By June 15, finish part III: financial markets and products
1. Book: Chapter 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 26
2. Notes III
By July 31, finish part IV: valuation and risk models
It is a generalized Wiener process in which the parameters a and b are functions of the variable x and t:
This is Markov because the value of x only depends on time t. Both the drift rate and volatility rate are changing overtime.
For the change in small time interval ,
If the change in a small period of time is independent, with a standardized normal distribution (0,1), then z follows the basic Wiener process (Brownian motion). ; for any period T, z = normal(0,T)
A generalized Wiener process of variable x: , where a and b are constants
In a , the change
has a normal distribution with an expected drift rate of a and a variance of .
x in any time interval T is normally distributed with mean of change in x = aT, and variance of change in x =