VaR in financial risk management

GARCH Models in Python

Chelsea Yang

Data Science Instructor

Risk management mindset

Rule No.1: Never lose money

Rule No.2 Never forget Rule No.1

-- Warren Buffett

Buffett cartoon

What is VaR

VaR stands for Value at Risk
Three ingredients:
1. portfolio
2. time horizon
3. probability

VaR examples

_1-day 5% VaR of $1 million _

5% probability the portfolio will fall in value by 1 million dollars or more over a 1-day period

10-day 1% VaR of $9 million

1% probability the portfolio will fall in value by 9 million dollars or more over a 10-day period

VaR in risk management

Set risk limits
VaR exceedance: portfolio loss exceeds the VaR

VaR exceedances

Dynamic VaR with GARCH

More realistic VaR estimation with GARCH
VaR = mean + (GARCH vol) * quantile

VaR = mean_forecast.values + np.sqrt(variance_forecast).values * quantile

Dynamic VaR calculation

Step 1: Use GARCH model to make variance forecast

# Specify and fit a GARCH model
basic_gm = arch_model(bitcoin_data['Return'], p = 1, q = 1, 
                      mean = 'constant', vol = 'GARCH', dist = 't')
gm_result = basic_gm.fit()

# Make variance forecast
gm_forecast = gm_result.forecast(start = '2019-01-01')

Dynamic VaR calculation (cont.)

Step 2: Use GARCH model to obtain forward-looking mean and volatility

mean_forecast = gm_forecast.mean['2019-01-01':]
variance_forecast = gm_forecast.variance['2019-01-01':]

Step 3: Obtain the quantile according to a confidence level
1. Parametric VaR
2. Empirical VaR

Parametric VaR

Estimate quantiles based on GARCH assumed distribution of the standardized residuals

# Assume a Student's t-distribution 
# ppf(): Percent point function

q_parametric = garch_model.distribution.ppf(0.05, nu)

Empirical VaR

Estimate quantiles based on the observed distribution of the GARCH standardized residuals

q_empirical = std_resid.quantile(0.05)

Let's practice!

GARCH Models in Python