Comparing Price Distributions

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Comparing Price Distributions

The Options Industry Council (OIC) · ⏱ 3:09 · 109 مشاهدة · 1 jaar geleden

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The interesting part about distributions, like said at the beginning, when you start to get into different levels of volatility, the shape of the distribution changes most of the time. Let's talk about it. Let's talk about three different stocks that have three different historical volatilities. Remember that these volatilities are backward looking. Stock is moving on 15 historical is moving on 25 and is moving on 35. want you to think about what the actual normal price distribution might look like if you overlay all three of these stock volatility normal price distributions on top of each other. And what can tell you is that they're going to look differently. Now, this isn't drawn to scale. It's not perfect. It's not like perfect examination of what it might look like. It's meant to give you an idea of the fact that as volatility rises, curves generally flatten as far as normal price distribution curves. You'll see here this 15 historical is stock that's not moving that much. What is its what are the characteristics of its normal price distribution? It has lot of amplitude and very little width relative to the other two. And then as you start to increase the historical volatility, what do you start to see? Less amplitude and more width. And then as you move to the 35 historical vault, you ultimately get even more width and less amplitude. And I'll give you hint. As you get up to basically infinity in the volatility space, these start to look like straight lines. they lose their curvature. Because if you theoretically take this to its extreme and say something is moving on an infinite instead of 15 or 25 or 35, you take an eight and you turn it sideways and you say this is moving on an infinite all of sudden the actual price distribution starts to look flat. The reason why is because as you get to infinite volatility, all of the price outcomes start to become equally as likely. And when something is equally as likely as something else, it doesn't have any amplitude on where it falls as far as how often or how far away from the mean it is. They're all the same. It becomes straight line. This concept is actually really tied into the idea of implied volatility. It's also tied into delta, gamma, and many of the Greeks that are associated with how we model options. want you to think about this as theoretical concept. It's not easy to always grasp for many people.