How is options implied volatility for a stock determined?
"There are a few different ""kinds"" of implied volatility. They are all based on the IVs obtained from the option pricing model you use. (1) Basically, given a few different values (current stock price, time until expiration, right of option, exercise style, strike of the option, interest rates, dividends, etc), you can obtain the IV for a given option price. If you look at the bid of an option, you can calculate the IV for that bid. If you look at the ask, there's a different IV for the ask. You can then look at the mid price, then you have a different IV, and so on and so on. And that's for each strike, in each expiration cycle! So you have a ton of different IVs. (2) In many option trading platforms, you'll see another kind of IV: the IV for each specific expiration cycle. That's calculated based on some of the IVs I mentioned on topic (1). Some kind of aggregation (more on this later). (3) Finally, people often talk about ""the IV of stock XYZ"". That's, again, an aggregation calculated from many of the IVs mentioned on topic (1). Now, your question seems to be: which IVs, from which options, from which months, with which weight, are part of the expiration cycle IV or for the IV of the stock itself? It really depends on the trading platform you are talking about. But very frequently, people will use a calculation similar to how the CBOE calculates the VIX. Basically, the VIX is just like the IV described on topic (3) above, but specifically for SPX, the S&P 500 index. The very detailed procedure and formulas to calculate the VIX (ie, IV of SPX) is described here: http://cfe.cboe.com/education/vixprimer/about.aspx If you apply the same (or a similar) methodology to other stocks, you'll get what you could call ""the IV of stock XYZ""."
While open interest usually correlates to volume, the mark of liquidity is the bid ask spread. Even when trading options with spreads as large as an ask 2x the bid, a more realistic price that traders are willing to accept lies somewhere in the middle. Any option can easily be exited at intrinsic value: underlying price - exercise price for calls, exercise price - underlying price for puts.  For illiquid options, this will be the best price obtained.  For longer term options, something closer to the theoretical price is still possible. If an underlying is extremely liquid, yet the options aren't quite then options traders will be much more ready to trade at the theoretical price. For exiting illiquid options, small, < 4 contracts, and infrequent, > 30 minute intervals, orders are more likely to be filled closer to the theoretical price; however, if one's sells are the only trades, traders on the other side will take note and accept ever lowering implied volatilities. With knowledge of what traders will accept, it is always more optimal to trade out of options rather than exercise because of the added costs and uncertainty involved with exercising and liquidating. "One thing I would like to clear up here is that Black Scholes is just a model that makes some assumptions about the dynamics of the underlying + a few other things and with some rather complicated math, out pops the Black Scholes formula. Black Scholes gives you the ""real"" price under the assumptions of the model. Your definition of what a ""real"" price entails will depend on what assumptions you make. With that being said, Black Scholes is popular for pricing European options because of the simplicity and speed of using an analytic formula as opposed to having a more complex model that can only be evaluated using a numerical method, as DumbCoder mentioned (should note that, for many other types of derivative contracts, e.g. American or Bermudan style exercise, the Black Scholes analytic formula is not appropriate). The other important thing to note here is that the market does not necessarily need to agree with the assumptions made in the Black Scholes model (and they most certainly do not) to use it. If you look at implied vols for a set of options which have the same expiration but differing strike prices, you may find that the implied vols for each contract differ and this information is telling you to what degree the traders in the market for those contracts disagree with the lognormal distribution assumption made by Black Scholes. Implied vol is generally the thing to look at when determining cheapness/expensiveness of an option contract. With all that being said, what I'm assuming you are interested in is either called a ""delta-gamma approximation"" or more generally ""Greek/sensitivities based profit and loss attribution"" (in case you wanted to Google some more about it). Here is an example that is relevant to your question. Let's say we had the following European call contract: Popping this in to BS formula gives you a premium of $4.01, delta of 0.3891 and gamma of 0.0217. Let's say you bought it, and the price of the stock immediately moves to 55 and nothing else changes, re-evaluating with the BS formula gives ~6.23. Whereas using a delta-gamma approximation gives: The actual math doesn't work out exactly and that is due to the fact that there are higher order Greeks than gamma but as you can see here clearly they do not have much of an impact considering a 10% move in the underlying is almost entirely explained by delta and gamma." "Currently, when ""implied volatility"" is spoken, the Black-Scholes-Merton model is implied.  This model has been shown to be deficient, thus the Variance Gamma Model should be used. However, as nearly no one uses VG, it can be assumed that BS is still being implied. The BS formula has multiple variables.  Some are external to the underlying in question.  The rest are internal. When all but one variable is known or assumed, the last variable can be calculated, so if one has the price of the underlying and all else except the volatility, the volatility can be calculated thus implied. If one selects an implied volatility, and all variables except the underlying price is known, the underlying price can be calculated. For the present, one uses the current price of the underlying to calculate the implied volatility.  For future option prices, one assumes an implied volatility at a later date to calculate a possible price. For prices not at the money, the BS model is extremely imprecise.  The VG model can better determine a potential future price." S&P/TSX 60 VIX (CAD) is an equation and as the implied volatility of two close to the money TSX 60 options change, the output changes. This is why the intra-day price fluctuates on a graph like a traded product.  Although VIXC can't be traded, it can still be used as an important signal for traders. The excerpt is from slide 12, more information can be found here. https://www.m-x.ca/f_publications_en/vixc_presentation_en.pdf Futures (stage 2) Options, ETFs, OTC Products (stage 3) have not been implemented. In India, in the money options get exercised automatically at the end of the day and is settled at T+1(Where T is expiry day). This means, the clearing house  takes the closing price of the underlying security while calculating the amount that needs to be credited/debited to its members. Source: - http://www.nseindia.com/products/content/derivatives/equities/settlement_mechanism.htm I agree that high volatility just means the underlying stock price fluctuates more, and it does not imply if the stock is going up or down. But a high volatility in the price of an underlying also means that there is a higher chance that the underlying price could reach extreme prices (albeit in either direction). However, if you purchased a call option then if the underlying price reached an extremely high value, then you will be richly rewarded. But if the underlying price reached an extremely low value, you won't lose any more than the initial premium that you paid. There is no additional risk on your side, it's capped to the premium that you paid for the call option. It's this asymmetric outcome (Heads - I win, Tails - I don't lose) combined with high volatility that means that call options will increase in value when the underlying price becomes more volatile. If the optionality wasn't there then the price wouldn't be related to the volatility of the underlying. But that would be called a Future or a Forward :-) "Currently, when ""implied volatility"" is spoken, the Black-Scholes-Merton model is implied.  This model has been shown to be deficient, thus the Variance Gamma Model should be used. However, as nearly no one uses VG, it can be assumed that BS is still being implied. The BS formula has multiple variables.  Some are external to the underlying in question.  The rest are internal. When all but one variable is known or assumed, the last variable can be calculated, so if one has the price of the underlying and all else except the volatility, the volatility can be calculated thus implied. If one selects an implied volatility, and all variables except the underlying price is known, the underlying price can be calculated. For the present, one uses the current price of the underlying to calculate the implied volatility.  For future option prices, one assumes an implied volatility at a later date to calculate a possible price. For prices not at the money, the BS model is extremely imprecise.  The VG model can better determine a potential future price." Who determines company value at IPO? The Owners based on the advice from Lead Bankers and other Independent auditors who would determine the value of the company at the time of listing. At times instead of determining a fixed price a range is given [lower side and higher side]. The Market participants [FI / Institutional Investor Segments] then decide the price by bidding at an amount. There are multiple aspects in play that help stabalize the IPO and roles of various parties. A quick read of question with IPO tag is recommended Edits: Generally at a very broad level, one of the key purpose of the IPO is to either encash Owner equity [Owner wants some profits immediately] or Raise additional Capital. More often it is a mix of both. If the price is too low, one loose out on getting the true value, this would go to someone else. If the price is too high, then it may not attract enough buyers or even there are buyers, there is substantial -ve sentiment. This is not good for the company. Read the question From Facebook's perspective, was the fall in price after IPO actually an indication that it went well?  This puts determining the price of IPO more in the realm of art than science. There are various mechanism [Lead bankers, Institutional Investors, Underwriters] the a company would put in place to ensure the IPO is success and that itself would moderate the price to realistic level. More often the price is kept slightly lower to create a positive buzz about the stock.