How does my broker (optionsXpress) calculate probabilities that the stock will hit a certain price?
"This chart concerns an option contract, not a stock. The method of analysis is to assume that the price of an option contract is normally distributed around some mean which is presumably the current price of the underlying asset. As the date of expiration of the contract gets closer the variation around the mean in the possible end price for the contract will decrease. Undoubtedly the publisher has measured typical deviations from the mean as a function of time until expiration from historical data. Based on this data, the program that computes the probability has the following inputs: (1) the mean (current asset price) (2) the time until expiration (3) the expected standard deviation based on (2) With this information the probability distribution that you see is generated (the green hump). This is a ""normal"" or Gaussian distribution. For a normal distribution the probability of a particular event is equal to the area under the curve to the right of the value line (in the example above the value chosen is 122.49). This area can be computed with the formula:  This formula is called the probability density for x, where x is the value (122.49 in the example above). Tau (T) is the reciprocal of the variance (which can be computed from the standard deviation). Mu (μ) is the mean. The main assumption such a calculation makes is that the price of the asset will not change between now and the time of expiration. Obviously that is not true in most cases because the prices of stocks and bonds constantly fluctuate. A secondary assumption is that the distribution of the option price around the mean will a normal (or Gaussian) distribution. This is obviously a crude assumption and common sense would suggest it is not the most accurate distribution. In fact, various studies have shown that the Burr Distribution is actually a more accurate model for the distribution of option contract prices." "Their algorithm may be different (and proprietary), but how I would to it is to assume that daily changes in the stock are distributed normally (meaning the probability distribution is a ""bell curve"" - the green area in your chart).  I would then calculate the average and standard deviation (volatility) of historical returns to determine the center and width of the bell curve (calibrating it to expected returns and implied volaility based on option prices), then use standard formulas for lognormal distributions to calculate the probability of the price exceeding the strike price. So there are many assumptions involved, and in the end it's just a probability, so there's no way to know if it's right or wrong - either the stock will cross the strike or it won't."
In a simple world yes, but not in the real world. Option pricing isn't that simplistic in real life. Generally option pricing uses a Monte Carlo simulation of the Black Scholes formula/binomial and then plot them nomally to decide the optimum price of the option. Primarily multiple scenarios are generated and under that specific scenario the option is priced and then a price is derived for the option in real life, using the prices which were predicted in the scenarios.  So you don't generate a single price for an option, because you have to look into the future to see how the price of the option would behave, under the real elements of the market. So what you price is an assumption that this is the most likely value under my scenarios, which I predicted into the future. Because of the market, if you price an option higher/lower than another competitor you introduce an option for arbitrage by others. So you try to be as close to the real value of the option, which your competitor also does. The more closer your option value is to the real price the better it is for all. Did you try the book from Hull ? EDIT: While pricing you generally take variables which would affect the price of your option. The more variables you take(more nearer you are to the real situation) the more realistic your price will be and you would converge on the real price faster. So simple formula is an option, but the deviations maybe large from the real value. And you would end up loosing money, most of the time. So the complicated formula is there for getting a more accurate price, not to confuse people. You can use your formula, but there will be odds stacked against you to loose money, from the onset, because you didn't consider the variables which might/would affect the price of your option. I just called options express, and apparently you need a margin account for futures and options, but you don't NEED margin to trade futures. I will have to debate the merits, but I think I may try playing with it once I build up my regular stock account. "My broker offers the following types of sell orders: I have a strategy to sell-half of my position once the accrued value has doubled.  I take into account market price, dividends, and taxes (Both LTgain and taxes on dividends).  Once the market price exceeds the magic trigger price by 10%, I enter a ""trailing stop %"" order at 10%.  Ideally what happens is that the stock keeps going up, and the trailing stop % keeps following it, and that goes on long enough that accrued dividends end up paying for the stock.  What happens in reality is that the stock goes up some, goes down some, then the order gets cancelled because the company announces dividends or something dumb like that. THEN I get into trouble trying to figure out how to re-enter the order, maintaining the unrealized gain in the history of the trailing stop order.  I screwed up and entered the wrong type of order once and sold stock I didn't want to. Lets look at an example. a number of years ago, I bought some JNJ -- a hundred shares at 62.18.  - Accumulated dividends are 2127.75  - My spreadsheet tells me the ""double price"" is 104.54, and double + 10% is 116.16.  - So a while ago, JNJ exceeded 118.23, and I entered a Trailing Stop 10% order to sell 50 shares of JNJ.  The activation price was 106.41.  - since then, the price has gone up and down...  it reached a high of 126.07, setting the activation price at 113.45.  - Then, JNJ announced a dividend, and my broker cancelled the trailing stop order.  I've re-entered a ""Stop market"" order at 113.45.  I've also entered an alert for $126.07 -- if the alert gets triggered, I'll cancel the Market Stop and enter a new trailing stop." Something like cost = a × avg_spreadb + c × volatilityd × (order_size/avg_volume)e. Different brokers have different formulas, and different trading patterns will have different coefficients. You want to buy when the stock market is at an all-time low for that day. Unfortunately, you don't know the lowest time until the end of the day, and then you, uh can't buy the stock... Now the stock market is not random, but for your case, we can say that effectively, it is. So, when should you buy the stock to hopefully get the lowest price for the day? You should wait for 37% of the day, and then buy when it is lower than it has been for all of that day. Here is a quick example (with fake data): We have 18 points, and 37% of 18 is close to 7. So we discard the first 7 points - and just remember the lowest of those 7. We bear in mind that the lowest for the first 37% was 5. Now we wait until we find a stock which is lower than 5, and we buy at that point: This system is optimal for buying the stock at the lowest price for the day. Why? We want to find the  best position to stop automatically ignoring. Why 37%? We know the answer to P(Being in position n) - it's 1/N as there are N toilets, and we can select just 1. Now, what is the chance we select them, given we're in position n? The chance of selecting any of the toilets from 0 to K is 0 - remember we're never going to buy then. So let's move on to the toilets from K+1 and onwards. If K+1 is better than all before it, we have this: But, K+1 might not be the best price from all past and future prices. Maybe K+2 is better. Let's look at K+2 For K+2 we have K/K+1, for K+3 we have K/K+2... So we have: This is a close approximation of the area under 1/x - especially as x → ∞   So 0 + 0 + ... + (K/N) x (1/K + 1/K+1 + 1/K+2 ... + 1/N-1) ≈ (K/N) x ln(N/K) and so P(K) ≈ (K/N) x ln(N/K) Now to simplify, say that x = K/N We can graph this, and find the maximum point so we know the maximum P(K) - or we can use calculus. Here's the graph:  Here's the calculus: To apply this back to your situation with the stocks, if your stock updates every 30 seconds, and is open between 09:30 and 16:00, we have 6.5 hours = 390 minutes = 780 refreshes. You should keep track of the lowest price for the first 289 refreshes, and then buy your stock on the next best price. Because x = K/N, the chance of you choosing the best price is 37%. However, the chance of you choosing better than the average stock is above 50% for the day. Remember, this method just tries to mean you don't loose money within the day - if you want to try to minimise losses within the whole trading period, you should scale this up, so you wait 37% of the trading period (e.g. 37% of 3 months) and then select. The maths is taken from Numberphile - Mathematical Way to Choose a Toilet. Finally, one way to lose money a little slower and do some good is with Kiva.org - giving loans to people is developing countries. It's like a bank account with a -1% interest - which is only 1% lower than a lot of banks, and you do some good. I have no affiliation with them. In order to see whether you can buy or sell some given quantity of a stock at the current bid price, you need a counterparty (a buyer) who is willing to buy the number of stocks you are wishing to offload. To see whether such a counterparty exists, you can look at the stock's order book, or level two feed. The order book shows all the people who have placed buy or sell orders, the price they are willing to pay, and the quantity they demand at that price. Here is the order book from earlier this morning for the British pharmaceutical company, GlaxoSmithKline PLC.  Let's start by looking at the left-hand blue part of the book, beneath the yellow strip. This is called the Buy side. The book is sorted with the highest price at the top, because this is the best price that a seller can presently obtain. If several buyers bid at the same price, then the oldest entry on the book takes precedence. You can see we have five buyers each willing to pay 1543.0 p (that's 1543 British pence, or £15.43) per share. Therefore the current bid price for this instrument is 1543.0. The first buyer wants 175 shares, the next, 300, and so on. The total volume that is demanded at 1543.0p is 2435 shares. This information is summarized on the yellow strip: 5 buyers, total volume of 2435, at 1543.0. These are all buyers who want to buy right now and the exchange will make the trade happen immediately if you put in a sell order for 1543.0 p or less. If you want to sell 2435 shares or fewer, you are good to go. The important thing to note is that once you sell these bidders a total of 2435 shares, then their orders are fulfilled and they will be removed from the order book. At this point, the next bidder is promoted up the book; but his price is 1542.5, 0.5 p lower than before. Absent any further changes to the order book, the bid price will decrease to 1542.5 p. This makes sense because you are selling a lot of shares so you'd expect the market price to be depressed. This information will be disseminated to the level one feed and the level one graph of the stock price will be updated. Thus if you have more than 2435 shares to sell, you cannot expect to execute your order at the bid price in one go. Of course, the more shares you are trying to get rid of, the further down the buy side you will have to go. In reality for a highly liquid stock as this, the order book receives many amendments per second and it is unlikely that your trade would make much difference. On the right hand side of the display you can see the recent trades: these are the times the trades were done (or notified to the exchange), the price of the trade, the volume and the trade type (AT means automatic trade).  GlaxoSmithKline is a highly liquid stock with many willing buyers and sellers. But some stocks are less liquid. In order to enable traders to find a counterparty at short notice, exchanges often require less liquid stocks to have market makers. A market maker places buy and sell orders simultaneously, with a spread between the two prices so that they can profit from each transaction. For instance Diurnal Group PLC has had no trades today and no quotes. It has a more complicated order book, enabling both ordinary buyers and sellers to list if they wish, but market makers are separated out at the top. Here you can see that three market makers are providing liquidity on this stock, Peel Hunt (PEEL), Numis (NUMS) and Winterflood (WINS). They have a very unpalatable spread of over 5% between their bid and offer prices. Further in each case the sum total that they are willing to trade is 3000 shares. If you have more than three thousand Dirunal Group shares to sell, you would have to wait for the market makers to come back with a new quote after you'd sold the first 3000. "Your scenario depicts 2 ""in the money"" options, not ""at the money"". The former is when the share price is higher than the option strike, the second is when share price is right at strike. I agree this is a highly unlikely scenario, because everyone pricing options knows what everyone else in that stock is doing. Much about an option has everything to do with the remaining time to expiration. Depending on how much more the buyer believes the stock will go up before hitting the expiration date, that could make a big difference in which option they would buy. I agree with the others that if you're seeing this as ""real world"" then there must be something going on behind the scenes that someone else knows and you don't. I would tread with caution in such a situation and do my homework before making any move.   The other big factor that makes your question harder to answer more concisely is that you didn't tell us what the expiration dates on the options are. This makes a difference in how you evaluate them. We could probably be much more helpful to you if you could give us that information." "Well, they don't have to enter a market order. I was just saying that for your benefit.   In practice what will really happen is they'll say to themselves   ""I want ABC for no more than 70.00""  The current bid is at 69.60 They'll use a limit order on 10,000 shares. If anyone offers them more than 70.00 the computer program they're using will not accept.  However, the shares won't be bought all at once. A limit order for 10,000 shares will be spit into 1,000 shares at 69.70 and 10,000 for 69.65  The HFT can then make a reasonable guess someone is buying in bulk. So then the HFT sends out a sell order saying ""10 shares at 70.10"". The guy doesn't want that so they do it over again at 70.09  Eventually they notice when the guy accepts at 70.00  So now they knew this guy is willing to pay that. Then HFT buys all the shares they can. ALL SHARES, not just the amount the guy wants. They buy it all at 69.95, which is higher than the 69.70 the guy just paid or whatever.  They then sell it all back to the guy at 70.00  The guy has no choice because all the shares are now gone. He has to pay his highest price.   Once the guy gets his order the HFT just dumps the rest of the shares back at the price they bought them at.  edit: Another way to pull this off is to just literally build your own exchange. Then you can do all of this without any clever tricks. You can just outright give yourself preference over everyone else because you can truly decide what order the trades are being executed." "There are a number of choices: I prefer Dilip's response ""Have you tried asking etrade?"" No offense, but questions about how a particular broker handles certain situations are best asked of the broker.  Last - one should never enter into any trade (especially options trades) without understanding the process in advance. I hope you are asking this before trading." A number of ways exist to calculate the chances of a particular outcome. Options, for example, use current price, cost of money, and volatility among other factors to price the chance of an underlying asset reaching a certain price in a certain timeframe.  A graphical forecast simply puts these calculations into a visual format. That said, it appears the image you offer shows the prediction as it existed in the past along with how the stock has done since.  A disclaimer - The odds of a fair die being rolled to a given number are 1 in 6. It's a fact. With stocks, on the other hand, models try to simulate real life and many factors can't be accounted for. Generally speaking.  1. Take the position size / average daily volume.  2. Multiply that number by 10 or whatever 1/whatever % of volume you think you can execute, ( you can at best acct for 10 percent of traded volume on a day).  3. You now have days until liquidation (x)  4. Take the days until liquidation sample the return over  time x. I.e. if days until liquidation is 10, you would sample 10 day returns.  5. Calculate the distribution characteristics of this window (mean, var, skew, kurt) and calculate VaR based on some confidence.  You can now have a liquidity risk expected loss and a VaR.  If position is on margin don't forget to add the interest cost.  Note: Instead of taking 10 day return, you can take the 10 day VWAP and calculate return between Open and 10 day vwap. "I think that pattern is impossible, since the attempt to apply the second half would seem to prevent executing the first. Could you rewrite that as ""After the stock rises to $X, start watching for a drop of $Y from peak price; if/when that happens, sell."" Or does that not do what you want? (I'm not going to comment on whether the proposed programmed trading makes sense. Trying to manage things at this level of detail has always struck me as glorified guesswork.)" If you plan to take profit at $1.00 then your profit will be $40. Then, if you set your stop at $0.88 then your loss if you get stopped will be $20.  So your Reward : Risk = 2:1.  Note, that this does not take into account brokerage in and out and any slippage from the price gapping past your stop loss. Ok, so disregarding passivity, could you help me through a simplified example?   Say I only had two assets, SPY and TLT, with a respective weight of 35 and 65% and I want want to leverage this to 4x.  Additionally, say daily return covar is:  * B/B .004% * B/S -.004% * S/S .02%   Now, if I read correctly, I should buy ATM calls xxx days in the future.  Which may look like: Ticker, S, K, Option Price, Delta, Lambda  * TLT  $126.04  $126.00  $4.35  0.50  14.5 * SPY  $134.91  $134.00  $6.26  0.55  11.8  ^ This example is pretty close but some assets are far off.   I feel like I'm on the wrong track so I'll stop here.    I just want to lever up my risk-parity. Margin rates are too high and I'm docked by Reg-T. "You'd need to know the delta and the theta of the option. You can either calculate them yourself using a model like Black-Scholes (assuming you have a market price and can imply a volatility, and know the other factors that go into the model) or, you can see if your broker quotes ""greeks"" as well (mine does). The delta is the sensitivity (rate of change in value) to the underlying stock price, and the theta is the sensitivity to time passing (usually expressed in $/day).  So if your option has a delta of .5 and a theta of -.04, when one day passes and the underlying stock goes up $3, the option will gain roughly $1.50 due to the underlying stock price and lose $0.04 due to time passing."