Remember, slides and presentations at this page are provided only as an extra source, while the basic reading is given in the column "Reading".
Lecture
Topics
Reading
Assignments
1
- General problems of computational finance - pricing, calibration, curve fitting. (slides #1)
- Fundamentals of Stochastic Calculus (brief overview) - slides #2 of Prof. S. Jaimungal
- Closed form solutions. The Black-Scholes world, option pricing and numerical techniques. (slides #3 from Hull's book)
- Old approaches. The binomial method. (slides #1, continue)
QMDP, chapter 1,2
IDM - chapter 1,2
1. Homework assignment 1
Solutions (by PING, GUANGHUI)
2
- Impied trees, calibration to the smile (Mordecki presentation), (Derman paper)
- From closed form solutions to almost closed-form solutions - FFT
- Characteristic function - short survey 1, 2
- FFT - Carr, Madan and Lewis methods
IDM, chapter 5
Carr, Madan paper
Itkin's presentation
2. Homework assignment 2
Solutions (by ANDRIYASH, EVGENY A)
)3
- BS-wise version of FFT
- Fractional Fourier transform (FYI only, also you can get an extra credit)
- MC - random number generators (1, 2, 3, 4)
- Quasi-random numbers (1)
Itkin's presentation
Chourdakis paper
QMDF - chapter 4
GL - chapter 2
3. Homework assignment 3
Solutions (by ZHENG, GUOHUI)
4
- Quasi-random numbers (1)
- Samling from arbitrary distruibutions (1)
- Smapling from joint distributions (1)
- Brownian bridge (1)
QMDF - chapter 4
GL - chapters 2,5
5
- Valuing European style options with Monte Carlo. Reducing the error in the estimate (slides here from slide 55)
- Estimation principle and Variance reduction technique (slides here from p.63-67, 72-76)
- Computing Greeks using Monte Carlo methods (1)
QMDF - chapter 5
Gl - chapter 4,, 6.1, 7
4. Homework assignment 4
Solutions (by MENG, XIAOXIANG)
6
- Introduction to Finite difference method (1)
- Convergency, accuracy, explicit and implicit method, Crank-Nicholson sheme (1, chapter 15)
QMDF - chapter 7
FD
MFE - chapter 6,8,9
7
- Coordinate transformation (1)
- Splitting (also see 1)
- Boundary conditions (also see 1)
- BDF2 and exponential fitting scheme (1, 2)
QMDF
FDMFE
5. Homework assignment 5 (deadline - 3/21)
Solutions (by Li Nan) code
8
- Stability of finite-difference scheme (1 from page 37, 2)
- American option and FD (1, 2, 3)
- Asian option (1)
QMDF -
FDMFE -chapter 19, 20, 23, 27,
6. Homework assignment 6 (deadline - 3/28)
Solutions (by Zheng Guohui)
9
- ADI, method of lines (1)
- Lookback option (1)
- Calibration, Levngberg-Marquardt (1)
FDMFE -chapter 19, 20, 23, 27
7. Homework assignment 7 (deadline - 4/5)
Solutions (by Jian Wu
10
- Variance and Volatility Swaps.
- Options on variance swaps
- Correlation and covariance swaps
Alexander Gairat
Anatoliy Swishchuk
Jim Gatheral
8. Homework assignment 8 (deadline - 4/12)
Solutions (by Guohui Zheng)
11
- Convertible bonds
Luke Olsen
survey
Grau, P.Forsyth, K.Vetzal
12
- How to call C++ dll from Excel
- Calling Matlab from C++
- Design of financial software
9. Homework assignment 9 (deadline - 4/25)
Solutions (by Jian Wu)
13
Interest rates models (site of Damiano Brigo)
BM
全部可在
http://www.math.rutgers.edu/courses/612/index.html 下载， Enjoy
