December 2015
Intermediate to advanced
522 pages
20h
English
Content preview from Stochastic Volatility Modeling
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Local volatility 55
For zero interest rate and repo this simplies to:
bσ
ST
(K) = bσ
KT
(S)
Thus knowledge of implied volatilities of all strikes for a given initial spot level
S
(the right-hand side) supplies information on the implied volatility of a particular
strike equal to the initial spot S, for all values of the spot level (the left-hand side).
The R = 2 rule
Taking the derivative of both sides of equation (2.78) with respect to
ln(K)
and
setting t = 0, K = F
T
and S = F
t
= S
0
then yields:
dbσ
KT
d ln K
K=F
T
=
dbσ
KT
d ln S
0
K=F
T
(2.79)
From this we derive the relationship linking the rate at which the ATMF implied
volatility moves as the spot moves to the ...
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