Explain or define the following relationships and concepts

$1.$ Why call and put options are more valuable the greater their underlying security$$s variability.

$2.$ The relation between the BOPM and the B$-$S OPM

$3.$ Neutral Delta Position with Positive and Negative Gamma

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$4.$ The value of Merton$$s continuous dividend$-$adjusted BOPM for puts over Merton$$s continuous dividend$-$adjust B$-$S OPM for puts.

$5.$ Why the mean is unimportant in the BOPM for large number of sub$-$periods and in the B$-$S OPM.

$6.$ The conditions for futures options to be equal to spot options.