I think I'm with you so far. We have variance where moves are random, and volatility which tries to measure that randomness right? How do we apply that to our trading and ACD?Are we trying to predict future volatility and if we are, is looking at past vol the best way to do it? Reading over that post the part that really has me confused is the "let me predict variance" comment, how do you predict something that for the most part is random?
I would just stick with the concept of volatility. ok the rest of your questions, mmmm there are libraries filled with this topic. Markets are priced on what is commonly called "random walk" we don't really know if stock x is going up or down, hence the random walk or price movement. When I get a minute I will show you using FIT (fitbit ) which just came out.
ok lets take a look at FIT ipo of fitbit. The stock just started trading and options just started traded so how do you know what the volatility is? simple the market gives it you. It is an input into the price of an option. I think a lot of the confusion regarding randomness is overstated. FIT doesn't trade 1, 5000, 13, 2046, etc. Its possible that FIT gets bought over the weekend for $100 a share but the actual probability of this happening by virtue of option pricing is almost nil. Regarding your comment, "how do you predict something that is for the most part random" its a great question. The market has to come up with pricing of events on a daily basis and the prices are wrong a lot for various reasons, news shocks, takeovers, bad/good earnings exceeding expectations, macro shocks. You can use option delta as a proxy for an event happening. What is the probability that FIT will trade 44 by November of this year. The option delta on the call is .29 so you can say there is about a 29% chance of this happening. The beauty is you could bet either way on this event. Maybe Jaqen H'qar aka Mav74 can add some wisdom here.
Let me try to explain it this way. A levels are based on volatility. But the volatility levels we use are backward looking. The A levels capture the mean of a specific period of historical volatility whether it be a day, a week, a month or a quarter. So there is some chance that the forward period (day, week, month, qtr) will be different then the previous period. Usually volatility is pretty constant per product but volatility transitions from low to high and high to low. It also has spikes. All these things lead to error. All we can do is estimate forward vol based on historical vol and put that vol into proper context. They are simply benchmarks. Not hard levels. The other idea that is important here is the concept of path dependency. It's assumed in finance that variance (or volatility) is normally distributed or random. But what if it trends? This is where number lines come in. The number lines are giving us a score card to evaluate a product's likelihood to trend in a given direction. In other words, the number lines minimize the tracking error of variance. This is why the two need to be used together.
In finance, sigma or sigma^2 is usually how we denote risk. Let me respond to these theories and give you only my opinion (which is often wrong). 1) Markets do NOT seek risk. Markets are risk averse. In economics a great deal of studying has gone into risk aversion theory (google it). One of the subsets of this theory is something known as "prospect theory". This theory states that if I offer the avg person a chance to receive $10 for sure or a 50/50 chance to either win $20 or $0 they almost always choose the $10 even though the expected value of the second bet is exactly the same ($10). We usually choose the "safe" bet. Now, say this same person has lost $10 and we offer them a 50/50 proposition to make $10 or lose $10. The expected value is zero but that same person will usually take this bet. Suddenly when faced with losses, we are willing to take on risk. Prospect theory is amazing at explaining the psychology of markets and also why most traders fail. Back to your number one, markets seek to maximize their return with the least amount of risk. Or another way, given a certain desired return, we want to pick the least riskiest path to achieve that return. 2) Value is in the eye of the beholder. What makes the word value tricky is time. Value has a different price in different periods of time and that value has to be discounted over time t by the appropriate risk factor taking into account the total opportunity cost. There is a lot of math here, I'll leave it out. LOL. 3) Hedging has to do with prospect theory again. So risk aversion theory is how and why insurance exists in the marketplace. It's been proven mathematically that consumers are willing to "overpay" for a policy to gain the positive utility that comes from having insurance. This explains how insurance companies make their profits. They can't drastically over price, but you can solve for the optimal level of what a consumer is "willing" to overpay and that is the level the market chooses. So one's willingness to hedge is determined by the utility they require to hold a certain amount of risk.
Noise is a part of volatility. Think of volatility as broken into two parts. One is the movement you "want". The other part is the movement you "don't want". Time is one way we deal with the movement we don't want. By our definition, if we have an adverse movement, we use time to confirm it. If the movement is purely noise, it should follow a stochastic process. If it's not noise, it won't. Think of time as an error correction model. When our models error, time should offset that error.
This is correct. The only difference between the two is standard deviation is measured in the same units as the determining variable. Variance is not. So we often solve for variance and then take the sq root so we are back in our original units of measurement.
Volatility is a broad term we use to put all the various measurements under. It simplifies the nomenclature. So variance is under the volatility tent. But it's more specific. Implied volatility of options uses the standard deviation of annual movement. It's forward looking. In other words, it's what the market is "expecting" the forward movement to be. Historical volatility is what we actually observed in the past.