Description. To teach students basic knowledge about the Black-Scholes theory for pricing options and some relevant numerical methods.
Textbooks. I will prepare lecture notes for this class. The content will be extracted from
1. Stochastic Computation in Finance (written by Chuan-Hsiang Han)
2. Numerical Integration of Stochastic Differential Equations (written by G. N. Milstein)
3. Options, Futures, and Other Derivatives (written by John Hull);
4. Introduction to the Mathematics of Finance: From Risk Management to Options Pricing (written by Steven Roman )
Enclosed please find the lecture notes of this course (February 15, 2016 ~ June 10, 2016).
Syllabus.
Week 1st : Introduction
Week 2nd: Random walks & Stock price models
Week 3-4th : Ito integral
Week 5-6th : Ito's formula
Week 7-8th : Introduction of stochastic differential equations (SDE)
The Vasicek model and Cox-Ingersoll-Ross model
Week 9th: Midterm
Week 10th: Introduction of European options
Week 11th: Deriving the Black–Scholes partial differential equation (BSPDE) & finding the hedge strategy
Week 12th: Solving BSPDE by the martingale pricing method
Week 13th: Greeks & Implied volatility
Week 14th: Changing the numeraire (the Girsanov theorem)
Week 15-16th: Introduction of some numerical methods
PDE approach: Euler and Milstein schemes
Probabilistic approach: Monte Carlo methods
Week 17th: Final exam
Grading. The final grade breakdown is as follows: homework 40%; midterm 30%; final exam 30%.