Is there a mathematical formula to determine a stock's price at a given time?
A stock market is just that, a market place where buyers and sellers come together to buy and sell shares in companies listed on that stock market. There is no global stock price, the price relates to the last price a stock was traded at on a particular stock market. However, a company can be listed on more than one stock exchange. For example, some Australian companies are listed both on the Australian Stock Exchange (ASX) and the NYSE, and they usually trade at different prices on the different exchanges. Also, there is no formula to determine a stock price. In your example where C wants to buy at 110 and B wants to sell at 120, there will be no sale until one or both of them decides to change their bid or offer to match the opposite, or until new buyers and/or sellers come into the market closing the gap between the buy and sell prices and creating more liquidity. It is all to do with supply and demand and peoples' emotions. "The fallacy in your question is in this statement: ""The formulas must exist, because prices can be followed real time."" What you see are snapshots of the current status of the stock, what was the last price a stock was traded at, what is the volume, is the price going up or down.  People who buy and hold their stock look at the status every few days or even every few months. Day traders look at the status every second of the trading day.  The math/formula comes in when people try to predict where the stock is going based on the squiggles in the line. These squiggles move based on how other people react to the squiggles.  The big movements occur when big pieces of news make large movements in the price. Company X announces the release of the key product will be delayed by a year; the founder is stepping down; the government just doubled the order for a new weapon system; the insiders are selling all the shares they can. There are no formulas to determine the correct price, only formulas that try to predict where the price may go." I found the answer. It was the Stock Ticker that I was looking for. So, if I understand correctly the price at certain moment is the price of the latest sale and can be used to get a global picture of what certain stock is worth at that certain instant. Try to find the P/E ratio of the Company and then Multiply it with last E.P.S, this calculation gives the Fundamental Value of the share, anything higher than this Value is not acceptable and Vice versa.
There's a key assumption made in the calculation of theta: that the future price movement of the underlying is a random walk. The amount of life left in the option times the volatility of the underlying creates a probability distribution of the price of the underlying at expiration. At any given price point, you can calculate the theta of the option. The at-the-money values are the most likely. The way-in-or-way-out-of-the-money values are much less likely. Theta is constructed mathematically to decay linearly over time. So the strikes with the most theta lose the most theta each day. If you are looking for a more intuitive answer, the OTM calls have less theta than the ATM calls because, while they are both 100% time value, the OTM calls cost much less. So it's 100% of a smaller number. Remember decay is linear. I don't have all the answers. On a illiquid stock, such situations do arise and there are specific mechanisms used by exchanges to match the order. It is generally not advisable to use market order on illiquid stock. There are lots of different variations here. I guess this comes down to specifications for individual exchanges, but I'm wondering if there's a standard here or a way to approach it from basic rules that clears up all these situations. There are quite a few variations and different treatments. Market order that are placed when the market is closed or just around market opening are traded at Market Open price that each exchange has a formulae to calculate. In the process Market Buy are matched to Market Sell at the Exchange calculated price. Not all order get matched and there could be spill over's. These are then matched to limit orders. Is this determined based on which sell order came first, or based on which would result in the best deal for the incoming buyer? Generally Market orders have highest priority of execution. Hopefully, before you invested in this stock, you evaluated the company.  You looked at the financial information about the company and where the company was headed, and evaluated whether the stock was undervalued or overvalued.  Hopefully, you determined that the stock was undervalued at the time you bought it. The thing to do now is to reevaluate the stock.  Do you think the stock is overvalued or undervalued right now?  If you didn't own it, would you buy it today?  Instead of looking at the past performance of the stock, you want to try to determine which direction the stock will go from today.  If you wouldn't buy it today at it's current price, then you should sell. If you have no idea how to do this evaluation, neither do I.  For me, with the investing knowledge I have right now, investing in an individual stock would be way too risky.  If you don't know how to evaluate a stock and determine if it is a good buy or not, then you should stay away from individual stocks and instead invest in stock mutual funds, which lower the risk by diversifying over lots of stocks. "Some thoughts on your questions in order, Duration: You might want to look at the longest-dated option (often a ""LEAP""), for a couple reasons. One is that transaction costs (spread plus commission, especially spread) are killer on options, so a longer option means fewer transactions, since you don't have to keep rolling the option. Two is that any fundamentals-based views on stocks might tend to require 3-5 years to (relatively) reliably work out, so if you're a fundamental investor, a 3-6 month option isn't great. Over 3-6 months, momentum, short-term news, short squeezes, etc. can often dominate fundamentals in determining the price. One exception is if you just want to hedge a short-term event, such as a pending announcement on drug approval or something, and then you would buy the shortest option that still expires after the event; but options are usually super-expensive when they span an event like this. Strike: Strike price on a long option can be thought of as a tradeoff between the max loss and minimizing ""insurance costs."" That is, if you buy a deeply in-the-money put or call, the time value will be minimal and thus you aren't paying so much for ""insurance,"" but you may have 1/3 or 1/2 of the value of the underlying tied up in the option and subject to loss. If you buy a put or call ""at the money,"" then you might have only say 10% of the value of the underlying tied up in the option and subject to loss, but almost the whole 10% may be time value (insurance cost), so you are losing 10% if the underlying stock price stays flat. I think of the deep in-the-money options as similar to buying stocks on margin (but the ""implied"" interest costs may be less than consumer margin borrowing rates, and for long options you can't get a margin call). The at-the-money options are more like buying insurance, and it's expensive. The commissions and spreads add significant cost, on top of the natural time value cost of the option. The annual costs would generally exceed the long-run average return on a diversified stock fund, which is daunting. Undervalued/overvalued options, pt. 1: First thing is to be sure the options prices on a given underlying make sense at all; there are things that ""should"" hold, for example a synthetic long or short should match up to an actual long or short. These kinds of rules can break, for example on LinkedIn (LNKD) after its IPO, when shorting was not permitted, the synthetic long was quite a bit cheaper than a real long. Usually though this happens because the arbitrage is not practical. For example on LNKD, the shares to short weren't really available, so people doing synthetic shorts with options were driving up the price of the synthetic short and down the price of the synthetic long. If you did actually want to be long the stock, then the synthetic long was a great deal. However, a riskless arbitrage (buy synthetic long, short the stock) was not possible, and that's why the prices were messed up. Another basic relationship that should hold is put-call parity: http://en.wikipedia.org/wiki/Put%E2%80%93call_parity Undervalued/overvalued options, pt. 2: Assuming the relationship to the underlying is sane (synthetic positions equivalent to actual positions) then the valuation of the option could focus on volatility. That is, the time value of the option implies the stock will move a certain amount. If the time value is high and you think the stock won't move much, you might short the option, while if the time value is low and you think the stock will move a lot, you might buy the option. You can get implied volatility from your broker perhaps, or Morningstar.com for example has a bunch of data on option prices and the implied components of the price model. I don't know how useful this really is though. The spreads on options are so wide that making money on predicting volatility better than the market is pretty darn hard. That is, the spread probably exceeds the amount of the mispricing. The price of the underlying is more important to the value of an option than the assumed volatility. How many contracts: Each contract is 100 shares, so you just match that up. If you want to hedge 100 shares, buy one contract. To get the notional value of the underlying multiply by 100. So say you buy a call for $30, and the stock is trading at $100, then you have a call on 100 shares which are currently priced at $10,000 and the option will cost $30*100=3,000. You are leveraged about 3 to 1. (This points to an issue with options for individual investors, which is that one contract is a pretty large notional value relative to most portfolios.)" "Company values (and thus stock prices) rely on a much larger time frame than ""a weekend"".  First, markets are not efficient enough to know what a companies sales were over the past 2-3 days (many companies do not even know that for several weeks).  They look at performance over quarters and years to determine the ""value"" of a company.  They also look forward, not backwards to determine value.  Prior performance only gives a hint of what future performance may be.  If a company shut its doors over a weekend and did no sales, it still would have value based on its future ability to earn profits." "When you buy a stock, you're really paying for a STREAM of earnings, from now till whenever. The job of an investor is to figure out how large that stream will be in the future. But if the stock price were the same as ""earnings"" (for one year), it would mean that you would get all future earnings for ""free."" That's not likely to happen unless 1) the company is in liquidation,"" meaning ""no future"" and 2) it earned ALL of the money it ever earned in the past year, meaning ""no past."" If there are likely to be any earnings in the future, you will have to pay for those future earnings, over and above what was earned in the most recent year." "(Value of shares+Dividends received)/(Initial investment) would be the typical formula though this is more of a percentage where 1 would indicate that you broke even, assuming no inflation to be factored. No, you don't have to estimate the share price based on revenues as I would question how well did anyone estimate what kind of revenues Facebook, Apple, or Google have had and will have. To estimate the value of shares, I'd likely consider what does my investment strategy use as metrics: Is it discounted cash flow, is it based on earnings, is it something else? There are many ways to determine what a stock ""should be worth"" that depending on what you want to believe there are more than a few ways one could go." The equation you show is correct, you've simply pointed out that you understand that you buy at the 'ask' price, and later sell at the 'bid.' There is no bid/ask on the S&P, as you can't trade it directly.  You have a few alternatives, however - you can trade SPY, the (most well known) S&P ETF whose price reflects 1/10 the value or VOO (Vanguard's offering) as well as others. Each of these ETFs gives you a bid/ask during market hours. They trade like a stock, have shares that are reasonably priced, and are optionable.  To trade the index itself, you need to trade the futures. S&P 500 Futures and Options is the CME Group's brief info guide on standard and mini contracts.  Welcome to SE.