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    Probability Distribution and Time?




    I saw the attached chart on an optionetics video on youtube and I'm struggling to understand it properly. It's a probability distribution placed sideways. The vertical axis is the share price going from bottom to top. The y axis is time from now increasing from left to right.

    If you turn the chart 90 degrees clockwise you will see the vertical bell curve (with the bottom cut off) where the current share price is where the average should be.

    What this diagram is saying is that as time goes on the chance of a wider dispersion of possible share prices increases . It's currently set to 70%. I'm just trying to understand how the Y axis (time) comes into this? Can this be done or is it a misuse of the bell curve? Please see the diagram below.

    Name:  prob_distribution.jpg
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    Re: Probability Distribution and Time?

    Anyone? If you're unsure what i mean then please ask questions.

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    Re: Probability Distribution and Time?

    Imagine an airplane located at position x(t) at time t - Sydney - it takes off with 700 passengers. Unfortunately the plane never reaches its destination.
    Last point of contact with the plane was at position x' at time t'. Obviously a search team should somehow look in a neighbourhood around x' to find the possibly crashed plane. How large the neighbourhood should be depend among other things on the speed of the plane. If the search is initiated at time t'' how far the plane could be from x' would depend on how far it could in time t''-t', which amounts to speed.

    Stocks are no different. They have a price and the price is assumed to change over time. P(t) is the price at time t and returns are changes in prices [P(t')-P(t)]/P(t).
    The variance is the speed with which prices changes, the longer the time horizon for a given variance pr. time the higher the variance.


    What is the probability that k1<R(t)<k2 as time increases?
    R(t) = s*t*Z

    k1<s*t*Z<k2

    k1/(s*t) < Z < k2/(s*t)


    If price are assumed lognormal the returns become normal so R(t) is normal with the variance s*t - Z standard normal - where t measure the time you hold the stock.

    Clearly my math is very sketchy here I do not know precisely how to set up the argument but neither is your question asking for a precise derivation of some mathematical property. In short I think it can be done within a classical model assuming prices are lognormally distributed.

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    Re: Probability Distribution and Time?

    Hi Jesper,, no maths needed here, I'm just trying to understand how a probability distribution relates to a time scale the way they have used it in the diagram above?

    You have half answered the question... 'As time increases from the time the stock price was a certain value the variance in stock prices increases', but I didn't know you could make this assumption with a probability distribution. I'm not looking for the math's but I am trying to gain an intuitive understanding behind why the distribution can be turned on it's side as in the diagram I provided and have a time relationship.. You could easily compress or expand out this lop-sided distribution to suit the time scale, but where's the relationship between time and this distribution?

    Just to be clear, what I'm asking is in the diagram below.

    Name:  time_probability.jpg
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    Last edited by tomydom; 05-27-2016 at 08:57 PM.

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    Re: Probability Distribution and Time?

    I don't want to be a pest, but does the above make no sense?

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    Re: Probability Distribution and Time?

    so there's no mathematicians out there who understand this?

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    Re: Probability Distribution and Time?

    I don't really understand what your question is asking. You didn't make it clear enough in a short enough amount of time so I honestly just didn't care. Keep in mind that it's on you to ask a question that 1) is understandable and 2) people care about http://www.talkstats.com/showthread....avior-pays-off

    Also could you post the youtube video? Is it possible you're misunderstanding what they're saying?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Probability Distribution and Time?

    I second Jasper and Dason's opinions. I think Jasper has made a close guess of what you want to know. I try to make my guess here also.

    To me the curve does not look like a bell curve. Rather it looks like a parabolic curve to me. It does not surprise us as, e.g. for a Wiener process W_t \sim \mathcal{N}(0, t), the \alpha and 1 - \alpha quantiles are given by \pm z_{\alpha}\sqrt{t} and that is how you obtain the parabolic curve.

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    Re: Probability Distribution and Time?


    Hi BGM, Dason, and Jasper. Thanks for coming back, I really appreciate the help.
    Here's the link... https://www.youtube.com/watch?v=hIoIZRJQiMI

    You could be right there, it may not be a distribution though I'm not sure. In this case it's used for odds analysis. I'm just trying to understand what they're doing here (regardless of whether it's pointless or not).
    Cheers

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