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Portfolio Greeks Aggregation
Hard
·
22 min read
Risk & Greeks
Portfolio Risk
Vega Ladder
Vanna
Volga
1
Article
2
Quiz
Quick Quiz
1.
A book is long an ATM straddle and short an OTM strangle, with zero net vega (
∑
k
n
k
ν
k
=
0
\sum_k n_k\nu_k=0
∑
k
n
k
ν
k
=
0
). Which risk does the zero-vega figure hide?
Volga (vol-convexity) risk: net vega is zero but net volga is not
Rho risk: the two structures have different rate sensitivities
Delta risk: the straddle and strangle carry different deltas
Theta risk: the legs decay at different rates
2.
Under a smile model the delta is
Δ
model
=
N
(
d
1
)
+
ν
∂
σ
^
/
∂
S
\Delta_{\text{model}}=N(d_1)+\nu\,\partial\hat\sigma/\partial S
Δ
model
=
N
(
d
1
)
+
ν
∂
σ
^
/
∂
S
. For a long call (
ν
>
0
\nu>0
ν
>
0
) with
∂
σ
^
/
∂
S
<
0
\partial\hat\sigma/\partial S<0
∂
σ
^
/
∂
S
<
0
(vol rises as spot falls), how does model delta compare to BS delta?
Model delta > BS delta: the smile term adds to the hedge
Model delta < BS delta: the negative smile term reduces the effective delta
The sign depends on whether the instrument is a call or a put
Model delta = BS delta: the adjustment cancels under put-call parity
3.
A risk-reversal is long an OTM call and short an OTM put. Using Vanna
=
−
n
(
d
1
)
d
2
/
σ
=-n(d_1)d_2/\sigma
=
−
n
(
d
1
)
d
2
/
σ
, what is the sign of its net vanna?
Zero: the call and put vannas cancel exactly
Indeterminate without the exact strikes and notionals
Negative: the short-put leg dominates
Positive
4.
By the standard fixed-income desk convention, DV01 is the P&L from a 1bp increase in yields, and is therefore negative for a long bond.
True
False
5.
Vanna-volga pricing hedges an FX exotic with three vanillas (ATM, 25Δ call, 25Δ put) to match its vanna and volga. What risk does this static hedge leave open?
Delta: net spot-direction exposure of the book
Higher-order vol sensitivities and path-dependent smile risk
Theta: net time-decay across the positions
Gamma: net spot-convexity exposure of the book
6.
A book has zero net delta, zero net gamma, but significant positive net volga. Which scenario hurts it most?
A big implied-vol move in either direction
A vol move equal to the average daily vol move
A large spot move with implied vol unchanged
A quiet day: spot and implied vol barely move
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