jump in volatility & jump in returns

15
+ Jump in Volatility & Jump in Returns Kyu Won Choi

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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 - PowerPoint PPT Presentation

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Page 1: Jump in Volatility &  Jump in Returns

+

Jump in Volatility & Jump in Returns

Kyu Won Choi

Page 2: Jump in Volatility &  Jump in Returns

+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

Page 3: Jump in Volatility &  Jump in Returns

+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

Page 4: Jump in Volatility &  Jump in Returns

+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,

Page 5: Jump in Volatility &  Jump in Returns

+ 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

Page 6: Jump in Volatility &  Jump in Returns

+ 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)

Page 7: Jump in Volatility &  Jump in Returns

+ Stacked Graph

Page 8: Jump in Volatility &  Jump in Returns

+ 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

Page 9: Jump in Volatility &  Jump in Returns

+ 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)

Page 10: Jump in Volatility &  Jump in Returns

+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)

Page 11: Jump in Volatility &  Jump in Returns

+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)

Page 12: Jump in Volatility &  Jump in Returns

+Fixed Window

Page 13: Jump in Volatility &  Jump in Returns

+ Rolling Window

Page 14: Jump in Volatility &  Jump in Returns

+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

Page 15: Jump in Volatility &  Jump in Returns

+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?