Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
Risk 1 - Hans Buehler
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Modeling <strong>Risk</strong> – Basics<br />
Setting<br />
• Given is a Stochastic Differential Equation<br />
Brownian<br />
Motion<br />
dS(<br />
t)<br />
S(<br />
t)<br />
= (<br />
t)<br />
dt s ( t,<br />
S(<br />
t))<br />
dW ( t)<br />
Drift<br />
Volatility<br />
Forward<br />
— In the risk-neutral world, the drift is implied by E[S(t)] = F(t) as<br />
dF(<br />
t)<br />
( t)<br />
dt = r(<br />
t)<br />
<br />
( t)<br />
F(<br />
t)<br />
— Black & Scholes [3]: s= s BS is a constant number.<br />
5
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