Jump Correlation between Two Companies in Financial Markets

• Research Goal

• Development of asset pricing methodology to consider jump correlation between two companies
• Development of efficient data process program for empirical analysis
• Development of simulation for proof of methodology
  
  

•  Research Statistics

• Research resource: 1 people
  (Advisor: Professor Lee, Suzanne, Ph.D.)
• Research term: 2008.10 ~ 2009.12 (15 months)
• My role responsible of this research: 100%
• Research output: Paper(on process) and data process program
  
  

• Techniques used for this research

• log return process: When we use S(t) for stock price at time t, dlogS(t) can be represented by the following stochastic differential equation (SDE):
  

  

  where W(t) is Ft-adapted standard Brownian motion and the drift mu(t) and spot volatility sigma(t) are Ft-adapted process.
• Test statistic for jump detection: The statistic L(i), which tests at time ti whether there was a jump from ti-1 to ti is defined as
  
  

  

• Extreme value theorem:When the number of observation goes to infinity, the maximum of L(i) converges to gumbel distribution as the following:
  
  

  

• Copula function: A copula with dimension n is an n-dimensional probability distribution function
  defined on [0, 1]^n that has uniform marginal distribution Ui
  

  

  In archimedean copula, we used gumbel copula as the following:
  

  

• My contribution to the research

• Data process program: Based on TAQ database of WRSD, I need to sample the stock price every 15 minutes. Starting form the raw data, this program that I made woks for separating trading hours, trading location and companies. That is, it can produce the data set that includes every 15 mins stock price of specific companies traded on New York stock exchange. Because it is made by C++, this can be operating on Windows.
  
• Empirical Analysis: Our selected sample extends from July 1, 2001 to June 30, 2006 for a total of 1,256 trading days including all available records from 9:30am to 4:00pm. And we select only DJIA firms that are traded on NYSE in order to maintain enough degrees of liquidity and to maintain similar organization of trading mechanisms and trading hours across stocks. Based on this data set, every pairs of 30 companies are tested by copula function to find their jump correlation. 
  
• Simulation: From generating time sequences of two companies, I simulate to test our hypothesis of jump correlation. In this context, Jump size and density are variables for Monte Carlo simulation. 
  
  

• Results

Figure1: Jump correlation between C and AXP. Highlighted points represent the time when they have jump occurences together.

• These tables present the average result of simulations under the some conditions. SE, LB
  and UB denote, respectively, the standard error, lower bound of confidence interval and upper bound of confidence
  interval. Tau represents Kendall tau rank correlation coefficient that is a non-parametric statistic used to measure the
  degree of correspondence between two rankings and assessing the significance of this correspondence.
  

• This table shows the characteristics of jump correlation between two companies in every pair of DJIA (I just posted some part of them).