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 />
• The formula is understood as<br />
Change of<br />
option value<br />
Change of<br />
Delta position<br />
value<br />
FV( t<br />
dt,<br />
S(<br />
t<br />
dt))<br />
FV( t,<br />
S(<br />
t))<br />
dFV(<br />
t)<br />
=<br />
=<br />
(<br />
t,<br />
S(<br />
t))<br />
<br />
S(<br />
t<br />
(<br />
t)<br />
dS(<br />
t)<br />
dt)<br />
S(<br />
t)<br />
<br />
• Practitioners often look at ―cash delta‖ rather than delta.<br />
It reflects the cash value of the delta position:<br />
— This gives<br />
<br />
$<br />
( t) : =<br />
dFV(<br />
t,<br />
S(<br />
t))<br />
=<br />
(<br />
t)<br />
S(<br />
t)<br />
<br />
$<br />
dS(<br />
t)<br />
( t)<br />
S(<br />
t)<br />
Return on the<br />
stock<br />
investment<br />
11
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