Week 10 Summary
LIBOR = London Interbank Oer Rate
LIBOR Loan: On day zero, bank pays N dollars. At time , bank receives
N (1 + L ) dollars.
Forward rate agreement
The forward rate agreement (FRA) involves an agreement to borrow/lend
Week 5 Summary
Geometric Brownian motion
log St = log S0 + at + Wt
with Wt a standard Brownian motion.
St is always positive.
Since the log increments have a distribution independent of stock size, the stock
increments have a distribution whi
Week 3 Summary
Martingale property: Future expectation is the current value.
Discrete time martingale
We have times T1 , T2 , . . . , Tk . T0 = 0.
We have independent random variables Xji . Xji is associated to the step Tj1
to Tj .
Let Fk d
Week 7 Summary
Features of the BS equation for the price of a European option
(t, St ) + 0.5 2 (t, St ) 2 St2 rD(t, St ) = 0,
(t, St ) + rSt
D(T, ST ) = f (ST ).
This equation does not involve .
It can be converted to the heat
Week 9 Summary
F (S + S, t + t, r + r, + ) = F (S, t, r, ) + S
Local behaviour with a delta hedge
F (S + S, t + t, r + r, + ) =
F (S, t, r, ) + S 2 2 + t
Gamma (or Vega) hedg
Week 4 Summary
t , where W
t is a standard
Wt is an arithmetic Brownian motion. Wt = W0 + t + W
Properties of Brownian motion
Covariance Cov(Ws , Wt ) = min(s, t).
Brownian motion is Markovian.
Brownian motion is a martin