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Introducing the Lee-Mykland Test Results for XOM, COP, and CVX Problems with the test Possible corrections to the test Results for corrected test Factor Analysis Jump Component Instantaneous Volatility Co-jumps in the oil sector and the market Extensions.
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Introducing the Lee-Mykland Test • Results for XOM, COP, and CVX • Problems with the test • Possible corrections to the test • Results for corrected test • Factor Analysis • Jump Component • Instantaneous Volatility • Co-jumps in the oil sector and the market • Extensions
-Creates a statistic L(i), for each price, comparing the change in price on the interval [ ti-1, ti] to an instantaneous volatility measure using the previous 270 returns
-The distribution of L(i) is normal under the null hypothesis that no jumps occur over a given set An {1,2,….n} -The asymptotic distribution of the absolute value of the maximum L(i)in a given day is exponential -Where Cn and Sn, given n= and c=sqrt(2/pi):
-The window size they suggest for 5-minute data is K=270 observations -Thus, they calculate the instantaneous volatility going back 2.5 days -While this accounts for changes in local volatility on a larger scale, it does not adequately correct for intra- and inter-day changes in volatility -Specifically, inter-day volatility follows a U-shape, with higher volatility in the morning and lower volatility in the afternoon
-Let t=day and j=observation number in a given day -So, R4,5 refers to the return of the 9:55 observation of the 4th day -If we scale the return Rt,j by the average BVj at time interval j, the resulting return should account for the daily trend in volatility -Thus, we could try R*= Rt,j/ sqrt(BVj) -Then, we can re-calculate the instantaneous volatility using the adjusted returns -Average BVj=(1/K) ∑ |Rt,j-1|^(1/2)*|Rt,j|*|Rt,j+1|^(1/2)
-Oil Futures -Oil Companies: ExxonMobile, ConocoPhillips, and Chevron -Drilling/Exploration/Oil-field Company: Baker Hughes -Energy Company: Entergy -Businesses with products related to oil: FedEx, Ford, and Boeing -Miscellaneous companies: Goldman Sachs, Proctor and Gamble, and Dell
-Hypothesis: oil sector stocks will jump simultaneously due to the common factor price of oil -Many oil stocks in fact do jump at the same time, on the same day. -However, the price of oil futures does not frequently jump simultaneously -Possible explanation: When the price of oil increases, the upstream sector sees huge profits while the downstream sector is hampered by decreased demand and increased input costs. -Following table: number of days experiencing common price jumps
More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility • Suggestions for investigating day-to-day operations • Correcting the Lee-Mykland test • Volatility correlation with small lag times • Can we use the implied volatility of same industry companies and oil futures to forecast volatility using the HAR-RV-CJ model?