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on a single bid or offer The more strike prices you include, the more accurate your data will be Traders often focus on individual strike prices as the underlying asset changes price, and they pick strike prices to try to pin the underlying price to, but by averaging, you are less likely to be affected by focused demand on a single strike price by a large hedger or fund For example, if you have ve strike prices each with a midrange implied volatility of 42 percent, 47 percent, 39 percent, 44 percent, and 49 percent, then you will add the ve volatilities together and divide by 5 This will get a 442 percent average IV (221/5 442) From that amount, take a look at the underlying current volatility and a recent history of volatility for the underlying asset If you have the data available, establish at least 90-day mean volatility average for the underlying asset It will be dif cult to get this information on the options, so we have to go with the underlying volatility Hypothetically let s say that the current volatility (standard 20-day) is at 47 percent and the 90-day average volatility is 39 percent There is an 8-point difference between the current and the mean volatility You can use this gure as a stop out point for the options If your average IV drops more than 8 percent, something is going wrong with the volatility picture and it is time to preserve capital If you do not have all these data available, you can certainly set a target of no more than a 10 percent loss in volatility without the calculations Remember to average the IV frequently so you know where you are Trailing stops: An example of a trailing stop is that if you have purchased a call option and the market on the underlying rallies making the option more valuable, the stop is moved.

5:

2 ( )d ,

W3 =

FIGURE 5-1

With these de nitions, eqn (D34) is equivalent to b(t2 ) = eW b(t1 ) (D35) Fortunately, the state transition matrix eW allows further simpli cation First, it is easily veri ed by direct multiplication that W2 = w 2 I Expanding eW using a power series eW = I+W+ W3 W2 + + 2! 3! W2 (W2 )2 (W2 )2 W2 = I+ + + + W I + + + 2! 4! 3! 5! sin ( w ) = cos ( w ) I + W w

Therefore, because the above derivation can be repeated over any interval of duration T for which the assumption of a constant angular rate is valid, we have the general equation b(tk ) = cos ( w ) I + sin ( w ) W b(tk 1 ) w (D36)

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software processes that reside on the database nodes and the Exadata Storage Servers, as shown in Figure 5-1 The Database Resource Manager (DBRM) component of the Oracle database performs management of CPU and I/O resources DBRM communicates with Exadata Storage Server processes for performing I/O Resource Management for intradatabase resource manager plans IORM utilizes the DBRM intradatabase plans generated by administrators, and regulates the I/O utilization among different consumer groups within the database

where w, w and W involve the integral of the angular rates over the k-th sampling interval t (tk 1 , tk ] Note that no approximations were made in this derivation, so the solution is in closed form given the assumption that Q(t) is constant over the interval of length T The solution is easily veri ed to be norm preserving by showing that the norm of the right side of eqn (D36) is equal to b(tk 1 ) The algorithm is not an exact solution to the di erential equation over any interval where the angular rates are not constant In [73] the algorithm of eqn (D36) is shown to be second order and a third order algorithm is also presented The algorithm being second order means the algorithm error contains terms proportional to T 3 and higher powers Because T is small, higher order algorithms have smaller errors; however, the tradeo is that they require additional computation

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