The Three Types of Value at Risk (VaR)

The value at risk (VaR) model is a mechanism of calculating the maximum probable loss from a given data set. It needs to be understood that the method being used is a statistical method. Hence, it uses the data given to calculate the probability and extent of the loss. Just like all other statistical models, this model is also dependent upon the integrity of the data being put into the model to guarantee the results that are generated from the model.

The value at risk (VaR) model is a statistical construct that can be used with different types of data. In the modern world, at least three different types of value at risk (VaR) models are used. These models are different from each other because they use different types of data. In this article, we will have a closer look at these three types of models as well as their advantages and disadvantages.

1. Parametric Value At Risk (VaR) Model

   The parametric value at risk (VaR) model is the type of VaR which is most commonly used in the world. This is because this model is the most convenient to use.

   The model does not require the entire dataset. Instead, it only needs some parameters of the dataset such as mean and standard deviation. Now, when this information is provided in the model, it assumes the data follows a certain kind of distribution such as the normal distribution.

   The model then calculates the value at risk (VaR) keeping the characteristics of the distribution as well as the variance in mind. This is the reason why this model is also known as the variance-covariance model.

   The parametric model is the most widely used model for a reason. It can provide a fairly accurate answer without too many complications. The model is useful for predicting the risk of traditional assets such as stocks and bonds. It can also be used to predict the risks of simple derivatives which have a linear payoff. However, the results provided by this model are not accurate when the payoffs are non-linear in nature.

2. Monte Carlo Value at Risk (VaR) Model

   The Monte Carlo value at risk (VaR) model uses hypothetical data in order to calculate the risk of loss to a certain portfolio. Hence, instead of providing parameters, the entire distribution is created and then the calculation of value at risk (VaR) is performed.

   The Monte Carlo method is considered to be extremely useful in cases where the payoffs are non-linear and hence the parametric method fails. Also, the benefit of the Monte Carlo method is that the analyst does not need to stick to a single distribution. This method of value at risk (VaR) can be used to create different distributions such as binomial, Poisson, etc.

   Also, the Monte Carlo method provides a lot more detail as compared to other models. This method is also very useful for financial instruments where there is no historical data available or where the future is expected to be significantly different than the past. In such cases, it would not make sense to use historical data in order to predict the future value at risk (VaR).

   The shortcoming of this model is that it is technologically as well as statistically intensive. Creating and interpreting Monte Carlo simulations is not an easy task. It requires a lot of time, skill, and expertise. This is why this method is often more expensive as compared to other methods.

3. Historical Value at Risk (VaR) Model

   The historical method of value at risk (VaR) calculation is somewhat similar to Monte Carlo simulations. Just like the Monte Carlo simulation, the historical method also uses the full distribution of data. It does not use only the parameters to calculate the value at risk (VaR) number.

   However, the difference here is that the Monte Carlo simulation uses hypothetical data whereas the historical model uses actual historical data. This means that just like Monte Carlo simulations, there is no need to make any assumptions about the distributions. Also, the results provided are quite detailed and can be used for a more detailed analysis as compared to the parametric model.

   Now, there is an obvious problem associated with this approach. In order to use this approach, the daily rate data for several years needs to be available. In many cases, the historical data may be unreliable or difficult to obtain.

   It is quite common to use these models in conjunction with one another. For instance, the parametric model is often used to provide an instant screenshot of the probable value at risk (VaR). This is quite useful since it allows the organization to make quick decisions.

   If no quick decisions have to be made, then after some time, the non-parametric models i.e. Monte Carlo and historical model can be used for a more detailed analysis. It is also common to compare the results from different models in order to gauge the accuracy of the assumptions as well as to understand how the numbers will change if the assumptions do.

The bottom line is that there are various methods to calculate the value at risk (VaR). It is important for organizations to explore the method which is best suited to their needs. Also, it is important to realize that it will not be prudent to compare the results generated by one model with the results generated by another model.

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