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 />
• What about the error if we only hedge daily (not instantaneous) ?<br />
— Black&Scholes PDE:<br />
dFV(<br />
t)<br />
<br />
$<br />
( t)<br />
dS(<br />
t)<br />
S(<br />
t)<br />
=<br />
1<br />
2<br />
<br />
$<br />
2<br />
dS(<br />
t)<br />
<br />
<br />
S(<br />
t)<br />
<br />
dt<br />
“Cash Gamma”<br />
$ := S 2<br />
Theta<br />
• Key message<br />
— Theta ―compensates‖ for Gamma (theta is negative – the option value<br />
decays in time)<br />
— The hedge works perfectly if Theta and the Gamma term cancel.<br />
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