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Power payoff in the Black-Scholes model
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Mathematics
Area of mathematics
Mathematical optimization
Mathematical finance
Black-Scholes model
Risk-neutral measure for the Black-Scholes model
Created
2026-09-24
Updated
2026-10-03
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For the payoff
S
T
p
,
risk-neutral valuation
gives
V
t
=
S
t
p
exp
[
(
(
p
−
1
)
r
+
2
1
p
(
p
−
1
)
σ
2
)
(
T
−
t
)
]
.
(1)
Its
delta hedge
holds
p
V
t
/
S
t
units of the risky
asset
.
Ancestors
(7)
Risk-neutral measure for the Black-Scholes model
Black-Scholes model
Mathematical finance
Mathematical optimization
Area of mathematics
Mathematics
Home
Incoming links
(3)
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 48
/
2
/
d
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 2
/
29K
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2022
/
ii
/
Paper 3
/
29K
/
c
/
Solution
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