Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
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Modeling <strong>Risk</strong> – Basics<br />
Black & Scholes<br />
• For this particular choice, the SDE has the analytical solution<br />
S<br />
BS<br />
1 2 <br />
( t)<br />
= F(<br />
t)exp<br />
s<br />
BSW<br />
( t)<br />
s<br />
BS<br />
t<br />
2 <br />
which allows computing vanilla option prices and, indeed, many more<br />
option prices analytically.<br />
The famous Black&Scholes formula for the value of an European call is:<br />
FV( T,Stoday)<br />
: =<br />
DF( T)<br />
= DF( T)<br />
E<br />
<br />
<br />
<br />
S<br />
BS<br />
( T)<br />
K<br />
F(T)N ( d<br />
<br />
<br />
<br />
<br />
) KN(<br />
d<br />
<br />
) <br />
d<br />
<br />
=<br />
ln( F(<br />
T) / K)<br />
<br />
s<br />
BS<br />
T<br />
1<br />
2<br />
s 2<br />
BS<br />
T<br />
7
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