(revised on 30 Aug, 2012.)

Lecturer Meifang Chu Office 318 Kemeny Tel 6461614 meifang.chu@dartmouth.edu 
Time and Place
Lectures: MWF 08:4509:50 am (9L) at 105 Kemeny in Fall
2012
Final Exam: TakeHome, Nov 16  19, 2012.
Office Hour: Thursdays
09:0012:00 (including xhour)
or by appointment.
Course Description and
Requirements
This course takes a mathematically rigorous approach to
understanding
the OptionPricing Theory and its applications to the
valuation and
risk management of financial derivatives products. Topics
includes:
Prerequisites:
CS 1 (computer science)
Math 23 (Differential Equations),
Math 20 (Discrete Probability) or Math 60
(Probability)
and Mathematics
50 (Probability and Statistical Inference).
Dist: QDS.
Grades are determined
at 65% from the homework problem sets and
35% from a takehome final exam. These problem sets
involve deriving and
solving equations numerically, analytically and
graphically. All the lecture notes,
problem sets, sample codes (Excel and Visual Basics) etc
will be accessed from
the Dartmouth Blackboard.
Stochastic Calculus for Finance. I : The Binomial Asset Pricing Model
Syllabus (S=Shreve,
H=Hull, n=chapter_number)
Module 
Reading 
1. Introduction to the Capital Markets and
Derivatives 
H14, H79 
(a) market dynamics and risk
factors
(b) contingency claims: futures, swaps, options and other derivatives (c) market completeness 

2. Probability,
Sigma Algebra, Random Variables and Markov Processes 
H12,13, S2 
(a) probability theory, sigma
algebra and conditional expectations
(b) Binomial, Gaussian, Poisson distributions and the tree models (c) random variables and probability density functions (d) Random Walk and Brownian motions (e) Martingales and Markov processes 

3. Discretetime
Formulation: no arbitrage, risk neutral valuation, the tree models 
H12,20 S1,3 
(a) binomial/trinomial
trees for a lognormal processMarkov
chain
(b) present value and the riskfree rate (c) no arbitrage argument (d) European Call/Put Options and American Call/Put Options 

4. Continuoustime Formulation (Martingale
method): State Prices and Risk Neutral Measure 
H27, S3 
(a) change of measure,
RadonNikodym Derivative
(b) Capital Asset Pricing Model (c) Risk Neutral valuation and the Martingale method (d) European options and the FeynmanKac formula 

5. Continuoustime
Formulation (PDE method): Itoh Calculus and BlackScholes Option Pricing Theory 
H5,6.13,14,16 
(a) Itoh Lemma and Itoh
Calculus
(b) 1factor BlackScholes model with constant volatility and interest rate (c) present value and the FeynmanKac formula (d) valuation of vanilla options 

6. Risk Management and Trading Strategies  H18,19,21 
(a) valutation and management of the
greeks (b) ValueatRisk and MonteCarlo simulations (c) trading strategies and counter party risk 

7.
FixedIncome Products  Interest Rate Models

H4,6,2832 S6 
(a) shortrate model
(b) multifactor forward rate models (HeathJarrowMorton & Libor models) (c) fixed income market (d) valuation of swaps, caps and floors. 

8. Other
Derivatives 
H2325 S4,5 
(a) American options and
other pathdependent options
(b) stopping times (c) first passage times (d) reflection principal (e) credit risks and prepayment risks 