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.
What if there is only one trading day and the volume is smaller than   the open interest on that one trading day. This is assuming there is   no open interest before that day? I pulled this from a comment. This can't happen. We have zero open interest on day one. On day 2, I buy 10 contracts. Volume is 10 and now open interest is also 10. Tomorrow, if I don't sell, open interest starts at 10 and will rise by whatever new contracts are traded.   This is an example. I removed the stock name. This happens to be the Jan'17 expiration. The 10 contract traded on the $3 strike happen to be mine. You can see how open interest is cumulative, representing all outstanding contracts. It's obvious to me the shares traded as high as $5 at some point which created the interest (i.e. the desire) to trade this strike. Most activity tends to occur near the current price. I understand that ITM have little time value, so they will have small time decay(theta), but why OTM has a lesser theta than ATM? The Time value represents uncertainty.  That uncertainty decreases the farther away from ATM you get (in either direction).  At-the-money, there is roughly a 50% chance that the option expires worthless. As you get deeper in-the-money, the change that is expires worthless decreases, so there is less uncertainty (there is more certainty that the option will pay off).  As you go deeper OTM, the probability that the option expires worthless increases, so there is also less uncertainty. At the TTM decreases, the uncertainty (theta) decreases as well, since there is less time for the option to cross the strike from either direction.  Similarly, as volatility decreases, theta decreases, since low-volatility stocks have a less change of crossing the strike. You are asking 'what if', do you have some anticipated answers? Having volume smaller than open interest is the norm. As far as I can tell, having only one trading day and no previous open interest only affects someone trying to sell a contract they are holding.  Meaning that if you only have one day to sell your contract then you need to offer it 'at market' or at the bid price (or even lower than the bid price). If you cannot sell your contract then you have to let it expire worthless or you have to exercise it. Those are your three options: let it expire, sell it (perhaps at a loss), and exercise it.  Edit: be careful about holding an in-the-money option. Many brokers will automatically exercise an in-the-money contract if you hold it till expiration date. Are you geometrically linking the spot rates for each spot period over of the next year? I.e. are you looking at the spot strip, or just taking today's spot rate and annualizing it?  If you are looking at the spot strip, then a YTM for a bond maturing in one year should equal the return from investing in rolling one month spot rates for the next year - more or less. If this variance is large, then there is scope for arbitrage. If we were to observe some call price (e.g., 15), and then derived implied volatilities from the BS formula depending on different strike prices but fixed maturity (i.e, maturity = 1, and strike goes from 80 to 140??), would we then see a smile? Yes. Market prices for various strikes and a given maturity often have higher implied volatilities from the Black-Scholes model away from at-the-money.   It is not accounted for in the Black-Scholes model in the fact that volatility is not a function of strike, so volatility is assumed to be constant across strikes, but the market does not price options that way. I don't know that a quantitative theory has ever been proven; I've always just assumed that people are willing to pay slightly more for options deep in or out of the money based on their strategy, but I have no evidence to base that theory on. "As I understand it, Implied Volatility represents the expected gyrations of an options contract over it's lifetime.  No, it represents that expected movement of the underlying stock, not the option itself.  Yes, the value of the option will move roughly in the same direction the value of the stock, but that's not what IV is measuring. I even tried staring at the math behind the Options pricing model to see if that could make more sense for me but that didn't help. That formula is correct for the Black-Scholes model - and it is not possible (or at least no one has done it yet) to solve for s to create a closed-form equation for implied volatility.  What most systems do to calculate implied volatility is plug in different values of s (standard deviation) until a value for the option is found that matches the quoted market value ($12.00 in this example).  That's why it's called ""implied"" volatility - the value is implied from market prices, not calculated directly. The thing that sticks out to me is that the ""last"" quoted price of $12 is outside of the bid-ask spread of $9.20 to $10.40, which tells me that the underlying stock has dropped significantly since the last actual trade.   If the Implied Vol is calculated based on the last executed trade, then whatever algorithm they used to solve for a volatility that match that price couldn't find a solution, which then choose to show as a 0% volatility.   In reality, the volatility is somewhere between the two neighbors of 56% and 97%, but with such a short time until expiry, there should be very little chance of the stock dropping below $27.50, and the value of the option should be somewhere around its intrinsic value (strike - stock price) of $9.18." It really varies based on the stock (volatility is the main determining factor), and whether you are talking about temporary or permanent price impact,  how long you are trading, etc. The below paper fits a functional form to a set of Citigroup data and estimates for a 10% dtv trade in a large cap like IBM the price would move on the order of 30bps. Presumably smallcaps would be more expensive. Their estimate seems a bit low to me but I'm more familiar with futures, so maybe it's not unreasonable  https://www.google.com/url?sa=t&amp;source=web&amp;rct=j&amp;ei=JjDsU_L-CI33yQSh4oKQDA&amp;url=http://www.math.nyu.edu/~almgren/papers/costestim.pdf&amp;cd=3&amp;ved=0CCQQFjAC&amp;usg=AFQjCNGN6LmPb9sHR5dljcJJ2rV4bNE4Jg&amp;sig2=WYhcCUFr8WcRfetA24wXLg Out of the money options often have the biggest changes in value, when the stock moves upward. This person could also gain, by the implied (underlying) volatility of the stock rising if it moves erratically to either side. Still seems to be a very risky game, given only 4 days to expiry. Volatility is a shitty metric and is sample dependent, What is more interesting is point recurrence, i.e. how many times has a certain point been touched in x time, you can make good day trading strategies off point recurrence (relative that is). It depends completely on the current order book for that security.  There is literally no telling how that buy order would move the price of a stock in general. No, it means what it says. Prices change, hence price of the derivative can go down even if the price of the underlying doesn't change (e.g. theta decay in options). I have an example of a trade I made some time ago.  By entering the position as a covered call, I was out of pocket $5.10, and if the stock traded flat, i.e. closed at the same $7.10 16 months hence, I was up 39% or nearly 30%/yr. As compared to the stock holder, if the stock fell 28%, I'd still break even, vs his loss of 28%. Last, if the stock shot up, I'd get 7.50/5.10 or a 47% return, vs the shareholder who would need a price of $10.44 to reflect that return. Of course, a huge jump in the shares, say to $15, would benefit the option buyer, and I would have left money on the table. But this didn't happen. The stock was at $8 at expiration, and I got my 47% return. The option buyer got 50 cents for his $2 bet.  Note, the $2 option price reflected a very high implied volatility. Robert is right saying that options' prices are affected by implied volatility but is wrong saying that you have to look at the VIX index. For two reasons:  1) the VIX index is for S&P500 options only. If you are trading other options, it is less useful. 2) if you are trading an option that is not at the money, your implied volatility may be very different (and follow a different dynamics) that the VIX index.  So please look at the right implied volatility.  In terms of strategy, I don't think that not doing anything is a good strategy. I accept any point of view but you should consider that option traders should be able to adjust positions depending on market view.  So you are long 1 call, suppose strike 10. Suppose the underlying price at the time of entry was 10 (so the call was at the money). Now it's 9.  1) you still have a bullish view: buy 1 call strike 9 and sell 2 calls strike 10. This way you have a bull call spread with much higher probability of leading to profit. You are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations).  2) you become bearish: you can sell 1 call strike 9. This way you end up with a bear call spread. Again, you are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations). 3) you become neutral: buy 1 call strike 8 and sell 2 calls strike 9. This way you end up with a call butterfly. You are almost delta neutral and you can wait until your view becomes clear enough to become directional. At that point you can modify the butterfly to make it directional.  These are just some opportunities you have. There is no reason for you to wait. Options are eroding contracts and you must be fast and adjust the position before time starts eroding your capital at risk.  It's true that buying a call doesn't make you loose more than the premium you paid, but it's better to reduce this premium further with some adjustment. Isn't it?  Hope that helps. :) It depends to some extent on how you interpret the situation, so I think this is the general idea. Say you purchase one share at $50, and soon after, the price moves up, say, to $55. You now have an unrealized profit of $5. Now, you can either sell and realize that profit, or hold on to the position, expecting a further price appreciation. In either case, you will consider the price change from this traded price, which is $55, and not the price you actually bought at. Hence, if the price fell to $52 in the next trade, you have a loss of $3 on your previous profit of $5. This (even though your net P&L is calculated from the initial purchase price of $50), allows you to think in terms of your positions at the latest known prices. This is similar to a Markov process, in the sense that it doesn't matter which route the stock price (and your position's P&L) took to get to the current point; your decision should be based on the current/latest price level. The credit scale is deceptive, it goes: AAA, AA, A, BBB, BBB-, BB+, BB, B, CCC, CC, C, D. In reality it should be A,B,C,D,E, F, G,H, I, etc. The current scale does not reflect with clarity the ranking of risks and ratings. AA is much worse than AAA, but the uncertainty involved can be scary. Check out these corporate and sovereign debt credit ratings.