Putting VaR to Work - Linear and Non-Linear Derivatives

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Putting VaR to Work

Financial Risk Manager (FRM®) Part 1 of the FRM Exam covers the fundamental tools and techniques used in risk management and the theories that underlie their use.

Putting VaR to Work

Welcome to the last module in your preparation for the first part of the FRM exam. This module on “Valuation and Risk Models” will introduce some practical concepts in the field of financial risk management. Some concepts have already been introduced in previous sessions and now we will apply those concepts and have an extensive discussion on a few of them, especially Value at Risk. Our first session is on VaR and how different approaches can be used to calculate the VaR of a portfolio. Let us begin our session.


The main agenda of this session will be describing the various approaches in calculating the VaR of a portfolio, such as the Delta-normal method, the full revaluation method, simulation methods, stress testing and scenario analysis. We will also highlight the worst-case scenario approach to the calculation of the VaR by focusing on the tail of the return distribution. In the exam, you will be tested mainly on the concepts presented in this session, and not many numerical questions will be asked.

Non-Linear Derivatives

In previous sessions on futures and options, we learned about their pricing. If you can recall, the expression was a non-linear function of the underlying risk factor. For linear derivatives, the relationship needs to be linear; i.e., the variation in the price of the derivative should be at a constant rate with the variation in the price of the underlying. As in the example given in the slide, the price of the derivative should be equal to the underlying price multiplied by a constant plus any other constant term. In the case of futures, we can approximate the expression to a linear function for short time intervals. For example, in the case of currency futures, the expression given in the slide can be approximated to a linear function in short time intervals.

In case of non-linear derivatives, the price of the derivative does not move at a constant rate with the change in the price of the underlying. For example, in the case of options, the price depends on multiple risk factors, such as time to expiry, underlying price, volatility and interest rate.