Value of a call option spread
On expiry, with the underlying share price at $46, we have : You ask :  How come they substract 600-100. Why ? Because you have sold the $45 call to open you position, you must now buy it back to close your position.  This will cost you $100, so you are debited for $100 and this debit is being represented as a negative (subtracted); i.e., -$100 Because you have purchased the $40 call to open your position, you must now sell it to close your position.  Upon selling this option you will receive $600, so you are credited with $600 and this credit is represented as a positive (added) ; i.e., +$600. Therefore, upon settlement, closing your position will get you $600-$100 = $500.  This is the first point you are questioning.   (However, you should also note that this is the value of the spread at settlement and it does not include the costs of opening the spread position, which are given as $200, so you net profit is $500-$200 = $300.) You then comment :  I know I am selling 45 Call that means : As a writer: I want stock price to go down or stay at strike. As a buyer: I want stock price to go up. Here, note that for every penny that the underlying share price rises above $45, the money you will pay to buy back your short $45 call option will be offset by the money you will receive by selling the long $40 call option.  Your $40 call option is covering the losses on your short $45 call option. No matter how high the underlying price settles above $45, you will receive the same $500 net credit on settlement.  For example, if the underlying price settles at $50, then you will receive a credit of $1000 for selling your $40 call, but you will incur a debit of $500 against for buying back your short $45 call.  The net being $500 = $1000-$500.  This point is made in response to your comments posted under Dr. Jones answer. I think you're missing the fact that the trader bought the $40 call but wrote the $45 call -- i.e. someone else bought the $45 call from him.  That's why you have to subtract 600-100.  At expiration, the following happens: So $600 + -$100 = $500 total profit. Note: In reality he would probably use the shares he gets from the first call to satisfy the shares he owes on the second call, so the math is even simpler: You have to look at the real price of the share to calculate the value of the spread. 42$ at the start, 46$ at the end.  Think of it this way: When price was 42$ the call 45$ was out of the money, worth 100$ of time value only=100 the call 40$ was in the money and worth 200$ of intrinsic + 100 time value=300 the difference was 200$ Now that price is 46$ the call 45$ is worth 100$ in the money, real or intrinsic value the call 40$ is worth 600$ in the money, real or intrinsic value the difference is 500$ NOTE: 1. Commission fees are not included. 2. Time value of 100$ on both calls when price is 42$ is incorrect and for teaching purpose only. The Explanation is correct. The Traders buys the 1st call and profits linearly form 40$ onwards. At at 45 the short call kick in and neutralizes any further profit on the first call.
The value of an option has 2 components, the extrinsic or time value element and the intrinsic value from the difference in the strike price and the underlying asset price. With either an American or European option the intrinsic value of a call option can be 'locked in' any time by selling the same amount of the underlying asset (whether that be a stock, a future etc).  Further, the time value of any option can be monitised by delta hedging the option, i.e. buying or selling an amount of the underlying asset weighted by the measure of certainty (delta) of the option being in the money at expiry. Instead, the extra value of the American option comes from the financial benefit of being able to realise the value of the underlying asset early. For a dividend paying stock this will predominantly be the dividend. But for non-dividend paying stocks or futures, the buyer of an in-the-money option can realise their intrinsic gains on the option early and earn interest on the profits today. But what they sacrifice is the timevalue of the option.  However when an option becomes very in the money and the delta approaches 1 or -1, the discounting of the intrinsic value (i.e. the extra amount a future cash flow is worth each day as we draw closer to payment) becomes larger than the 'theta' or time value decay of the option. Then it becomes optimal to early exercise, abandon the optionality and realise the monetary gains upfront. For a non-dividend paying stock, the value of the American call option is actually the same as the European. The spot price of the stock will be lower than the forward price at expiry discounted by the risk free rate (or your cost of funding). This will exactly offset the monetary gain by exercising early and banking the proceeds. However for an option on a future, the value today of the underlying asset (the future) is the same as at expiry and its possible to fully realise the interest earned on the money received today. Hence the American call option is worth more. For both examples the American put option is worth more, slightly more so for the stock. As the stock's spot price is lower than the forward price, the owner of the put option realises a higher (undiscounted) intrinsic profit from selling the stock at the higher strike price today than waiting till expiry, as well as realising the interest earned. Liquidity may influence the perceived value of being able to exercise early but its not a tangible factor that is added to the commonly used maths of the option valuation, and isn't really a consideration for most of the assets that have tradeable option markets. It's also important to remember at any point in the life of the option, you don't know the future price path. You're only modelling the distribution of probable outcomes. What subsequently happens after you early exercise an American option no longer has any bearing on its value; this is now zero! Whether the stock subsequently crashes in price is irrelevent. What is relevant is that when you early exercise a call you 'give up' all potential upside protected by the limit to your downside from the strike price. "It depends on the volatility of the underlying stock. But for ""normal"" levels of volatility, the real value of that option is probably $3.50! Rough estimates of the value of the option depending on volatility levels: Bottom line: unless this is a super volatile stock, it is trading at $3.50 for a reason. More generally: it is extremely rare to find obvious arbitrage opportunities in the market." "Bull means the investor is betting on a rising market. Puts are a type of stock option where the seller of a put option promises to buy 100 shares of stock from the buyer of the put option at a pre-agreed price called the strike price on any day before expiration day.  The buyer of the put option does not have to sell (it is optional, thats why it is called buying an option).  However, the seller of the put is required to make good on their promise to the buyer. The broker can require the seller of the put option to have a deposit, called margin, to help make sure that they can make good on the promise.   Profit... The buyer can profit from the put option if the stock price moves down substantially.   The buyer of the put option does not need to own the stock, he can sell the option to someone else.  If the buyer of the put option also owns the stock, the put option can be thought of like an insurance policy on the value of the stock.  The seller of the put option profits if the stock price stays the same or rises.  Basically, the seller comes out best if they can sell put options that no one ends up using by expiration day. A spread is an investment consisting of buying one option and selling another. Let's put bull and put and spread together with an example from Apple. So, if you believed Apple Inc. AAPL (currently 595.32) was going up or staying the same through JAN you could sell the 600 JAN put and buy the 550 put.  If the price rises beyond 600, your profit would be the difference in price of the puts.  Let's explore this a little deeper (prices from google finance 31 Oct 2012): Worst Case:  AAPL drops below 550.  The bull put spread investor owes (600-550)x100 shares = $5000 in JAN but received $2,035 for taking this risk. EDIT 2016: The ""worst case"" was the outcome in this example, the AAPL stock price on options expiry Jan 18, 2013 was about $500/share. Net profit = $2,035 - $5,000 = -$2965 = LOSS of $2965 Best Case:  AAPL stays above 600 on expiration day in JAN. Net Profit = $2,035 - 0 = $2035 Break Even:  If AAPL drops to 579.65, the value of the 600 JAN AAPL put sold will equal the $2,035 collected and the bull put spread investor will break even. Commissions have been ignored in this example." Your math shows that you bought an 'at the money' option for .35 and when the stock is $1 above the strike, your $35 (options trade as a contract for 100 shares) is now worth $100. You knew this, just spelling it out for future readers.  1 - Yes 2 - An execute/sell may not be nesesary, the ooption will have time value right until expiration, and most ofter the bid/ask will favor selling the option. You should ask the broker what the margin requirement is for an execute/sell. Keep in mind this usually cannot be done on line, if I recall, when I wanted to execute, it was a (n expensive) manual order. 3 - I think I answered in (2), but in general they are not identical, the bid/ask on options can get crazy. Just look at some thinly traded strikes and you'll see what I mean. "The blue line is illustrating the net profit or loss the investor will realise according to how the price of the underlying asset settles at expiry. The x-axis represents the underlying asset price.  The y-axis represents the profit or loss. In the first case, the investor has a ""naked put write"" position, having sold a put option.  The strike price of the put is marked as ""A"" on the x-axis.  The maximum profit possible is equal to the total premium received when the option contract was sold.  This is represented by that portion of the blue line that is horizontal and extending from the point above that point marked ""A"" on the x-axis.  This corresponds to the case that the price of the underlying asset settles at or above the strike price on the day of expiry.  If the underlying asset settles at a price less than the strike price on the day of expiry, then the option with be ""in the money"".  Therefore the net settlement value will move from a profit to a loss, depending on how far in the money the option is upon expiry.  This is represented by the diagonal line moving from above the ""A"" point on the x-axis and moving from a profit to a loss on the y-axis.  The diagonal line crosses the x-axis at the point where the underlying asset price is equal to ""A"" minus the original premium rate at which the option was written - i.e., net profit = zero.  In the second case, the investor has sold a put option with a strike price of ""B"" and purchase a put option with a strike price ""A"", where A is less than B.  Here, the reasoning is similar to the first example, however since a put option has been purchase this will limit the potential losses should the underlying asset move down strongly in value. The horizontal line above the x-axis marks the maximum profit while the horizontal line below the x-axis marks the maximum loss. Note that the horizontal line above the x-axis is closer to the x-axis that is the horizontal line below the x-axis.  This is because the maximum profit is equal to the premium received for selling the put option minus the premium payed for buying the put option at a lower strike price.  Losses are limited since any loss in excess of the strike price ""A"" plus the premium payed for the put purchased at a strike price of ""A"" is covered by the profit made on the purchased put option at a strike price of ""A""." "A covered call risks the disparity between the purchase price and the potential forced or ""called"" sale price less the premium received. So buy a stock for $10.00 believing it will drop you or not rise above $14.00 for a given period of days. You sell a call for a $1.00 agreeing to sell your stock for $14.00 and your wrong...the stock rises and at 14.00 or above during the option period  the person who paid you the $1.00 premium gets the stock for a net effective price of $15.00. You have a gain of 5$. Your hypothecated loss is unlimited in that the stock could go to $1mil a share. That loss is an opportunity loss you still had a modest profit in actual $. The naked call is a different beast. you get the 1.00 in commission to sell a stock you don't own but must pay for that right. so lets say you net .75 in commission per share after your sell the option. as long as the stock trades below $14.00 during the period of the option you sold your golden. It rises above the strike price you must now buy that stock at market to fill the order when the counter party choses to exercise the option which results in a REAL loss of 100% of the stocks market price less the .75 a share you made.   in the scenarios a 1000 shares that for up $30.00 a share over the strike price make you $5,000 in a covered call and lose you $29,250 in a naked call.Naked calls are speculative. Covered calls are strategic." Not to be a jerk, since I'm learning about options myself, but I think you have a few things wrong about your tesla put postion.  First, assuming it was itm or atm within a week of strike it would maybe be worth $12-15, I glanced at the 11/10 put strikes ~325 trades for $12.65 https://www.barchart.com/stocks/quotes/TSLA/options?expiration=2017-11-10  The closer it gets to expiry theta decay reduces put value significantly, the 325's that expire tomorrow are only worth $2.60.   Expecting TSLA to drop from 325 to 50 a share by Jan has a .006% chance of occuring according to the current delta. It's a lottery ticket at best.  _____ Lastly the $50 price is the expected share price at the date of expiry. The price you pay is 57c for the options. So in order to get to your 494k number TSLA would need to decline $50 dollars to a price of 275 a share. You wouldn't want to buy 50 dollar puts, just the 275 puts, provided it declines very quickly.   EDIT: I was looking at the recent expiration to get an idea of atm or itm prices, since it's not like you would hold to expiration. Also the Jan has a 0.6% chance of hitting 50, not .006%. That said what I've noticed when things start to slide is that puts have a weird way of pricing themselves. For example when something gradually goes up all of the calls go up down the chain through time frames, but puts do not in the same fashion. Further out lower priced puts won't move nearly as much unless the company is basically headed for bankruptcy. "The question you are asking concerns the exercise of a short option position.  The other replies do not appear to address this situation. Suppose that Apple is trading at $96 and you sell a put option with a strike price of $95 for some future delivery date - say August 2016.  The option contract is for 100 shares and you sell the contract for a premium of $3.20. When you sell the option your account will be credited with the premium and debited with the broker commission.  The premium you receive will be $320 = 100 x $3.20.  The commission you pay will depend on you broker. Now suppose that the price of Apple drops to $90 and your option is exercised, either on expiry or prior to expiry.  Then you would be obliged to take delivery of 100 Apple shares at the contracted option strike price of $95 costing you $9,500 plus broker commission.  If you immediately sell the Apple shares you have purchased under your contract obligations, then assuming you sell the shares at the current market price of $90 you would realise a loss of $500 ( = 100x($95-$90) )plus commission.  Since you received a premium of $320 when you sold the put option, your net loss would be $500-$320 = $180 plus any commissions paid to your broker. Now let's look at the case of selling a call option.  Again assume that the price of Apple is $96 and you sell a call option for 100 shares with a strike price of $97 for a premium of $3.60.  The premium you receive would be $360 = 100 x $3.60.  You would also be debited for commission by your broker. Now suppose that the price of Apple shares rises to $101 and your option is exercised.  Then you would be obliged to deliver 100 Apple shares to the party exercising the option at the contracted strike price of $97.  If you did not own the shares to effect delivery, then you would need to purchase those shares in the market at the current market price of $101, and then sell them to the party exercising the option at the strike price of $97.  This would realise an immediate loss of $400 = 100 x ($101-$97) plus any  commission payable.  If you did own the shares, then you would simply deliver them and possibly pay some commission or a delivery fee to your broker.  Since you received $360 when you sold the option, your net loss would be $40 = $400-$360 plus any commission and fees payable to the broker. It is important to understand that in addition to these accounting items, short option positions carry with them a ""margin"" requirement.  You will need to maintain a margin deposit to show ""good faith"" so long as the short option position is open.  If the option you have sold moves against you, then you will be called upon to put up extra margin to cover any potential losses." "I think the issue you are having is that the option value is not a ""flow"" but rather a liability that changes value over time. It is best to illustrate with a balance sheet. The $33 dollars would be the premium net of expense that you would receive from your brokerage for having shorted the options. This would be your asset. The liability is the right for the option owner (the person you sold it to) to exercise and purchase stock at a fixed price. At the moment you sold it, the ""Marked To Market"" (MTM) value of that option is $40. Hence you are at a net account value of $33-$40= $-7 which is the commission. Over time, as the price of that option changes the value of your account is simply $33 - 2*(option price)*(100) since each option contract is for 100 shares. In your example above, this implies that the option price is 20 cents. So if I were to redo the chart it would look like this If the next day the option value goes to 21 cents, your liability would now be 2*(0.21)*(100) = $42 dollars. In a sense, 2 dollars have been ""debited"" from your account to cover your potential liability. Since you also own the stock there will be a credit from that line item (not shown). At the expiry of your option, since you are selling covered calls, if you were to be exercised on, the loss on the option and the gain on the shares you own will net off. The final cost basis of the shares you sold will be adjusted by the premium you've received. You will simply be selling your shares at strike + premium per share (0.20 cents in this example)" 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. 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. "Joke warning: These days, it seems that rogue trading programs are the big market makers (this concludes the joke) Historically, exchange members were market makers. One or more members guaranteed a market in a particular stock, and would buy whatever you wanted to sell (or vice-versa). In a balanced market -- one where there were an equal number of buyers and sellers -- the spread was indeed profit for them. To make this work, market makers need an enormous amount of liquidity (ability to hold an inventory of stocks) to deal with temporary imbalances. And a day like October 29, 1929, can make that liquidity evaporate. I say ""historically,"" because I don't think that any stock market works this way today (I was discussing this very topic with a colleague last week, went to Wikipedia to look at the structure of the NYSE, and saw no mention of exchange members as market makers -- in fact, it appears that the NYSE is no longer a member-based exchange). Instead, today most (all?) trading happens on ""electronic crossing networks,"" where the spread is simply the difference between the highest bid and lowest ask. In a liquid stock, there will be hundreds if not thousands of orders clustered around the ""current"" price, usually diverging by fractions of a cent. In an illiquid stock, there may be a spread, but eventually one bid will move up or one ask will move down (or new bids will come in). You could claim that an entity with a large block of stock to move takes the role of market maker, but it doesn't have the same meaning as an exchange market maker. Since there's no entity between the bidder and asker, there's no profit in the spread, just a fee taken  by the ECN. Edit: I think you have a misconception of what the ""spread"" is. It's simply the difference between the highest bid and the lowest offer. At the instant a trade takes place, the spread is 0: the highest bid equals the lowest offer, and the bidder and seller exchange shares for money. As soon as that trade is completed, the spread re-appears. The only way that a trade happens is if buyer and seller agree on price. The traditional market maker is simply an entity that has the ability to buy or sell an effectively unlimited number of shares. However, if the market maker sets a price and there are no buyers, then no trade takes place. And if there's another entity willing to sell shares below the market maker's price, then the buyers will go to that entity unless the market's rules forbid it." A long call options spread. In this case, a bet that the USO ETF would recover to $35. You can see, I got in when USO was $28, and it's continued to drop, but it has till Jan '17 to recover. The spread is set up to give leverage, when I entered the trade, a 50% recovery would result in a 200% gain, or 3X my bet. An option spread can be bought using any two strikes, and with different payouts depending on how far out of the money the strikes are. "When the buyout happens, the $30 strike is worth $10, as it's in the money, you get $10 ($1000 per contract). Yes, the $40 strike is pretty worthless, it actually dropped in value today. Some deals are worded as an offer or intention, so a new offer can come in. This appears to be a done deal. From Chapter 8 of CHARACTERISTICS AND RISKS OF STANDARDIZED OPTIONS - FEB 1994 with supplemental updates 1997 through 2012; ""In certain unusual circumstances, it might not be possible for uncovered call writers of physical delivery stock and stock index options to obtain the underlying equity securities in order to meet their settlement obligations following exercise. This could happen, for example, in the event of a successful tender offer for all or substantially all of the outstanding shares of an underlying security or if trading in an underlying security were enjoined or suspended. In situations of that type, OCC may impose special exercise settlement procedures. These special procedures, applicable only to calls and only when an assigned writer is unable to obtain the underlying security, may involve the suspension of the settlement obligations of the holder and writer and/or the fixing of cash settlement prices in lieu of delivery of the underlying security. In such circumstances, OCC might also prohibit the exercise of puts by holders who would be unable to deliver the underlying security on the exercise settlement date. When special exercise settlement procedures are imposed, OCC will announce to its Clearing Members how settlements are to be handled. Investors may obtain that information from their brokerage firms."" I believe this confirms my observation. Happy to discuss if a reader feels otherwise." You would need additional information (login information [username and which service]) to fully make use of it though.  I'm not sure how you would collect that? You could use such a service to build a dictionary for a dictionary attack I guess. It's only after this sort of attack that people start explicitly checking their passwords though?   edit: From re-reading your comment I see you've already come up with the same limitations. To answer the question you actually asked, I would say you have no way of knowing these sha1 generators don't store the queries, just that it would be difficult to use the resulting dictionary. You would see which hashes are on your list versus the hashes on the leaked list. And then use those matches as a dictionary to attack someone's linkedin account.