What is the fair value of a stock given the bid and ask prices? Is there such a relationship?
None of the above. The fair value is a term used to describe an analytical result of projecting the company's future dividends and profits into a present value.  Such estimates are published by the likes of Morningstar, S&P and Value Line.  It is quite common for a stock to trade well above or below such estimated fair values. Fair value can mean many different things depending on the context. And it has nothing to do with the price at which your market order would be executed. For example if you buy market, you could get executed below 101 if there are hidden orders, at 101 if that sell order is large enough and it is still there when your order reaches the market, or at a higher price otherwise. "If you need to show that the sale/purchase was at FMV, then showing that you made a trade on a public exchange with an unrelated counterpart is enough to establish FMV. However, this is only one of the possible ""fair market value"" definitions. This is usually used to determine basis or value for tax purposes. For valuation purposes or general accounting, one specific trade is not enough to establish FMV, and much more research is required."
"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""." You can always trade at bid or ask price (depending if you are selling or buying). Market price is the price the last transaction was executed at so you may not be able to get that. If your order is large then you may not even be able to get bid/ask but should look at the depth of the order book (ie what prices are other market participants asking for and what is the size of their order). Usually only fast traders will trade at bid/ask, those who believe the price move is imminent. If you are a long term trader you can often get better than bid or ask by placing a limit order and waiting until a market participant takes your offer. The price of a share has two components: Bid: The highest price that someone who wants to buy shares is willing to pay for them. Ask: The lowest price that someone who has a share is willing to sell it for. The ask is always higher than the bid, since if they were equal the buyer and seller would have a deal, make a transaction, and that repeats until they are not equal. For stock with high volume, there is usually a very small difference between the bid and ask, but a stock with lower volume could have a major difference. When you say that the share price is $100, that could mean different things. You could be talking about the price that the shares sold for in the most recent transaction (and that might not even be between the current bid and ask), or you could be talking about any of the bid, the ask, or some value in between them. If you have shares that you are interested in selling, then the bid is what you could immediately sell a share for. If you sell a share for $100, that means someone was willing to pay you $100 for it. If after buying it, they still want to buy more for $100 each, or someone else does, then the bid is still $100, and you haven't changed the price. If no one else is willing to pay more than $90 for a share, then the price would drop to $90 next time a transaction takes place and thats what you would be able to immediately sell the next share for. The situation you're proposing is an over-simplification that wouldn't occur in practice. Orders occur in a sequence over time. Time is an important part of the order matching process. Orders are not processed in parallel; otherwise, the problem of fairness, already heavily regulated, would become even more complex. First, crossed and locked markets are forbidden by regulators.  Crossed orders are where one exchange has a higher bid than another's ask, or a lower ask than another's bid.  A locked market is where a bid on one exchange is equal to the ask on another.  HFTs would be able to make these markets because of the gap between exchange fees. Since these are forbidden, and handling orders in parallel would ensure that a crossed or locked market would occur, orders are serialized (queued up), processed in order of price-time priority. So, the first to cross the market will be filled with the best oldest opposing order. Regulators believe crossed or locked markets are unfair.  They would however eliminate the bid ask spread for many large securities thus the bid-ask cost to the holder. "In the case of an ""initial public offering"", the brokers underwriting the share issue will look at the current earnings being generated by the company and compare these to those of other competitor companies already listed in the stock market.  For example, if a new telephone company is undertaking an initial public offering, then the share price of those telephone companies which are already traded on the stock market will serve as a reference for how much investors will be willing to pay for the new company's shares.  If investors are willing to pay 15 times earnings for telecom shares, then this will be the benchmark used in determining the new share price. In addition, comparative growth prospects will be taken into account.  Finally, the underwriter will want to see a successful sale, so they will tend to ""slightly under price"" the new shares in order to make them attractive. None of this is an exact science and we often see shares trading at a large premium to the initial offer price during the first few days of trading.  More often that not, prices then settle down to something closer to the offer price.  The initial price spike is usually the result of high demand for the shares by investors who believe that past examples of a price spike will repeat with this initial public offering.  There will also usually be high demand for the new shares from funds that specialise in shares of the type being issued. In the case of a ""rights issue"", where an existing publicly traded company wishes to raise capital by issuing new shares, the company will price the new shares at a significant discount to the current market price.  The new shares will be initially offered to existing shares holders and the discounted price is intended to encourage the existing shareholders to exercise their ""rights"" since the new shares may have the effect of diluting the value of their shares.  Any shares which are not purchased by existing share holder will then be offered for sale in the market." I was merely trying to be helpful - Conceptually, you have dump this idea that something is skewed. It isn't. Firm A sold for $500 (equity value aka purchase price to shareholders) + debt (zero) - cash (50) for 450.  Enterprise value is the cash free, debt free sale price.  The implied ev multiple is 4.5x on A - that is the answer. The other business sold for a higher multiple of 5x.  If you would pile on more cash onto A, the purchase price would increase, but the EV wouldn't.      The idea is to think hard about the difference between equity value and enterprise value when examining a transaction. A stock is only worth what someone is willing to pay for it. If it trades different values on different days, that means someone was willing to pay a higher price OR someone was willing to sell at a lower price.  There is no rule to prevent a stock from trading at $10 and then $100 the very next trade... or $1 the very next trade. (Though exchanges or regulators may halt trading, cancel trades, or impose limits on large price movements as they deem necessary, but this is beside the point I'm trying to illustrate). Asking what happens from the close of one day to the open of the next is like asking what happens from one trade to the next trade... someone simply decided to sell or pay a different price.  Nothing needs to have happened in between. This is a tough question SFun28.  Let's try and debug the metric. First, let's expand upon the notion share price is determined in an efficient market where prospective buyers and sellers have access to info on an enterprises' cash balance and they may weigh that into their decision making.  Therefore, a desirable/undesirable cash balance may raise or lower the share price, to what extent, we do not know.   We must ask How significant is cash/debt balance in determining the market price of a stock?   As you noted, we have limited info, which may decrease the weight of these account balances in our decision process. Using a materiality level of 5% of net income of operations, cash/debt may be immaterial or not considered by an investor. investors oftentimes interpret the same information differently (e.g. Microsoft's large cash balance may show they no longer have innovative ideas worth investing in, or they are well positioned to acquire innovative companies, or weather a contraction in the sector) My guess is a math mind would ignore the affect of account balances on the equity portion of the enterprise value calculation because it may not be a factor, or because the affect is subjective.