Financial Mathematics 33000
Lecture 3
Roger Lee
2016 October 12
L3.2
Stochastic processes in continuous time
It
o integrals
It
os rule/lemma/formula
Stochastic processes in continuous time
It
o integrals
It
os rule/lemma/formula
L3.3
Filtrations
I
Recall:

FINM 33000: Homework 2
Due October 12, 2016
Problem 1
Let f : (0, ) R be twice continuously differentiable.
(a) Prove that for any K > 0 and any s > 0,
f (s) = f (K ) + f 0 (K )(s K ) +
Z
K
f 00 (K)(K s)+ dK +
0
Z
f 00 (K)(s K)+ dK.
K
Hint: First consider

FINM 33000: Homework 1 Solutions
TA: Hongcen Wei
September 29, 2016
Problem 1
Recall from L1.25 the diagram of the payoff of a call spread, long a standard call struck at K1 ,
and short a standard call struck at K2 > K1 . If we scale this call spread by 1

FINM 33000: Homework 1
Due Wednesday, October 5, 2016, 6:30pm Chicago time.
Submit via Chalk
Notation: Lx.y refers to Lecture x, Slide y.
Problem 1
Assume that discount bonds maturing at T have time-0 price 0.95 per unit. Assume that T -expiry
standard (p

Financial Mathematics 33000
Lecture 2
Roger Lee
2016 October 5
L2.2
One period, two states
The Fundamental Theorem
FAQs
One-period, more discrete states
Multi-period, more discrete states
One period, two states The Fundamental Theorem FAQs One-period, mor

Financial Mathematics 33000
Lecture 1
Roger Lee
2016 September 28
L1.2
Introduction
General properties of arbitrage-free prices
General properties of forwards and options
Introduction
General properties of arbitrage-free prices
General properties of forwa

Financial Mathematics 33000
Lecture 1
Roger Lee
2016 September 28
L1.2
Introduction
General properties of arbitrage-free prices
General properties of forwards and options
Introduction
General properties of arbitrage-free prices
General properties of forwa

FINM 33000 Homework 2 Solutions
Triwit Ariyathugun
October 13, 2016
Problem 1
+
(a) When s > K? , (K s)
= 0 for all K < K? , so the first integral vanishes. Additionally, because
+
(s K) = 0 for all K > s, the upper limit of integration on the last RHS te

Financial Mathematics 33000
Lecture 4
Roger Lee
2016 October 19
L4.2
Arbitrage in continuous time
Black-Scholes model
B-S formula via replication
Delta, Gamma, Theta
Arbitrage in continuous time
Black-Scholes model
B-S formula via replication
Delta, Gamma

Financial Mathematics 33000
Lecture 2
Roger Lee
2016 October 5
L2.2
One period, two states
The Fundamental Theorem
FAQs
One-period, more discrete states
Multi-period, more discrete states
One period, two states The Fundamental Theorem FAQs One-period, mor