Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
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Modeling <strong>Risk</strong> – Local Volatility<br />
Dupire’s Local Volatility<br />
• Classic Solution: Dupire’s Local Volatility [2]<br />
the second most used model in equity derivatives<br />
— Idea: find s as a function of spot and time such that<br />
dS<br />
S<br />
LV<br />
LV<br />
( t)<br />
( t)<br />
= (<br />
t)<br />
dt s<br />
LV<br />
( t,<br />
S<br />
LV<br />
( t))<br />
dW ( t)<br />
reprices all market prices, ie<br />
<br />
<br />
!<br />
<br />
S ( t)<br />
K MarketCallPrice( t,<br />
K)<br />
DF( t)<br />
E<br />
LV<br />
=<br />
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