outcome created by a VaR model is basic for all levels of employees in an organization to understand its mode of operation and appreciate through the application on their daily activities. This is the advantage the VaR system has been exercising to find its way quickly within the corporate corridors. Presentation of methods used for computation of VaR, like the traditional and copula approach which are believed to provide an effective tool for modeling reliant on integrated risk management. The choice of the method to adopt, in regard to the computational aspect and data used is capable of reducing the general cost and computational time. Value-at-Risk (VaR), Value-at-Risk (VaR), is universally applied method of quantifying and managing the risk of the portfolio. Since its conception in 1993 in response to diverse financial disasters, has been referred to the new science of risk management. The initial work on its development started in1988 when central banks were trying to look for a methodology for establishing a minimum requirement in the commercial banks to guard against credit risk. The adoption of the concept by the commercial banks gained momentum in 1993-1995, as a key element of the management of market risk for many financial organizations (Glyn, 213) The application of VaR as an internal risk management tool gained the backing from committee on banking supervision as the international standard for external, regulatory function. Currently, VaR has gained popularity from the non-financial institution like the majority of oil or energy companies and end users who started using the VaR method for risk management. The approaches employed for measuring VaR are many. The valuation model for computing VaR essentially represents an outcome or possible reality, founded on probability and percentage parameters. VaR quantifies the worst anticipated loss within a time horizon with an appropriate probability (Dowd, 1998), This tool enables the management to see the presumable risk their organization is taking, or a reduction in possible financial exposure in case of company hedging. The VaR is capable od adding up all the market risks of the total portfolio of a bank, or a company as one number such as any financial institution uses VaR for examining exposure to losses in the market through derivative and physical positions, despite regular use of VaR to assess credit risk. Furthermore, VaR is not known to provide a consistent method for risk measurement, because different VaR models generate their own results. The risks measured by VaR do not include political risk, liquidity risk or regulatory risk but only measures quantifiable risks. During periods of extreme volatility like war, VaR cannot be relied to measure the risk involved. Hence, it should be used besides stress testing (James, 114). VaR as a risk measure has numerous advantageous. The provision of a consistent measure of risk across, all kinds of position and all across types of risk and markets factors, for example, a fixed income position VaR number can be intelligently compared to a VaR number for an equity position in case they have been calculated by applying the same assumptions. However, this was evident until people embraced VaR as a methodology, there existed no other measure used widely. For example, measures such as convexity and duration were applied in standard deviation and fixed incomes were used for equity purposes. The other advantage is that VaR can consider interrelationships existing between risk factors. Overall, a risk factor is anything that has effects on portfolio value and would embrace a undetermined path in the future. This functionality can vary from using basic correlations to making use of more delicate interrelationships, and considering the methodology in use. Besides risks reporting, VaR can be applied in many ways, in an enterprise, like setting risks targets and limits at different levels of the enterprise, for capital allotment at various levels including comparing risks adapted performance measurement and risks of deals before being finalized at different levels of the enterprise. Therefore, it is vital to acknowledge that VaR can be applied effectively and efficiently as a strategic tool and not merely as a regulatory requirement (Stulz, 43). Risk measure methods According to Lopez, (96-51), approximating the VaR of a portfolio requires determining a probability for the change in the portfolio worthiness over the holding period. The portfolio value of financial instruments, at the T relies on the risk K risk factors (market variables). The risk factors comprise stock prices, interest rates, and exchange rates. Hence, the approximation VaR is carried through the estimation of the distribution of the existing risk factors. The common techniques employed include analytic techniques: 1. Parametric. a) Monte Carlo simulation (full valuation method), b) Variance-Covariance method (local valuation method), 2. Non-Parametric such as Historical Simulation. The objective of this paper is to give an account and compare VaR methods on portfolios. Figure 1: Risk measure method (James, 233) Variance-Covariance method McNeil, Rüdiger and, Embrechts, (103) argues that this method is also known as Delta-Normal method, which is parametric and analytic technique where distributional assumption created, is that everyday geometric returns of the market changes are multivariate normally distributed with mean return zero. The historical data are utilized to quantify key parameters e.g standard deviations, means and correlations. In case the market value of the portfolio is a linear function of the existing parameters, the profit distribution is also normal. The VaR is estimated by multiplying the vector of the first derivative of the portfolio value while considering the risk factor variables, by the definite covariance matrix, and so multiplying by a multiplier factor that relies on the usual distribution quintile point for the confidence level at which VaR is being computed. As described by Jorion (127), this methodology was introduced by the JPMorgan’s Risk Metrics TM system. The Variance-Covariance method has numerous advantages, and they include: a) the -Speed b) -Simplicity c) -Distribution of return need not be assumed to be stationary through time due to the inclusion of volatility updating into the parameter estimation. The distribution its normal and its valuation is linear. It is also time varying making it easy to implement. It is precise on VAR and accurate. According to communicability, it is easily communicable and considered perfect for VAR analysis                   Confidence interval 90%     Confidence interval 99%                     Method VaRp     Method VaRp     Variance-Covariance £ 145,157.63     Variance-Covariance £263,498.67     Historical Simulation £ 126,832.87     Historical Simulation £278,545.32     Monte-Carlo Simulation £ 135,978.08     Monte-Carlo Simulation £246,987.83                   The Variance-Covariance has demerits too, and they include; underlying fat tails within the distribution of returns on most financial assets. A significant amount of positive kurtosis could be realized from the daily distribution returns of any risks factor. These results to fatter tails and exceptional outcomes take place more regularly than would be anticipated by the usual distribution assumption, which would cause underestimation of VaR because VaR is associated with distribution tails. a) This method does not adequately quantify the non-linear risk instruments like mortgage or options. Fig .2 Variance-Covariance methods (Jorion, 132) Consider the case of a given financial model at a 90% confidence level. It assumes: confidence level, which replaces the model and the VaR of the portfolio at that confidence level ,l is represented by a relatively smaller value such as . In this way, the probability that the loss represented by the will exceed the is less than or equal to If represents the return of a portfolio, it makes negative. This equation satisfies the probability distribution curve. There are some of the risk managers that s there are some events that are likely to have defined and undefined losses because the market is closed. This may also be because the entity that bears the loss has lost its probability to compute accounts Historical simulation This method of simulation creates a forthright execution of full valuation. The condition of simulated market is produced by totaling to the base case the period-period changes in market variables in a particular historical time series. Fig.3: Historical simulation method (Jorion, 115) The main assumption in the historical simulation is that the setting of a possible future scenario is represented by whatever occurred within a particular historical window. The historical simulation method entails acquiring the set of risk factor changes within a historical window, e.g. everyday changes within the last five years. The set of scenarios that are acquired is anticipated to be a fair representation of all possibilities that might occur between today and tomorrow. The portfolio instruments are then re-valued repeatedly against each scenario. This creates a distribution of portfolio values, or a distribution of variations in portfolio value around today’s value. Generally, some of the changes will losses while others gain profits. Arranging the changes in portfolio value from worst to best, the 99% VaR, in essence is calculated as the loss such that the profit of 1% or losses are below it, and 99 % are above it. The key advantages of historical simulation are: 1. That it makes no assumptions about the risk factors changes being from a specific distribution. Hence, this methodology is consistent with risks factor changes being from any distribution b) The historical simulation does not entail the approximation of any statistical parameters, like the variance and covariance and is thereupon exempted from unavoidable estimation errors. c) The methodology can be easily explained, understood and defend to an important audience like the corporate board of directors who may not be privy to this technical knowledge. 2. disadvantages Although, as is always the case, the method has some demerits too, the main ones are: a) Historical simulation is complex to implement since it needs information on entire risk sources to be available between long historical periods in order to provide a compliant presentation of whatever may happen in the future. b) The historical simulation does not entail any distributional assumptions, the scenarios that are used in calculating VaR, are subject to those that eventuated in the historical sample (Balbás, Garrido, &, Mayoral, 385). Monte Carlo simulation method The Monte Carlo simulation technique is the most powerful and flexible method because they are able to take into accounts the none—linearity of the portfolio value with regards to its existing risk factors. It also brings in the desirable distributional properties like the fat tails and time varying vitalities. The method can also be expected to leas over long holding period, the Monte Carlo, giving room for this technique for measuring credit risks. The technique of Monte Carlo is also computationally expensive. Fig.4 Monte Carlo Method, (Jordon, 120) The main difference between Monte Carlo and historical simulation The historical simulation model executes the stimulation via the real observed changes within the market place over the last X periods to generate Y hypothetical profits or losses, while the Monte Carlo simulation a fatal number institutor is employed to create tens of thousands of hypothetical changes in the market. Later used to create thousands of hypothetical losses and profits, and later distribution of possible portfolio losses or profits. Lastly, VaR is decided on from this distribution with respect to the parameters set (Xianyi and Zhou, 324–334). Most Suitable VAR Method The most suitable method to apply is determined by the formation of the portfolio and the time limitation for the VAR measure. The degree of variation between analytic variance-covariance differs from Monte Carlo simulation and historical simulation VARs is dependent on the degree of nonlinearity of the portfolio, which is also dependent on; A) Size-the comparative magnitude of the linear and non-linear elements of the portfolio B Sign-In case the option positions cancel out or not. Hence it appears that for a single day the VARs for portfolios which are unsteady non-linear, the analytic variance-covariance may be the best option. The analytic variance –covariance method is quite straightforward, by virtue of the fact that pricing models are not required for it to achieve the required results. Potentially valuable is the availability of the necessary data. Not forgetting the advantages of variance-covariance from a number of software vendors. If the VAR payoff profile has a stronger non-linear portfolio or a longer time horizon, the appropriate method to adopt is the Monte Carlo simulation or the historical simulation method (Sereda, Bronshtein, Rachev, &, Fabozzi, 649). The historical simulation is hypothetically honest and easy to implement because the pricing models for products are currently available as add-ins to spreadsheet software’s or programs. Nevertheless, a serious problem with the method of historical simulation is that the sensitivity analysis and stress testing is complex to execute. The act of stress testing and sensitivity analysis is convenient, effective and necessary. Hence, the method of Monte Carlo simulation is suitable, although a significant problem exists in the form of implementation of the method completely. In this simulation, executing the simulation is done by yield curves, instead of individual interest rates. In a complete Monte Carlo, the simulations are done to avoid speculative opportunities, either between the yield curves for currency X and Y or the yield curve for currency X. The outcome indicates that a full Monte Carlo simulation is difficult to implement, and the run time for this model can be extraordinarily long. The honor that Monte Carlo simulation method embraced has made researchers focus their attention to develop ways of having a Monte Carlo simulation run faster. Researchers have also tried to determine the means of estimating the precision of a full Monte Carlo simulation with some basic technique. Conclusion The valuation methods have varying advantages, however, the most effective is the delta normal based on the advantages and ease of implementation. The model promises more advantages in terms of valuation, distribution, implementation and communicability. It is also it is also imperative to note that the methods have some pitfall that call for extreme care. For example, the delta normal has non linearity’s and fat tails, however, does not consider time variation in risks and unusual events. On the other hand, montecarlo simulation methods have issues with the model risk. The most important factors to consider are the ease of implementation and effectiveness. This leaves us with the delta normal as the optimal model. Works Cited Basel Committee on Banking Supervision. Amendment to the capital accord to incorporate market risks. Www.bis.org/publ/bcbs24.htm, January 1996. Print Balbás, A.; Garrido, J.; Mayoral, S. "Properties of Distortion Risk Measures". Methodology and Computing in Applied Probability 11 (3): 385. 2008. Print Beneda, N. Managing An Asset Management Firms Risk Portfolio. Journal Asset Management. Charles W. Smithson, Managing Financial Risk: A Guide to Derivative Products, Financial, USA:McGraw-Hill Professional Book Group, Dowd, K. (1998), Beyond Value at Risk, The New Science of Risk Management, Wiley and sons. Chichester. Dowd, Kevin. Measuring Market Risk. John Wiley & Sons. 2005. Print Engelbrecht, R.: A Comparison Of Value-at-Risk Methods for Portfolios Consisting of Interest Rate Swaps and FRAs. www.cam.wits.ac.za/mfinance/projects/robyn.pdf Holton, Glyn Value-at-Risk: Theory and Practice. Academic Press. ISBN 978-0-12- 354010-2. 2003. Print James, T. Energy Price Risk: Trading and Price Risk Management. Gordonsvile, VA, USA: Palgrave Macmillan, 2003, p.133 Jorion, P. Value at Risk: The Benchmark for Controlling Market Risk. Blacklick, OH, USA: McGraw-Hill Professional Book Group, 2000, 535 s Jose A. 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