Course 2016 Spring (Financial Math)

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%.