The most comprehensive educational resources for finance

VaR Calculation: The Assumptions of Standard Distribution

While calculating VaR using one of the statistical models, we make many assumptions, one of them is that the asset returns are i.i.d. normally distributed. This means that just like a coin toss, each return is an independent draw from the normal distribution. However, in reality, there is empirical evidence that the financial data is

Problems with the VaR Models

We have learned about three important Value-at-Risk models that are most commonly used by banks and financial institutions, namely, analytical VaR, historical simulation VaR, and Monte Carlo simulation VaR. None of these models are perfect and have certain assumptions which make their results not entirely suitable to how the financial markets behave. Here are a

Economic Capital Calculation: Approaches

We know that economic capital is the amount of capital a bank needs to maintain to absorb the impact of unexpected losses during a time horizon at a certain level of confidence. The approaches to calculating economic capital can be broadly classified into top-down and bottom-up approaches. Top-down Approaches Under the top-down approaches, the economic

Northern Rock: A Case in Low Frequency High Impact Event

In 2007 Northern Rock experienced a bank run, the first since 1886 by its depositors. The bank saw a withdrawal of 3 billion pounds which constituted about 11% of Northern Rock’s retail assets. It had to ask the Bank of England to intervene to save it. It eventually was taken over by Bank of England

Regulatory Capital Vs. Economic Capital

Unlike a corporation, the role of capital within a bank is not that of an additional source of funding. Banks are primarily deposit taking institutions which then lend this money in the form of loans and other activities. To expand their exposure, it’s fairly easy for a bank to increase their deposit. Instead the capital

VaR Mapping for Options Positions

In the previous article we learned about how to map various complex positions such as coupon paying bonds, FRAs, and swaps. All these complex positions had linear payoffs and were fairly straightforward to map. However, there are other positions such as options where the payoff is non-linear. In such a case the mapping process becomes

Stock Market Distribution

There is no doubt that the way our stock markets and other financial markets behave is largely governed by the statistical concepts such as the Central Limit Theorem, or the law of large numbers. According to the Central Limit Theorem, the mean of a large number of independent random variables will be approximately close to

Backtesting Value at Risk (VaR)

In the previous articles we learned a lot about how VaR is calculated using various methodologies. We also learned about stress testing our portfolios. But can we really rely on these VaR methods and accept the results they throw at us? In other words, how accurate are these models in doing their job, and estimating

Mapping Complex Financial Positions

We have now learned about how VaR can be calculated for primitive positions including spot FX positions, equity positions, zero-coupon bonds, and futures/forward positions. We will now look at how complex positions can be decomposed into these primitive instruments which are mapped to risk factors. In this article we will take a look at some

Mapping Futures/Forward Positions to Risk Factors

We have learned about how various complex positions can be broken down into elementary blocks which can be further mapped to risk factors. The four such elementary blocks/instruments are Spot FX positions, Equity Positions, Zero-coupon bonds, and Future/Forward positions. In this article we will look at mapping futures/forward positions. A forward contract is an agreement