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Introducing the Lee-Mykland Test Results for XOM, COP, and CVX Problems with the test

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

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  1. 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

  2. -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

  3. -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):

  4. -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

  5. -Average BVj=(1/K) ∑ |Rt,j-1|^(1/2)*|Rt,j|*|Rt,j+1|^(1/2)

  6. -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)

  7. -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

  8. -XOM in Red, CVX in Blue

  9. -XOM in Red, Oil in Black

  10. -XOM in Red, Goldman Sachs in Blue

  11. -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

  12. 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?

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