 # Seminars

The practical content of the course is designed to be delivered in eight seminars. Each seminar consists of a notebook with the material that will be covered in the session and homework exercises that students are expected to solve on their own.

The course also includes a support notebook with discussion on more advanced R topics.

## Seminar One

#### Classwork

• Familiarize ourselves with R and RStudio
• Learn some basic commands
• Create a simple plot

#### Homework

• Download the stock prices and returns from Amazon and Apple between January 1st, 1990 and December 31st, 2010
• Load the data into R
• Create two variables “amazon” and “apple” that hold the downloaded data of each stock
• Do a simple plot for each of the stock’s returns

## Seminar Two

#### Classwork

• Install and load packages in R
• Basic Data Handling
• Save created Data Frames
• Create, customize and export plots

#### Homework

• Open the data from Amazon and Apple from the previous seminar
• Use the dcast function to create RET and PRC data frames with the returns and prices
• Make sure your returns are compounded and not simple
• Save each data frame in your working directory
• Plot the returns and prices for each stock, well-labeled, using a 2x2 grid

## Seminar Three

#### Classwork

• Learn how to work with statistical distributions
• Explore random numbers and the Monte Carlo simulation
• Visualize, analyse, and comment on the prices of a stock
• Perfrom graphical analyses and statistical tests

#### Homework

Elaborate a commentary on the price of the Amazon stock. To do this:

• Load the returns data frame you created in Seminar Two
• Plot the returns for Amazon
• Zoom into the dot-com years (2000-2002)
• Find the best and worst perfoming days, and find out what happened on those dates
• Compare the returns to a normal distribution graphically and using a test
• Plot the ACF of the returns and returns squared
• Use a 2x2 grid to elaborate four QQplots comparing the returns to a Student-T of 2, 3, 4 and 5 degrees of freedom

## Seminar Four

#### Classwork

• Build unvariate GARCH models
• Plot GARCH outputs
• Work with various specifications (ARCH, Student t, apARCH)
• Relax the GARCH stationarity condition
• Assess model quality using likelihood ratio tests and residual analysis
• Learn about half-life and GARCH simulations

#### Homework

Choose a stock between Amazon and Apple and:

• Fit a univariate GARCH(1,1) where conditional returns follow a normal distribution
• Fit a univariate GARCH(1,1) where conditional returns follow a T-distribuion
• Plot the estimated conditional volatilities against each other and comment
• Fit an ARCH(1,1) model and perform a LR test versus the GARCH(1,1)

## Seminar Five

#### Classwork

• Introduce multivariate volatility models
• Build a bivariate EWMA model
• Run DCC models with different specifications
• Compare models

#### Homework

• Load the Amazon and Apple returns
• Build a bivariate EWMA model for these stocks
• Build a loop that creates an EWMA for values of lamba = 0.9, 0.91, 0.92,… 0.99
• Create one plot for each stock with the estimated conditional volatilies for the different lambda
• Fit a DCC tapARCH model and calculate the conditional correlation
• Plot it and zoom into the dot-com bubble period (2000-2002)
• Comment any findings

## Seminar Six

#### Classwork

• Solve exam-like questions regarding risk measures
• Perform univariate and multivariate estimations of ES and VaR using Historical Simulation
• Experiment with different estimation windows for Historical Simulation VaR
• Build an EWMA VaR model

#### Homework

• Load the Amazon and Apple returns
• Perform a Historical Simulation VaR 99% forecast for each stock, use an estimation window of 1000 days
• Perform a Historical Simulation VaR 95% forecast for each stock, use an estimation window of 1000 days
• For each stock, plot the HS VaR forecast for both 95% and 99% in the same plot
• Comment

## Seminar Seven

#### Classwork

• Implement GARCH VaR
• Analyze and compare VaR forecasts between models
• Perform backtests with violation ratios
• Implement multivariate EWMA and HS VaR
• Perform stress-testing

#### Homework

• Use the six models covered (EWMA, HS300, HS1000, HS2000, GARCH300, GARCH2000) to backtest 1% VaR for both Amazon and Apple stocks individually.
• Perform a stress-test in the dot-com years (2000-2002)

## Seminar Eight

#### Classwork

• Use the Black-Scholes equation to price an option
• Simulate option prices with Monte Carlo
• Experiment with different simulation sizes
• Use analytical and simulation methods to get VaR
• Calculate VaR for an option
• Calculate VaR for a portfolio of stock and option

#### Homework

• Repeat the seminar for a Call option instead of a Put