Define the concept of Value-at-Risk (VaR) Value-at- Risk (VaR) is a general measure of risk developed to equate risk across products and to aggregate risk on a portfolio basis. VaR is defined as the predicted worst-case loss with a specific confidence level (for example, 95%) over a period of time (for example, 1 day). For […]

# Value at Risk

## Analytical Approach to Calculating VaR (Variance-Covariance Method)

We earlier saw how VaR can be calculated using the parametric method. We will now look at this method in detail, and also understand how VaR can be easily calculated using matrices. VaR of a Single Asset VaR of a single asset is the value of the asset multiplied by its volatility. Here, the volatility […]

## Three Methodologies for Calculating VaR

There are three major methodologies for calculating VaR. Parametric Monte Carlo Historical Note that the risk of nonlinear instruments (for example, options) is more complex to estimate than the risk of linear instruments (for example, traditional stocks, bonds, swaps, forwards, and futures), which can be approximated with simple formulas. Financial instruments are nonlinear when their […]

## Calculating VaR Using Historical Simulation

The fundamental assumption of the Historical Simulations methodology is that you base your results on the past performance of your portfolio and make the assumption that the past is a good indicator of the near-future.

The below algorithm illustrates the straightforwardness of this methodology. It is called Full Valuation because we will re-price the asset or the portfolio after every run. This differs from a Local Valuation method in which we only use the information about the initial price and the exposure at the origin to deduce VaR.

## Calculating VaR using Monte Carlo Simulation

Computing VaR with Monte Carlo Simulations very similar to Historical Simulations. The main difference lies in the first step of the algorithm – instead of using the historical data for the price (or returns) of the asset and assuming that this return (or price) can re-occur in the next time interval, we generate a random number that will be used to estimate the return (or price) of the asset at the end of the analysis horizon.

## Monte Carlo Simulation – Example

In the previous post, we learned the algorithm to compute VaR using Monte Carlo Simulation. Let us compute VaR for one share to illustrate the algorithm.

We apply the algorithm to compute the monthly VaR for one stock. We will only consider the share price and thus work with the assumption we have only one share in our portfolio. Therefore the value of the portfolio corresponds to the value of one share.

## Application of VaR to Non-Market Areas

Financial Institutions are often faced with risks other than normal market risk. That is especially true with derivative transactions. In derivative transactions, institutions need to increase their estimate of allowable loss amount by incorporating the following risks: Pre-settlement risk Settlement risk Pre-settlement risk is the risk that a counterparty will default on a derivative transaction […]