Extreme value theory (EVT) aims to remedy a deficiency with value at risk (i.e., it gives no information about losses that exceed the VaR) and glaring weakness of delta normal value at risk (VaR): the dreaded-fat tails. The key is the idea that the tail has it’s own “child” distribution. This video explains the extreme

# FRM Exam

## How to Scale Autocorrelated Returns?

We know that the square root rule can be used to scale volatility with time. This rule assumes that the returns are independent and identically distributed. However, this assumption is not very realistic. This video illustrates a scaling factor that adjusts the square root rule for for autocorrelation. This video is developed by David from

## How to Forecast Volatility Using GARCH (1,1)

This video discusses how to use GARCH(1,1) to forecast future volatility. The key parameter is persistence (alpha + beta): high persistence implies slow decay toward the long run average. GARCH models were developed by Robert Engle to deal with the problem of auto-correlated residuals (which occurs when you have volatility clustering for example) in time-series

## Using GARCH (1,1) Approach to Estimate Volatility

This video provides an introduction to the GARCH approach to estimating volatility, i.e., Generalized AutoRegressive Conditional Heteroskedasticity. GARCH is a preferred method for finance professionals as it provides a more real-life estimate while predicting parameters such as volatility, prices and returns. GARCH(1,1) estimates volatility in a similar way to EWMA (i.e., by conditioning on new

## Volatility: Exponentially Weighted Moving Average (EWMA)

The EWMA approach to volatility is an improvement over simple volatility because it assigns greater weight to more recent observations (in fact, the weights are proportional). This video explains the EWMA approach. This video is developed by David from Bionic Turtle.

## Volatility: Moving Average Approaches

Within stochastic volatility, moving average is the simplest approach. It simply calculates volatility as the unweighted standard deviation of a window of X trading days. This video demonstrates three “flavors:” population variance (volatility = SQRT[variance]), sample, and simple. This video is developed by David from Bionic Turtle.

## Using Excel’s Goal Seek Function to Estimate Implied Volatility

In this video, you will learn how to estimate implied volatility. Using the market price for an option on Google’s stock, the video demonstrates how to use Excel’s GOAL SEEK function to estimate implied volatility. Implied volatility is a reverse-engineering exercise: we find the volatility that produces a Model Value = Market Price. This video

## Approaches to Estimating Volatility

There are lots of ways to estimate volatility. This video provides you an overview of the different approaches. It talks about implied volatility (forward looking) and deterministic (constant) and focus on stochastic volatility: volatility that changes over time, either via (conditional) recent volatility and/or random shocks. This video is developed by David from Bionic Turtle.

## How to Calculate Historical Volatility

This video illustrates how to calculate the historical volatility (moving average volatility), using the example of historical returns. Historical daily volatility is the square root of the daily variance estimate. This video is developed by David from Bionic Turtle.

## Compute Bond Price with Zero (Spot) Rate Curve Using TI BAII+

This video demonstrates how to compute the theoretical price of a coupon paying bond using spot rates. What is the price of a 2-year bond that pays a 6% semi-annual coupon given a zero rate curve? The calculation is shown using the Texas Instruments BA II Plus Financial Calculator This video is developed by David