Week 10 Summary
Lecture 17
LIBOR
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
Lecture 8
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
Lecture 5
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
Lecture 12
Features of the BS equation for the price of a European option
D
D
2D
(t, St ) + 0.5 2 (t, St ) 2 St2 rD(t, St ) = 0,
(t, St ) + rSt
t
St
St
D(T, ST ) = f (ST ).
This equation does not involve .
It can be converted to the heat

Week 9 Summary
Lecture 15
Approximation
F (S + S, t + t, r + r, + ) = F (S, t, r, ) + S
F
F
F
F
+ t
+ r
+
S
t
r
Local behaviour with a delta hedge
F (S + S, t + t, r + r, + ) =
1
2F
F
F
F
F (S, t, r, ) + S 2 2 + t
+ r
+
.
2
S
t
r
Gamma (or Vega) hedg

Week 4 Summary
Lecture 7
t , where W
t is a standard
Wt is an arithmetic Brownian motion. Wt = W0 + t + W
Brownian motion.
Properties of Brownian motion
Covariance Cov(Ws , Wt ) = min(s, t).
Brownian motion is Markovian.
Brownian motion is a martin