jump in volatility & jump in returns
DESCRIPTION
Jump in Volatility & Jump in Returns. Kyu Won Choi. Clearing up the Data (SP500 & VIX). Data cleared up 5-minutes from 9:35am to 15:55pm (77 price data per day) S&P 500 price data at 16:00pm is absent Total 1233 days (94941 prices) from 9/22/2003 to 12/31/2008 2003 - PowerPoint PPT PresentationTRANSCRIPT
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Jump in Volatility & Jump in Returns
Kyu Won Choi
+Clearing up the Data (SP500 &
VIX) Data cleared up
5-minutes from 9:35am to 15:55pm (77 price data per day) S&P 500 price data at 16:00pm is absent
Total 1233 days (94941 prices) from 9/22/2003 to 12/31/2008
2003 62 days from 9/22/2003 to 12/31/2003
225 days in Year 2004
236 days in Year 2005
242 days in Year 2006
233 days in Year 2007
235 days in Year 2008
+Outline
Studied the jumps in the S&P500 and VIX Using Realized Correlation between squared jumps
(Tauchen, Todorov 2010) Using test statistics (Jacod and Todorov 2009) Using simple jump detection method
+Realized Correlation Measure
X = every 5 minutes S&P 500 index (per day)
Y = every 5 minute VIX (per day)
Rcj (calculated daily) closer to 1 if co-arrival of jumps in two processes over the given period. Because when common arrivals are present,
+ Frequency of Realized Correlation
~0.1
~0.2
~0.3
~0.4
~0.5
~0.6
~0.7
~0.8
~0.9
~1.0
Total
4 32 62 85 114 142 238 265 204 87 1233
+ Year by Year result
Mean (Median)
2003
0.5536 (0.5520)
2004
0.5782 (0.6127)
2005
0.5757 (0.6144)
2006
0.6527 (0.6858)
2007
0.7264 (0.7525)
2008
0.6886 (0.7169)
Total 0.6401 (0.6761)
+ Stacked Graph
+ Test statistics
High frequency 10 minutes versus 5 minutes price data
If common arrival of jumps converges to 1. Otherwise, Tcj closer to 2. Because when common jumps are present,
Tcj calculated daily
+ Unexpected Result
-A number of daily Tcj exceeds 2.0
Mean (Median)
2003
2.0941 (2.0141)
2004
2.0528 (1.7971)
2005
1.9872 (1.7976 )
2006
2.0190 (1.7942)
2007
2.1147 (1.7566)
2008
2.1461(1.9014 )
Total 2.0318 (1.8084)
+Adjusted Result
- Tcj that exceeds 2.0were removed.- Then about 2/5 Tcj wereremoved (maybe not Allowed to do this)
Mean (Median)
2003
1.0978 (0.9893)
2004
1.2958 (1.3247)
2005
1.2897 (1.3352)
2006
1.3029 (1.3989)
2007
1.3192 (1.3400)
2008
1.3802(1.3925 )
Total 1.2987 (1.3051)
+Simple Jump Detection Method
90167 price data (5minutes price data) excluded first 4774 number of data (~ 5% of the data)
Fixed Window Used the average jump size of the Year 2003 as standard Considered to be jump if it is greater than
2 times the standardized size jump 3 times the standardized size jump 4 times the standardized size jump
Rolling Window As time passes, includes next 5 minute prices (and removed the
previous one)
+Fixed Window
+ Rolling Window
+Consideration
Considered arriving two series of jump every 5 minutes
Is it too frequent?
Should consider only within the day?
Maybe the method to find the standardized size of jump is incorrect?
Then, from the standardized size of jump, use the squared root measure? (Instead of multiplying the constant)
Size 2 Times(3)
4 Times 2 Times 3 Times 4 Times
SP500 41844 41586 44202 44214 44146
VIX 48609 48609 45285 45182 45065
Together 10275 10154 9960 9920 9814
Fixed Window Rolling Window
+Final Thoughts
Improve the measure for detecting the jumps What to do with the test statistics?
Order of occurrences of jumps Does one jump lead to another when not occurring at the same
time? Are jumps in volatility followed by jump in prices? Or Jump in prices followed by volatility jumps?