ECO743 Stochastic Differential Equations [2015]

Aims and Objectives

This course aims to introduce stochastic differential equations and application of continuous time time series modeling in finance and economics. At the end of the course, the students shall be able to model the real world time series data. The software used in this course for statistical programming is R. Students shall be able to use R and its related packages. The content of the course is dynamic and changing in every year. This year content includes (but not limited):

• Introduction to Time Series
  • Discrete Time Series, Continuous Time Series, probability-time-frequency Domains
• Elements of Probability and Random Variables
• Stochastic Process and Stochastic Differential Equations
• Ito’s Lemma, Stochastic Integral
• Wiener Process, Brownian Motions, Geometric Brownian Motions
• Some widely used Stochastic Differential Equations
• Numerical Methods
  • Euler-Maruyama
  • Milstein
  • Runge-Kutta
  • Taylor
• Estimation
• Simulation - Monte Carlo Sampling
• Applications
  • Vasicek Model Download Irates
  • Stock Prices
  • Risk Management

References and Suggested Readings

Stefano Iacus, Simulation and Inference for Stochastic Differential Equations with R examples, Springer Science, 2008

S. Neftci, An Introduction to the Mathematics of Financial Derivatives, Academic Press, 2000

B. Oksendal, Stochastic Differential Equations, 5th Edition, Springer Verlag

R Software and General Steps for Learning from Data

To install the main statistical software R, go to web site, click the verson link for your operationg system then download files (for example click Download R for Windows link), then click base and download executable file). I do recommend RStudio as Powerful IDE for R (i.e., editor, viewer and lots of facilitator). Download RStudio Desktop and install it. The next step is to download some packages related with this course (the list of packages may change). You can use the following script to download the packages initially needed.

# Time series Analysis related packages
packagests <- c("forecast","TSA","timeSeries","xts","xtsExtra","zoo","lubridate","chron","rugarch","rmgarch","tempdisagg","mFilter","depmixS4","qualV","sde","yuima")
packagesdt<-c("WDI","quantmod","countrycodes","dplyr", "reshape","reshape2","data.table","stringr","xlsx")
packagesgr<-c("ggplot2","lattice")
install.packages(c(packagests, packagesdt, packagesgr))

Several useful references about R may be found on internet. However, the following adresses are good starting points: R manual and R Contributed Documentation.In addition, I want to recommend Quick-R and R-bloggers. Students who haven’t taken any time series courses before could refer to the following pages related with (undergrad) Time Series Analysis course: (these are not complete modelling exercises, these pages present scripts that were used for in-class discussions)

• Introduction to R
• Basic Data Importing Facilities in R

Please visit Time Series Analysis task view maintained by Rob J. Hyndman for a good collection and summary of packages related with time series analysis in R.