How much does the volatility change for a 1$ move in the underlying
The volatility measures how fast the stock moves, not how much. So you need to know the period during which that change occurred. Then the volatility naturally is higher the faster is the change.
"The blue line is illustrating the net profit or loss the investor will realise according to how the price of the underlying asset settles at expiry. The x-axis represents the underlying asset price.  The y-axis represents the profit or loss. In the first case, the investor has a ""naked put write"" position, having sold a put option.  The strike price of the put is marked as ""A"" on the x-axis.  The maximum profit possible is equal to the total premium received when the option contract was sold.  This is represented by that portion of the blue line that is horizontal and extending from the point above that point marked ""A"" on the x-axis.  This corresponds to the case that the price of the underlying asset settles at or above the strike price on the day of expiry.  If the underlying asset settles at a price less than the strike price on the day of expiry, then the option with be ""in the money"".  Therefore the net settlement value will move from a profit to a loss, depending on how far in the money the option is upon expiry.  This is represented by the diagonal line moving from above the ""A"" point on the x-axis and moving from a profit to a loss on the y-axis.  The diagonal line crosses the x-axis at the point where the underlying asset price is equal to ""A"" minus the original premium rate at which the option was written - i.e., net profit = zero.  In the second case, the investor has sold a put option with a strike price of ""B"" and purchase a put option with a strike price ""A"", where A is less than B.  Here, the reasoning is similar to the first example, however since a put option has been purchase this will limit the potential losses should the underlying asset move down strongly in value. The horizontal line above the x-axis marks the maximum profit while the horizontal line below the x-axis marks the maximum loss. Note that the horizontal line above the x-axis is closer to the x-axis that is the horizontal line below the x-axis.  This is because the maximum profit is equal to the premium received for selling the put option minus the premium payed for buying the put option at a lower strike price.  Losses are limited since any loss in excess of the strike price ""A"" plus the premium payed for the put purchased at a strike price of ""A"" is covered by the profit made on the purchased put option at a strike price of ""A""." You appear to be thinking of option writers as if they were individuals with small, nondiversified, holdings and a particular view on what the underlying is going to do.  This is not the best way to think about them. Option writers are typically large institutions with large portfolios and that provide services in all sorts of different areas. At the same time as they are writing calls on a particular stock, they are writing puts on it and options on other stocks.  They are buying and selling the underlying and all kinds of different derivatives.  They are not necessarily writing the option because they are expecting or hoping to benefit from a price move.  It's just small part of their business.  They write the option if the option price is good enough that they think they are selling it for very slightly more than it's worth.   Asking why an option writer creates a call is like asking why a grocery store keeps buying groceries from their distributors.  Don't they know the price of food may not always rise?  Sure, but their business is selling the food for slightly more than they pay for it, not speculating on what will happen to its price.  Most option writers are doing the same thing, except what they are buying and selling is sets of cash flows and risk.   As a general rule, the business model of option writers is to profit from the few cents of spread or mispricing, not from aggregate changes in the price of the underlying.  They should and often do maintain balanced portfolios so their option writing activities don't expose them to a lot of risk. Also note that there could be lots of reasons for writing options, even if you do have a particular view.  For example, perhaps the option writer thinks volatility of the underlying will decrease.  Writing a call could be part of an overall strategy that profits from this view. "So, if an out-of-the-money option (all time value) has a price P (say $3.00), and there are N days... The extrinsic value isn't solely determined by time value as your quote suggests. It's also based on volatility and demand. Here is a quote from http://www.tradingmarkets.com/options/trading-lessons/the-mystery-of-option-extrinsic-value-767484.html distinguishing between extrinsic time value and extrinsic non-time value: The time value of an option is entirely predictable. Time value premium declines at an accelerating rate, with most time decay occurring in the last one to two months before expiration. This occurs on a predictable curve. Intrinsic value is also predictable and easily followed. It is worth one point for every point the option is in the money. For example, a call with a strike of 30 has three points of intrinsic value when the current value of the underlying stock is $33 per share; and a 40 put has two points of intrinsic value when the underlying stock is worth $38. The third type of premium, extrinsic value, increases or decreases when the underlying stock changes and when the distance between current value of stock and strike of the option get closer together. As a symptom of volatility, extrinsic value may be greater for highly volatile underlying stock, and lower for less volatile stocks. Extrinsic value is the only classification of option premium that is unpredictable. The SPYs you point out probably had a volatility component affecting value. This portion is a factor of expectations or uncertainty. So an event expected to conclude prior to expiration, but of unknown outcome can cause theta to be higher than p/n. For example, a drug company is being sued and the outcome of a trial will determine whether that company pays out millions or not. The extrinsic will be higher than p/n prior to the outcome of the trial then drops after.  Of course, the most common situation where this happens is earnings. After the announcement, it's not unusual to see a dramatic drop in the extrinsic portion of options. This is why sometimes a new option trader gets angry when buying calls prior to earnings. When 'surprise' good earnings are announced as hoped, the rise is stock price is largely offset by a fall in extrinsic value giving call holders little or no gain! As for the reverse situation where theta is lower than p/n would expect? Well you can actually have negative theta meaning the extrinsic portion rises over time. (this statement is a little confusing because theta is usually described as negative, but since you describe it as a positive number, negative here means the opposite of what you'd expect).  This is a quote from ""Option Volatility & Pricing"". Keep in mind that they use 'positive' theta to mean the time value increases up over time: Is it ever possible for an option to have a positive theta such that if nothing changes the option will be worth more tomorrow than it is today? When futures options are subject to stock-type settlement, as they currently are in the United States, the carrying cost on a deeply in-the-money option, either a call or a put, can, under some circumstances, be greater than the volatility component. If this happens, and the option is European (no early exercise permitted), it will have a theoretical value less than parity (less than intrinsic value). As expiration approaches, the value of the option will slowly rise to parity. Hence, the option will have a positive theta. Sheldon Natenberg. Option Volatility & Pricing: Advanced Trading Strategies and Techniques (Kindle Locations 1521-1525). Kindle Edition." "We measure the value of gold by comparing it to other things. Sorry, but there is no better answer than that. There is no gold standard (pun intended) by which objects can be measured in value because ""value"" is a subjective term. It would be comparable to asking how funny is an object. Different objects are funny to different people. Even if we gathered all the really ""funny"" object together, there is no guaranty those objects would be funny next year - unless we all agreed they were as part of a social contract. Which is basically what we do with currency. While gold does not need a social contract in order for it to retain its value, this is only because it is has been (1) very useful and (2) rare. If either of these two factors change, the value of gold will change - which it has on several occasions. WARRING: Rant about ""Intrinsic Value"" of gold below. Gold has no ""intrinsic"" value. None whatsoever.  ""Intrinsic value"" makes just as much sense as a ""cat dog"" animal. ""Dog"" and ""cat"" are referring to two mutually exclusive animals, therefore a ""cat dog"" is a nonsensical term. Intrinsic Value: ""The actual value of a company or an asset based on an underlying perception of its true value ..."" Intrinsic value is perceived, which means it is worth whatever you, or a group of people, think it is. Intrinsic value has nothing, I repeat, absolutely nothing, to do with reality.  The most obvious example of this is the purchase of a copy-right. You are assigning an intrinsic value to a copy-right by purchasing it. However, when you purchase a copy-right you are not buying ink on a page, you are purchasing an idea. Someone's imaginings that, for all intensive purposes, doesn't even exist in reality! By definition, things that do not exist do not have ""intrinsic"" properties - because things that don't exist, don't have any natural properties at all. ""Intrinsic"" according to Websters Dictionary:  ""Belonging to the essential nature or constitution of a thing ... (the intrinsic brightness of a star)."" An intrinsic property of an object is something we know that exists because it is a natural property of that object. Suns emit light, we know this because we can measure the light coming from it. It is not subjective. ""Intrinsic Value"" by definition is the OPPOSITE of ""Intrinsic""" As you point out, the moving average is just MA(k)t = (Pt-1 + … + Pt-k )/k and is applied in technical analysis (TA) to smooth out volatile (noise) price action. If it has any logic to it, you might want to think in terms of return series (Pt - Pt-1 / Pt-1) and you could hypothesize that prices are in fact predictable and will oscillate below and above a running moving average.  Below is a link to a study on MA trading rules, published in the Journal of Finance, with the conclusion of predictive power and abnormal returns from such strategies. As with any decision made upon historical arguments, one should be aware of structural changes and or data mining.  Simple  technical trading rules and the stochastic properties of stock  returns Brock, W., J. Lakonishok and B. Le Baron, 1992, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance, 47, 1731-64. MA rules betterthan chance in US stock market, 1897-1986 I don't know whether you are new to TA or not, but a great commercial site, with plenty of computer-generated signals is FinViz. Yes, you've got it right.  The change in price is less meaningful as the instrument is further from the price of the underlying.  As the delta moves less, the gamma is much less. Gamma is to delta as acceleration is to speed.  Speed is movement relative to X, and acceleration is rate of change in speed.  Delta is movement relative to S, and gamma is the rate of change in delta. Delta changes quickly when it is around the money, which is another way of saying gamma is higher.  Delta is the change of the option price relative to the change in stock price.  If the strike price is near the market price, then the odds of being in or out of the money could appear to be changing very quickly - even going back and forth repeatedly. Gamma is the rate of change of the delta, so these sudden lurches in pricing are by definition the gamma.  This is to some extent a little mundane and even obvious.  But it's a useful heuristic for analyzing prices and movement, as well as for focusing analyst attention on different pricing aspects. You've got it right.  If delta is constant (zero 'speed' for the change in price) then gamma is zero (zero 'acceleration'). If you buy for $1 and sell $1 when the price goes to $2, you would have sold only half of your initial investment. So your investment would now be worth $2 and you sell $1 leaving $1 still in the market.  This means you would have sold half your initial investment, making a profit of $0.50 on this half of your initial investment, and having to pay CGT on this amount. based on my understanding of your query...well you need to understand ATM and ITM options. The  delta and gamma factor specifically. Usually delta of ATM is around 0.5 while ITM option is above than that say 0.6 or 0.8 or 0.9 and deep ITM is very close to 1. for every movement of 1 buck the ITM will move say 1.6, ATM 0.5 and OTM 0.3 approx Say a ABC stock price is Rs. 300 so if you check option chart you try to see which one is closer. Suppose you find strikeprice of 320 / 300 / 280. So  320 is ITM, 300 is ATM and 280 is OTM for call options. So will the delta value (e.g 0.66 / 0.55 / 0.35). So suppose if stock price rise by 7% i.e Rs. 321 then strikeprice will rise simultaneously. Say ATM CE300 is rs.10 it will start rising by 0.55 i.e. Rs.10.55. The moment the share price move from Rs.300 to Rs.320 your ATM will turn to ITM. Now the tricker part if you buy OTM and the share price rise by 15% your OTM will now become ITM and your profit will roll around 100% to 120% approx. Hope it answers your query