How can I calculate how much an option would be worth after X days if the underlying stock changed by +/- $Y?
"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."
"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." Robert is right saying that options' prices are affected by implied volatility but is wrong saying that you have to look at the VIX index. For two reasons:  1) the VIX index is for S&P500 options only. If you are trading other options, it is less useful. 2) if you are trading an option that is not at the money, your implied volatility may be very different (and follow a different dynamics) that the VIX index.  So please look at the right implied volatility.  In terms of strategy, I don't think that not doing anything is a good strategy. I accept any point of view but you should consider that option traders should be able to adjust positions depending on market view.  So you are long 1 call, suppose strike 10. Suppose the underlying price at the time of entry was 10 (so the call was at the money). Now it's 9.  1) you still have a bullish view: buy 1 call strike 9 and sell 2 calls strike 10. This way you have a bull call spread with much higher probability of leading to profit. You are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations).  2) you become bearish: you can sell 1 call strike 9. This way you end up with a bear call spread. Again, you are limiting your profit potential but you are also reducing the costs and managing the greeks in a proper way (and in line with your expectations). 3) you become neutral: buy 1 call strike 8 and sell 2 calls strike 9. This way you end up with a call butterfly. You are almost delta neutral and you can wait until your view becomes clear enough to become directional. At that point you can modify the butterfly to make it directional.  These are just some opportunities you have. There is no reason for you to wait. Options are eroding contracts and you must be fast and adjust the position before time starts eroding your capital at risk.  It's true that buying a call doesn't make you loose more than the premium you paid, but it's better to reduce this premium further with some adjustment. Isn't it?  Hope that helps. :) Thank you for replying. I'm not sure I totally follow though, aren't you totally at mercy of the liquidity in the stock? I guess I'm havinga hard time visualizing the value a human can add as opposed to say vwapping it or something. I can accept that you're right, just having a difficult time picturing it A bullish (or 'long') call spread is actually two separate option trades.  The A/B notation is, respectively, the strike price of each trade. The first 'leg' of the strategy, corresponding to B, is the sale of a call option at a strike price of B (in this case $165).  The proceeds from this sale, after transaction costs, are generally used to offset the cost of the second 'leg'. The second 'leg' of the strategy, corresponding to A, is the purchase of a call option at a strike price of A (in this case $145). Now, the important part: the payoff.  You can visualize it as so. This is where it gets a teeny bit math-y.  Below, P is the profit of the strategy, K1 is the strike price of the long call, K2 is the strike price of the short call, T1 is the premium paid for the long call option at the time of purchase, T2 is the premium received for the short call at the time of sale, and S is the current price of the stock.  For simplicity's sake, we will assume that your position quantity is a single option contract and transaction costs are zero (which they are not). P = (T2 - max(0, S - K2)) + (max(0, S - K1) - T1) Concretely, let's plug in the strikes of the strategy Nathan proposes, and current prices (which I pulled from the screen).  You have: P = (1.85 - max(0, 142.50 - 165)) - (max(0, 142.50 - 145)) = -$7.80 If the stock goes to $150, the payoff is -$2.80, which isn't quite break even -- but it may have been at the time he was speaking on TV. If the stock goes to $165, the payoff is $12.20. Please do not neglect the cost of the trades!  Trading options can be pretty expensive depending on the broker.  Had I done this trade (quantity 1) at many popular brokers, I still would've been net negative PnL even if NFLX went to >= $165. "Yes, long calls, and that's a good point. Let's see... if I bought one contract at the Bid price above...          $97.13 at expiry of $96.43 option = out of the money =- option price(x100)          = $113 loss.     $97.13 at expiry of $97.00 option = out of the money =- option price(x100)          = $77 loss.     $97.13 at expiry of $97.14 option = in the money by 1-cent=$1/contract profit - option price(x100) = $1-$58          = $57 loss   The higher strike prices have much lower losses if they expire with the  underlying stock at- or near-the-money. So, they carry ""gentler"" downside potential, and are priced much higher to reflect that ""controlled"" risk potential.  That makes sense. Thanks." "Options are generally viewed as having two types of value: ""Intrinsic value"" and ""time value.""  The intrinsic value is based on the difference between the strike price on the option and the spot price of the underlying.  The time value is based on the volatility of the underlying and the amount of time left until expiration.  As the days pass toward expiration, the time value generally decreases, and the intrinsic value may move up or down depending on the spot price of the underlying. (In theory, time value could increase at some points if the volatility is also rising.) In your case, it looks like the time value is decreasing faster than the intrinsic value is increasing. This may happen because the volatility is also going down (as suggested in the answer by CQM) or may just happen because the time to expiration is getting shorter at equal volatility. As noted by DumbCoder in a comment to the original question, the Black-Scholes formula will give you more analytical insight into this if you're interested." Option prices consist of two parts: the intrinsic value (the difference between the strike and the current price of the stock) and a time premium, representing the probability that the stock will end up above the strike for a call (or below for a put).   All else being equal, options decline in value as time passes, since there is less uncertainty about the expected value of the stock at expiration and thus the time premium is smaller.  Theta is the measure of the change in value in one day.  So for every day that passes, the calls you sold are going down by $64.71 (which is positive to you since you sold them at a higher value) and the calls you sold are going down by $49.04. So your position (a short spread) is gaining $15.67 each day (assuming no change in stock price or volatility). In reality, the stock price and volatility also change every day, and those are much stronger drivers of the value of your options.  In your case, however, the options are deep out of the money, meaning it's very likely that they'll expire worthless, so all you have left is time premium, which is decaying as time goes on. As the option approaches expiry, the delta will approach zero or one, depending on whether you're in or out of the money. This might be easiest to conceptualise if you look at the option value as a function of the stock price, and then realise that the delta is the slope of that curve. Now, as we get closer to expiry, time value fades away, and we get closer and closer to the intrinsic value, which looks like this hockey stick: __/ As you see, close to expiry, if you're out of the money, you have nothing (with delta zero), while if you're in the money, you have a forward (with delta one). "So, if an out-of-the-money option (all time value) has a price P (say $3.00), and there are N days... The extrinsic value isn't solely determined by time value as your quote suggests. It's also based on volatility and demand. Here is a quote from http://www.tradingmarkets.com/options/trading-lessons/the-mystery-of-option-extrinsic-value-767484.html distinguishing between extrinsic time value and extrinsic non-time value: The time value of an option is entirely predictable. Time value premium declines at an accelerating rate, with most time decay occurring in the last one to two months before expiration. This occurs on a predictable curve. Intrinsic value is also predictable and easily followed. It is worth one point for every point the option is in the money. For example, a call with a strike of 30 has three points of intrinsic value when the current value of the underlying stock is $33 per share; and a 40 put has two points of intrinsic value when the underlying stock is worth $38. The third type of premium, extrinsic value, increases or decreases when the underlying stock changes and when the distance between current value of stock and strike of the option get closer together. As a symptom of volatility, extrinsic value may be greater for highly volatile underlying stock, and lower for less volatile stocks. Extrinsic value is the only classification of option premium that is unpredictable. The SPYs you point out probably had a volatility component affecting value. This portion is a factor of expectations or uncertainty. So an event expected to conclude prior to expiration, but of unknown outcome can cause theta to be higher than p/n. For example, a drug company is being sued and the outcome of a trial will determine whether that company pays out millions or not. The extrinsic will be higher than p/n prior to the outcome of the trial then drops after.  Of course, the most common situation where this happens is earnings. After the announcement, it's not unusual to see a dramatic drop in the extrinsic portion of options. This is why sometimes a new option trader gets angry when buying calls prior to earnings. When 'surprise' good earnings are announced as hoped, the rise is stock price is largely offset by a fall in extrinsic value giving call holders little or no gain! As for the reverse situation where theta is lower than p/n would expect? Well you can actually have negative theta meaning the extrinsic portion rises over time. (this statement is a little confusing because theta is usually described as negative, but since you describe it as a positive number, negative here means the opposite of what you'd expect).  This is a quote from ""Option Volatility & Pricing"". Keep in mind that they use 'positive' theta to mean the time value increases up over time: Is it ever possible for an option to have a positive theta such that if nothing changes the option will be worth more tomorrow than it is today? When futures options are subject to stock-type settlement, as they currently are in the United States, the carrying cost on a deeply in-the-money option, either a call or a put, can, under some circumstances, be greater than the volatility component. If this happens, and the option is European (no early exercise permitted), it will have a theoretical value less than parity (less than intrinsic value). As expiration approaches, the value of the option will slowly rise to parity. Hence, the option will have a positive theta. Sheldon Natenberg. Option Volatility & Pricing: Advanced Trading Strategies and Techniques (Kindle Locations 1521-1525). Kindle Edition." The time when you might want to do this is if you think BBY is undervalued already.  If you'd be happy buying the stock now, you'd be happy buying it lower (at the strike price of the put option you sold).  If the stock doesn't go down, you win.  If it does, you still win, because you get the stock at the strike price. If I recall correctly Warren Buffett did this with Coca-Cola.  But that's Warren Buffett. 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. The average price would be $125 which would be used to compute your basis. You paid $12,500 for the stock that is now worth $4,500 which is a loss of $8,000 overall if you sell at this point. "Your company actually will most likely use some sort of options pricing model, either a binomial tree or black-scholes to determine the value for their accounting and, subsequently, for their issuance and realization.  First, market value of equity will be determined. Given you're private (although ""pre-IPO could mean public tomorrow,""), this will likely revolve around a DCF and/or market approaches.  Equity value will then be compared to a cap table to create an equity waterfall, where the different classes of stock and the different options will be valued along tranches. Keep in mind there might be liquidation preferences that would make options essentially further out of the money.  As such, your formulae above do not quite work. However, as an employee, it might be difficult to determine the necessary inputs to determine value.  To estimate it, however, look for three key pieces of information:  1. Current equity value  2. Option strike price  3. Maturity for Options  If the strike is close to the current equity value, and the maturity is long enough, and you expect the company to grow, then it would look like the options have more value than not.   Equity value can be derived from enterprise value, or by directly determining it via a DCF or guideline multiples.   Reliable forecasts should come from looking at the industry, listening to what management is saying, and then your own information as an insider." "As JoeTaxpayer says, there's a lot you can do with just the stock price. Exploring that a bit: Stock prices are a combination of market sentiment and company fundamentals. Options are just a layer on top of that. As such, options are mostly formulaic, which is why you have a hard time finding historical option data -- it's just not that ""interesting"", technically. ""Mostly"" because there are known issues with the assumptions the Black-Scholes formula makes. It's pretty good, and importantly, the market relies on it to determine fair option pricing. Option prices are determined by: Relationship of stock price to strike. Both distance and ""moneyness"". Time to expiration. Dividends. Since dividend payments reduce the intrinsic value of a company, the prospect of dividend payments during the life of a call option depresses the price of the option, as all else equal, without the payments, the stock would be more likely to end up in the money. Reverse the logic for puts. Volatility. Interest rates. But this effect is so tiny, it's safe to ignore. #4, Volatility, is the biggie. Everything else is known. That's why option trading is often considered ""volatility trading"". There are many ways to skin this cat, but the result is that by using quoted historical values for the stock price, and the dividend payments, and if you like, interest rates, you can very closely determine what the price of the option would have been. ""Very closely"" depending on your volatility assumption. You could calculate then-historical volatility for each time period, by figuring the average price swing (in either direction) for say the past year (year before the date in question, so you'd do this each day, walking forward). Read up on it, and try various volatility approaches, and see if your results are within a reasonable range. Re the Black-Scholes formula,  There's a free spreadsheet downloadable from http://optiontradingtips.com. You might find it useful to grab the concept for coding it up yourself. It's VBA, but you can certainly use that info to translate in your language of choice. Or, if you prefer to read Perl, CPAN has a good module, with full source, of course. I find this approach easier than reading a calculus formula, but I'm a better developer than math-geek :)" "When you buy a put on a stock, you buy the right to sell the stock at fixed price, F, that his usually different from the market price, M. You paid a price, P, for the put.  Your potential profit, going forward, is represented by the DIFFERENCE you get to collect between your fixed price F, and that market price M, plus the price you paid for the put, or F-(M+P). (This assumes that F>(M+P). P is fixed, but the smaller M gets, the larger the term F-(M+P), and therefore the higher your potential profit from owning the put. So when M ""tanks,"" the put goes higher.  The $395 put is already in the money. If it were settled today, the value would be $395-$376 or $19. This, minus the cost of the put itself, represents your profit. The $365 put is ""out of the money."" The stock has to fall $11 more before the put is exercised. But if the stock went down 8 points today, that is less than the $19 difference at the start of the day. Because there is time between now and October, there is a chance for the stock to go down further, thereby going into the money. The current value of the put is represented by this ""chance."" Obviously, the chances of the stock going down $11 more (from today) is greater than the chance of it going down $19 more. On the other hand, the closer it gets to the expiration date, the less an out of the money put is worth. It's a race between the stock's fall, and the time to expiration."