Advanced Value at Risk Models by Edu Pristine

Author of lecture Advanced Value at Risk Models

Edu Pristine

Customer reviews

Excerpts from the accompanying material

... - Demonstrate Standard Distributional Assumptions - Demonstrate Volatility Clustering Models - Demonstrate impact of Volatility Clustering on VaR - Discuss GARCH model - Demonstrate VaR with the Student’s distribution ...

... is usually observed i.e. high returns volatility is followed by still higher volatility and vice-versa. This can be examined by seeing autocorrelation (correlation of returns data with itself, with a time-lag) in squared returns data-series. VaR estimation on basis of these assumptions usually underestimate extreme risks in case of high ...

... - Volatility clustering states that in most cases market shock generally leads to large returns for a time period. ...

... average (equally weighted average) of previous ‘n’ days’ squared returns. This method of variance (and std. deviation) estimation ignores conditional volatility i.e. present volatility maybe conditional on volatility observed in the recent past. ...

... Moving Average (EWMA): Variance estimate for next day (t+1) is given by (1-Lambda) weight-age to ...

... estimate for Tuesday was 1%. Find volatility estimate for Wednesday using Lambda of 0.94–Variance estimate for Wednesday=(1-0.94)*(4%)2 +(0.94)*(1%)2 = 0.019%; Std. dev. =0.019%=1.378% - Tuesday volatility (Std. Dev.) estimate was 1%. ...

...Illustration 1: On Tuesday, return on a stock was 4%. Volatility (Std. deviation) estimate for Tuesday was 1%. Find volatility estimate for Wednesday using Lambda of 0.94 - Variance estimate for Wednesday=(1-0.94)*(4%)2 +(0.94)*(1%)2 = 0.019%; Std. dev. = 0.019%=1.378% - Tuesday volatility (Std. Dev.) estimate was 1%. Actual return on Tuesday was 4%. ...

... latest return and latest volatility estimate. Consider the equation. In this equation, variance for time ‘t’ was also ...

... and latest volatility estimate. Consider the equation, In this equation, variance for time ‘t’ was also an estimate. So we can substitute for it as follows: We can see that when estimating variance for tomorrow (t+1), latest squared return gets weight of 6%. But previous day’s squared return (mu_sq_t-1) gets weight of ...

... in handling fat tails (return distribution being negatively skewed and high kurtosis) is addressed to an extent. GARCH stands for Generalized Autoregressive Conditional Heteroscedasticity. Scedasticity means variance. Therefore, Heteroscedasticity means variance is ...

... So, EWMA is a special case of GARCH. Alpha, Beta and Gamma are estimated using Maximum Likelihood Estimation (MLE) and their sum is equal to 1. Higher the Gamma, greater is the mean-reverting ...

... return was 1% and the volatility (std. deviation) estimate for that was 1.8%. Calculate the volatility estimate for next day (t+1) & long-term average volatility (to which the model shows reversion over-time). Solution: In the GARCH model, 12% is the weight given to latest squared return (reactive factor). ...

... The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by 1 + ?. In this case the persistence factor is the second lowest: 1+? = 0.02 + 0.95 = 0.97. ...

... 3. Fitting t distribution to observed data-Mean of observed returns (especially daily return) is usually 0. So no calibration is required–Variance of observed data is not likely to be v/(v-2), it need to be calibrated. Find degrees of freedom by equation 3*(v-2)/(v-4) equal to ...

... and daily standard deviation of 0.5%. Calculate 99% 1-day VaR. Solution: Raw kurtosis = Excess kurtosis + 3 = 6 +3 = 9. Equation we find that degree of freedom v = 5. Scaled variance daily scaled volatility= Critical value of t distribution at 5v and ...

... VaR would be exceeded 10 times in 1000 days. Conditional VaR is the average of these 10 losses. EVT examines the value of extreme values of a random event like portfolio losses, portfolio returns etc. EVT consists of two distribution families: Generalized extreme value distribution (GEV): it models maximum and ...

... a portfolio follow a normal distribution with mean of 3% and volatility of 5%. In extreme stress scenario, mean return declines to 30% with volatility of 20%. Probability of a stress scenario is ...

... where VAR1 and VAR2 are the two components and ? is the correlation between the two. Direct estimation of total VaR ...

... Incremental VaR = VaR including a new exposure – VaR without considering the new exposure. This is ‘before and after’ approach. Marginal VaR: It is computed to know the change in VaR of the portfolio with one ...

... VaR = $5.75mn; Marginal VaR = 0.171mn D.Component VaR = $7.12mn; Marginal VaR = 0.171mn Stock Position Return std. dev Beta A 25mn ...

... Portfolio Value = 2.58*0.078*$100MN = 20.124mn Component VaR for A = DVAR * Beta(A)* Weight ...

... % of variance of the original data. Advantage is that PC are independent, so their impact on portfolio can simply be added (remember, in portfolio variance formula, if correlation between market variables is zero then one can simply add impact of movements in the variable on the portfolio). Usually when PC are identified for term structure of interest rates, three PC ...

... cash flow–MC simulation VaR method for interest-rate options portfolios. For estimating the total VaR, we need to use a covariance matrix of the whole system–Apply PCA ...