# How can I evaluate how poor a fit a parametric VaR result would be for a given holding?

I'm currently working on an application that, among other things, computes a one-day parametric VaR for security positions. I understand that the parametric method of computing VaR is a poor fit for non-linear instruments, such as options and fixed income. Thus my question:

How can I evaluate how poor a fit a parametric VaR result would be for a given holding?

I'm interested in both rules of thumb - for example, "credit default swaps are always a poor fit for a parametric VaR computation" and guidelines, such as "fixed income securities become increasingly non-linear as duration increases, and are a poor fit for a parametric VaR computation once duration is above X" I have no idea if either of those statements are true. I made them up.

• out of sample tests – pyCthon Feb 23 '13 at 6:33

## 1 Answer

@pyCthon's comment hit home. So I did some tests.

I compared a parametric computation to a Monte Carlo computation of IR Vol for a small set of fixed income securities. I was particularly concerned whether I could identify factors that would indicate that the difference would exceed 10% of the MC result.

Here's are my summary findings:

• Vanilla IR Swaps (3) - difference ranged from 16% to 40% across my sample
• Convertible Bonds (2) - FUGIT > 7 corresponding to an IR Var difference > 500%, FUGIT < 1 corresponded to a difference of < 1% -- however sample size of 2 bonds is too small to generalize
• Swaptions (3) - difference ranged from 3.1% to 0.3% -- the small magnitude and lack of variation in the % difference for these securities is unexplained.

• Non-callable Bonds (8) - This was the most interesting finding. Three of the holdings had a % difference below 7% while the percentage difference of the other five ranged from 36% to 77% -- After examining various factors (duration, dv01, convexity, theta, years to maturity, etc.) I was finally able to predict and rank the percentage difference by comparing the scaled weighted average term vol(2) used in the parametric IR Vol calculation. When the scaled avg vol was below 1, the percentage difference was below 10%, and the percentage difference increased with increasing scaled avg vol.

(1) FUGIT: Expected life of a convertible bond in years
(2) scaled weighted average term vol computed as

$$\sum{(vol * dv01 * rate)} \frac {Median_{WeightedVols} }{ Range_{WeightedVols}}$$