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Floating Strike Lookback Option pricing question

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I have included my question in the attached Word document, since it was easier to type everything out accordingly, what with superscripts and subscripts et al.


Actually, as of today, 7/19/2018, at 8:54 a.m., I just realized an error I made yesterday when referencing the Fixed Strike Lookback Call Option.....when the minimum value is the stock price at expiration instead of the strike price, I should have included an "e^x" term as part of the PDF to be integrated, since the stock price is Lognormal, and the expected value of the Lognormal is always "e^x = e^(Normal mean + 0.5 * Normal variance)".

Plus, if "X" is Normal, the probability values would implicitly incorporate the STANDARD Normal table values and the respective probabilities to go with those.

That is, any calculated probabilities will take into consideration their respective z-values, but the formulaic setup of X would look like an integral for a Normal density function of X over its desired range. But we can't do ordinary integration for a Normal density function, so, we'd find the corresponding z-value, we'd find its respective probability (either by looking at the z-table of values or by finding it long way by writing out a Taylor series of "e^-0.5*z^2" and then integrating that,) and then we'd finish the equation.

Sorry, but I've been recently digesting and clarifying some of the nuances of this, so, I wanted to at least attempt to correct myself as much as I can on anything I said earlier that may be either erroneous or misleading.
 

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