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Strategies & Market Trends : Options -- Ignore unavailable to you. Want to Upgrade?

To: RoseCampion who wrote (1278)	1/20/2000 3:05:00 PM
From: rkral	Read Replies (1) \| Respond to of 8096

Rose, Thanks for your reply about stock price variance and standard deviation. It was very educational. Your reply proves that one can have an excellent understanding of options without a need to be skilled at the math involved. This is meant to be a compliment .. though somehow it doesn't sound like one. I apologize for not having better command of the English language. Besides, after the BlackRose calculator, I already have respect for your math skills. <<the underlying stock would have to exhibit a yearly standard deviation of +/- 64% of its current price to make the theoretical value of this option or options match their current actual market prices>> You are exactly correct. I now have a copy of McMillan's OSI and he defines variance(v) as standard deviation(sigma) divided by the stock price. IOW, standard deviation is volatility times the current price of the underlying. <<Assuming it's not just as simple as going plus or minus 64% from the current stock price and dividing the time period of interest by 365>> Let me clarify the above. The volatilities for different time periods are related by the square root of the ratio of the time periods involved, as stated in McMillan OSI. The volatility for three-months, e.g., would then be one-half (the square root of 1/4) of the annual volatility. The interesting result of this mathematical exercise is that the expected profit from my covered call position in AOL, on the day it was placed, was about ZERO. Long AOL at 61 7/8 and wrote Jan 01 LEAPS @ 60 for 16 3/4 putting the break-even at 45 1/8 and max profit at 14 7/8 (everything ignoring commissions). My profit expectation equation (corrected from a prior post) = M - v * U / (( 2 * pi)^ 1/2). Plugging in the numbers: 14.875 - (0.66 * 61.875 / 2.507) = Minus 1.40. Does a number in this area make any sense to anyone? (I'm pretty sure about my profit expectation equation ..except that it needs refinements, lognormal distribution instead of normal, and allowing for strike prices not being equal to the stock price.) Does anyone on the thread know of an options book that includes mathematically derived profit expectations? Or is it all irrelevant?