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Expression 20: Theta equals negative StartFraction, sigma squared Over 2 , EndFraction Gamma
Θ
=
−
σ
2
2
Γ
20
It reads, theta is proportional to volatility and concavity (negative convexity)
It reads, theta is proportional to volatility and concavity (negative convexity)
21
This relationship in LVR equation 16 can be derived from the above equation:
https://arxiv.org/pdf/2208.06046.pdf
This relationship in LVR equation 16 can be derived from the above equation: https://arxiv.org/pdf/2208.06046.pdf
22
Points on graph
Points on graph
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23
Expression 36:
36
Expression 37:
37
Expression 38:
38
Expression 39:
39
Expression 40:
40
Expression 41:
41
Expression 42:
42
Expression 43:
43
Expression 44: Gamma Subscript, "v" 2 , Baseline left parenthesis, "x" , right parenthesis equals negative StartFraction, "L" Over 2 "x" Superscript, 3 halves , Baseline , EndFraction
Γ
v
2
x
=
−
L
2
x
3
2
44
Expression 45: Theta Subscript, "v" 2 , Baseline equals negative StartFraction, sigma squared Over 2 , EndFraction Gamma Subscript, "v" 2 , Baseline left parenthesis, "x" , right parenthesis
Θ
v
2
=
−
σ
2
2
Γ
v
2
x
45
Expression 46: Theta Subscript, "v" 2 , Baseline equals StartFraction, sigma squared Over 2 , EndFraction StartFraction, "L" Over 2 "x" Superscript, 3 halves , Baseline , EndFraction
Θ
v
2
=
σ
2
2
L
2
x
3
2
46
Expression 47: StartFraction, left parenthesis, StartNestedFraction, sigma squared NestedOver 2 , EndNestedFraction StartNestedFraction, "L" NestedOver 2 "x" Superscript, 3 halves , Baseline , EndNestedFraction , right parenthesis Over 2 "L" StartRoot, "x" , EndRoot , EndFraction equals StartFraction, left parenthesis, StartNestedFraction, sigma squared NestedOver 8 , EndNestedFraction StartNestedFraction, "L" NestedOver "x" Superscript, 3 halves , Baseline , EndNestedFraction , right parenthesis "x" Superscript, negative 1 half , Baseline Over "L" , EndFraction equals left parenthesis, StartFraction, sigma squared Over 8 , EndFraction "x" Superscript, negative 3 halves , Baseline , right parenthesis "x" Superscript, negative 1 half , Baseline equals left parenthesis, StartFraction, sigma squared Over 8 , EndFraction "x" Superscript, negative 4 halves , Baseline , right parenthesis equals left parenthesis, StartFraction, sigma squared Over 8 , EndFraction "x" to the negative 2nd power , right parenthesis equals StartFraction, sigma squared Over 8 "x" squared , EndFraction
σ
2
2
L
2
x
3
2
2
L
x
=
σ
2
8
L
x
3
2
x
−
1
2
L
=
σ
2
8
x
−
3
2
x
−
1
2
=
σ
2
8
x
−
4
2
=
σ
2
8
x
−
2
=
σ
2
8
x
2
47
Expression 48:
48
Expression 49: Gamma
Γ
49
Expression 50: sigma
σ
equals
=
1
1
50
Expression 51: Theta
Θ
51
52
powered by
powered by
LP Value :
2
2
Delta Subscript, "l" "p" , Baseline
Δ
l
p
:
1
1
Gamma Subscript, "l" "p" , Baseline
Γ
l
p
:
negative 0.5
−
0
.
5
nu Subscript, "l" "p" , Baseline
ν
l
p
:
0.5
0
.
5
Theta Subscript, "l" "p" , Baseline
Θ
l
p
:
0.1 2 5
0
.
1
2
5
rho Subscript, "l" "p" , Baseline
ρ
l
p
:
0.0 2
0
.
0
2
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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