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Stressed Scenarios and Model Risk
Hard
·
25 min read
Risk & Greeks
Scenario Analysis
Model Risk
P&L Attribution
VaR
1
Article
2
Quiz
Quick Quiz
1.
Why is Expected Shortfall (ES) preferred over Value at Risk (VaR) as a regulatory risk measure?
ES always yields a smaller number, so it lowers capital requirements
ES is easier to estimate from limited historical data
ES needs fewer assumptions about the return distribution
ES is coherent (subadditive), whereas VaR can violate subadditivity
2.
A delta-hedged options book shows a systematic negative P&L residual (actual < Greek-attributed) on days the market falls sharply. What does this most likely indicate?
The theta estimate is too small, overstating time decay
The gamma hedges are too large, over-hedging the spot move
A missing risk factor (vanna or jump risk)
The book is accidentally net long delta and loses on down moves
3.
A barrier option prices at 3.5 under local vol and 5.2 under Heston, both calibrated to the same vanilla surface. With local vol as the base model, the model-risk reserve is:
max
(
3.5
,
5.2
)
=
5.2
\max(3.5,5.2)=5.2
max
(
3.5
,
5.2
)
=
5.2
(
5.2
−
3.5
)
/
2
=
0.85
(5.2-3.5)/2=0.85
(
5.2
−
3.5
)
/2
=
0.85
∣
5.2
−
3.5
∣
=
1.7
|5.2-3.5|=1.7
∣5.2
−
3.5∣
=
1.7
3.5
×
0.5
%
=
0.0175
3.5\times 0.5\%=0.0175
3.5
×
0.5%
=
0.0175
(a fixed regulatory percentage)
4.
Under FRTB, a desk may use its internal model for capital as long as its pricing model is independently validated, regardless of P&L attribution test results.
True
False
5.
In
δ
V
≈
Δ
δ
S
+
1
2
Γ
(
δ
S
)
2
+
ν
δ
σ
+
Vanna
δ
S
δ
σ
+
1
2
Volga
(
δ
σ
)
2
\delta V\approx\Delta\delta S+\tfrac12\Gamma(\delta S)^2+\nu\delta\sigma+\text{Vanna}\,\delta S\,\delta\sigma+\tfrac12\text{Volga}(\delta\sigma)^2
δ
V
≈
Δ
δ
S
+
2
1
Γ
(
δ
S
)
2
+
ν
δ
σ
+
Vanna
δ
S
δ
σ
+
2
1
Volga
(
δ
σ
)
2
, which term dominates for a short-dated ATM straddle on a big-spot-move, stable-vol day?
The vega term
ν
δ
σ
\nu\,\delta\sigma
ν
δ
σ
The gamma term
1
2
Γ
(
δ
S
)
2
\tfrac12\Gamma(\delta S)^2
2
1
Γ
(
δ
S
)
2
The delta term
Δ
δ
S
\Delta\,\delta S
Δ
δ
S
The vanna term
Vanna
δ
S
δ
σ
\text{Vanna}\,\delta S\,\delta\sigma
Vanna
δ
S
δ
σ
6.
Historical-simulation VaR applies the last 250 days of factor changes to today's book and takes the 1% empirical quantile. Its main weakness for an exotic options book is:
It is backward-looking: scenarios outside the window are missed
It always overestimates VaR because history contains stress events
It requires 250 full repricings, which is impractical
It requires the portfolio to be delta-neutral to apply
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