VRM3 - Measuring and Monitoring Volatility Flashcards
Explain how asset returns tend to deviate from the normal distribution
Asset returns can differ from normal by:
- fatter tails
- non-symmetrical
- unstable with parameters through time
Explain reason for fat tails in a return distribution and describe their implications
When volatility parameter is unstable through time, fatter tails because more uncertain about returns
Distinguish between conditional and unconditional distributions and describe the implications of regime switching on quantifying volatility
Returns conditionally normal when constant mu and sigma, unconditional when constant mu and sigma varies with time
Apply the exponentially weighted moving average (EWMA) approach to estimate volatility, and describe alternative approaches to weighting historical return data
EWMA applies lambda = 0.94 weight to give more weight to more recent observations, lamda^2 for second most recent, lambda^3 etc
Then volatility can be updated by
sigma^2 = (1 - lambda) * r^2(n-1) + lambda * simga^2(n-1)
Other lambdas can be calculated by finding realised volatility for last 30 days then minimise difference between forecasted volatility and realised
Apply GARCH(1,1) model to estimate volatility
Extends EWMA:
simga^2_ n = alpha * r^2_ (n-1) + beta * sigma^2_(n-1) + gamma * V2
V2 = long run average variance rate
alpha + beta <= 1
gamma = 1 - alpha - beta
Explain and apply approaches to estimate long horizon volatility / VaR and describe the process of mean reversion according to GARCH(1,1) model
Mean reversion is where there is a pull toward the mean, volatility can show this in the GARCH model
Evaluate implied volatility as a predictor of future volatility and its shortcomings
Volatility implied from option prices
+ forward looking which is better than backwards looking
- sometimes not available for not actively traded assets
Describe an example of updating correlation estimates
Use EWMA to update by lamda * cov(n-1) + (1- lambda)* x_(n-1) * y_(n-1)
