Options price vs implied volatility - who drives who?
"Currently, when ""implied volatility"" is spoken, the Black-Scholes-Merton model is implied.  This model has been shown to be deficient, thus the Variance Gamma Model should be used. However, as nearly no one uses VG, it can be assumed that BS is still being implied. The BS formula has multiple variables.  Some are external to the underlying in question.  The rest are internal. When all but one variable is known or assumed, the last variable can be calculated, so if one has the price of the underlying and all else except the volatility, the volatility can be calculated thus implied. If one selects an implied volatility, and all variables except the underlying price is known, the underlying price can be calculated. For the present, one uses the current price of the underlying to calculate the implied volatility.  For future option prices, one assumes an implied volatility at a later date to calculate a possible price. For prices not at the money, the BS model is extremely imprecise.  The VG model can better determine a potential future price."
Really all you need to know is that American style can be exercised at any point, European options cannot be exercised early. Read on if you want more detail.  The American style Call is worth more because it can be exercised at any point. And when the company pays a dividend, and your option is in the money, if the extrinsic value is worth less than the dividend you can be exercised early. This is not the case for a European call. You cannot be exercised until expiration. I trade a lot of options, you wont be exercised early unless the dividend scenario I mentioned happens. Or unless the extrinsic value is nothing, but even then, unless the investor really wants that position, he is more likely to just sell the call for an equivalent gain on 100 shares of stock. So in a sense, I can think of the employees / option-holders as another investor?   That makes sense - but many of the examples I'm finding online are still confusing me. Based on the example above, it seems like option-holders would be paying the same exercise price as the VC. Per [Andreesen Horowitz](https://a16z.com/2016/08/24/options-ownership/) this seems uncommon:   &gt; The exercise price of employee options — the price per share needed to actually own the shares — is often less than the original issue price paid by the most recent investor, who holds preferred stock.    In reality, would option-holders receive, say, 40% (using example above) for their $6m in exercise value due to receiving common stock, with the founder being diluted to even further? Option prices can predict the range of movement of the underlying, but not if the underlying is going up or down. An option price gives an implied volatility for an underlying . That IV number helps predict a range for the underlying price over the next few days,months, upto a year. "I thought the other answers had some good aspect but also some things that might not be completely correct, so I'll take a shot. As noted by others, there are three different types of entities in your question:  The ETF SPY, the index SPX, and options contracts. First, let's deal with the options contracts.  You can buy options on the ETF SPY or marked to the index SPX.  Either way, options are about the price of the ETF / index at some future date, so the local min and max of the ""underlying"" symbol generally will not coincide with the min and max of the options.  Of course, the closer the expiration date on the option, the more closely the option price tracks its underlying directly.  Beyond the difference in how they are priced, the options market has different liquidity, and so it may not be able to track quick moves in the underlying. (Although there's a reasonably robust market for option on SPY and SPX specifically.) Second, let's ask what forces really make SPY and SPX move together as much as they do.  It's one thing to say ""SPY is tied to SPX,"" but how?  There are several answers to this, but I'll argue that the most important factor is that there's a notion of ""authorized participants"" who are players in the market who can ""create"" shares of SPY at will.  They do this by accumulating stock in the constituent companies and turning them into the market maker.  There's also the corresponding notion of ""redemption"" by which an authorized participant will turn in a share of SPY to get stock in the constituent companies. (See http://www.spdrsmobile.com/content/how-etfs-are-created-and-redeemed and http://www.etf.com/etf-education-center/7540-what-is-the-etf-creationredemption-mechanism.html) Meanwhile, SPX is just computed from the prices of the constituent companies, so it's got no market forces directly on it.  It just reflects what the prices of the companies in the index are doing. (Of course those companies are subject to market forces.) Key point: Creation / redemption is the real driver for keeping the price aligned.  If it gets too far out of line, then it creates an arbitrage opportunity for an authorized participant.  If the price of SPY gets ""too high"" compared to SPX (and therefore the constituent stocks), an authorized participant can simultaneously sell short SPY shares and buy the constituent companies' stocks.  They can then use the redemption process to close their position at no risk.  And vice versa if SPY gets ""too low."" Now that we understand why they move together, why don't they move together perfectly.  To some extent information about fees, slight differences in composition between SPY and SPX over time, etc. do play.  The bigger reasons are probably that (a) there are not a lot of authorized participants, (b) there are a relatively large number of companies represented in SPY, so there's some actual cost and risk involved in trying to quickly buy/sell the full set to capture the theoretical arbitrage that I described, and (c) redemption / creation units only come in pretty big blocks, which complicates the issues under point b. You asked about dividends, so let me comment briefly on that too.  The dividend on SPY is (more or less) passing on the dividends from the constituent companies. (I think - not completely sure - that the market maker deducts its fees from this cash, so it's not a direct pass through.)  But each company pays on its own schedule and SPY does not make a payment every time, so it's holding a corresponding amount of cash between its dividend payments.  This is factored into the price through the creation / redemption process.  I don't know how big of a factor it is though." My level of analysis is not quite that advanced. Can you share what that would show and why that particular measure is the one to use?  I've run regression on prices between the two. VIX prices have no correlation to the s&amp;p500 prices. Shouldn't true volatility result in the prices (more people putting options on the VIX during the bad times and driving that price up) correlate to the selloff that occurs within the S&amp;P500 during recessions and other events that would cause significant or minor volatility? My r2 showed no significance within a measurement of regression within Excel.  But, *gasp* I could be wrong, but would love to learn more about better ways of measurement :) "Bob should treat both positions as incomplete, and explore a viewpoint which does a better job of separating value from volatility. So we should start by recognizing that what Bob is really doing is trading pieces of paper (say Stocks from Fund #1 or Bonds from Fund #2, to pick historically volatile and non-volatile instruments.*) for pieces of paper (Greenbacks).  In the end, this is a trade, and should always be thought of as such.  Does Bob value his stocks more than his bonds?  Then he should probably draw from Fund #2.  If he values his bonds more, he should probably draw from Fund #1. However, both Bob and his financial adviser demonstrate an assumption: that an instrument, whether stock bond or dollar bill, has some intrinsic value (which may raise over time).  The issue is whether its perceived value is a good measure of its actual value or not. From this perspective, we can see the stock (Fund #1) as having an actual value that grows quickly (6.5% - 1.85% = 4.65%), and the bond (Fund #2) as having an actual value that grows slower (4.5% - 1.15$ = 3.35$).  Now the perceived value of the stocks is highly volatile.  The Chairman of the Fed sneezes and a high velocity trader drives a stock up or down at a rate that would give you whiplash. This perspective aligns with the broker's opinion.  If the stocks are low, it means their perceived value is artificially low, and selling it would be a mistake because the market is perceiving those pieces of paper as being worth less than they actually are.  In this case, Bob wins by keeping the stocks, and selling bonds, because the stocks are perceived as undervalued, and thus are worth keeping until perceptions change. On the other hand, consider the assumption we carefully slid into the argument without any fanfare: the assumption that the actual value of the stock aligns with its historical value.  ""Past performance does not predict future results.""  Its entirely possible that the actual value of the stocks is actually much lower than the historical value, and that it was the perceived value that was artificially higher.  It may be continuing to do so... who knows how overvalued the perceived value actually was!  In this case, Bob wins by keeping the bonds.  In this case, the stocks may have ""underperformed"" to drive perceptions towards their actual value, and Bob has a great chance to get out from under this market. The reality is somewhere between them.  The actual values are moving, and the perceived values are moving, and the world mixes them up enough to make Scratchers lottery tickets look like a decent investment instrument.  So what can we do? Bob's broker has a smart idea, he's just not fully explaining it because it is unprofessional to do so.  Historically speaking, Bobs who lost a bunch of money in the stock market are poor judges of where the stock market is going next (arguably, you should be talking to the Joes who made a bunch of money. They might have more of a clue.).  Humans are emotional beings, and we have an emotional instinct to cut ties when things start to go south.  The market preys on emotional thinkers, happily giving them what they want in exchange for taking some of their money.  Bob's broker is quoting a well recognized phrase that is a polite way of saying ""you are being emotional in your judgement, and here is a phrasing to suggest you should temper that judgement."" Of course the broker may also not know what they're doing!  (I've seen arguments that they don't!)  Plenty of people listened to their brokers all the way to the great crash of 2008.  Brokers are human too, they just put their emotions in different places.  So now Bob has no clear voice to listen to.  Sounds like a trap! However, there is a solution.  Bob should think about more than just simple dollars.  Bob should think about the rest of his life, and where he would like the risk to appear.  If Bob draws from Fund #1 (liquidating stocks), then Bob has made a choice to realize any losses or gains early... specifically now.  He may win, he may lose.  However, no matter what, he will have a less volatile portfolio, and thus he can rely on it more in the long run. If Bob draws from Fund #2 (liquidating bonds) instead, then Bob has made a choice not to realize any losses or gains right away.  He may win, he may lose.  However, whether he wins or loses will not be clear, perhaps until retirement when he needs to draw on that money, and finds Fund #1 is still under-performing, so he has to work a few more years before retirement.  There is a magical assumption that the stock market will always continue rewarding risk takers, but no one has quite been able to prove it! Once Bob includes his life perspective in the mix, and doesn't look just at the cold hard dollars on the table, Bob can make a more educated decision.  Just to throw more options on the table, Bob might rationally choose to do any one of a number of other options which are not extremes, in order to find a happy medium that best fits Bob's life needs: * I intentionally chose to label Fund #1 as stocks and Fund #2 as bonds, even though this is a terribly crude assumption, because I feel those words have an emotional attachment associated to them which #1 and #2 simply do not.  Given that part of the argument is that emotions play a part, it seemed reasonable to dig into underlying emotional biases as part of my wording.  Feel free to replace words as you see fit to remove this bias if desired." 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. You're correct. The VIX price is calculated based on the price of all of SPX options which are expiring (IIRC 2) weeks after the expiration of that VIX contract. It's an index measuring implied vol not realized vol.  VIX futures/options are calculated slightly differently than the VIX index. Volatility typically decreases when stocks rise except pending news events or fast markets.  It has a great impact of the premium of the option. Option liquidity and underlying liquidity tend to go hand in hand. According to regulation, what kinds of issues can have options even trading are restricted by volume and cost due to registration with the authorities. Studies have shown that the introduction of option trading causes a spike in underlying trading. Market makers and the like can provide more option liquidity if there is more underlying and option liquidity, a reflexive relationship. The cost to provide liquidity is directly related to the cost for liquidity providers to hedge, as evidenced by the bid ask spread. Liquidity providers in option markets prefer to hedge mostly with other options, hedging residual greeks with other assets such as the underlying, volatility, time, interest rates, etc because trading costs are lower since the two offsetting options hedge most of each other out, requiring less trading in the other assets. What you should compare is SPX, SPY NAV, and ES fair value.   Like others have said is SPX is the index that others attempt to track. SPY tracks it, but it can get a tiny bit out of line as explained here by @Brick .  That's why they publish NAV or net asset value.  It's what the price should be.  For SPY this will be very close because of all the participants.  The MER is a factor, but more important is something called tracking error, which takes into account MER plus things like trading expenses plus revenue from securities lending.  SPY (the few times I've checked) has a smaller tracking error than the MER.  It's not much of a factor in pricing differences. ES is the price you'll pay today to get SPX delivered in the future (but settled in cash).  You have to take into account dividends and interest, this is called fair value.  You can find this usually every morning so you can compare what the futures are saying about the underlying index. http://www.cnbc.com/pre-markets/ The most likely difference is you're looking at different times of the day or different open/close calculations. You appear to be thinking of option writers as if they were individuals with small, nondiversified, holdings and a particular view on what the underlying is going to do.  This is not the best way to think about them. Option writers are typically large institutions with large portfolios and that provide services in all sorts of different areas. At the same time as they are writing calls on a particular stock, they are writing puts on it and options on other stocks.  They are buying and selling the underlying and all kinds of different derivatives.  They are not necessarily writing the option because they are expecting or hoping to benefit from a price move.  It's just small part of their business.  They write the option if the option price is good enough that they think they are selling it for very slightly more than it's worth.   Asking why an option writer creates a call is like asking why a grocery store keeps buying groceries from their distributors.  Don't they know the price of food may not always rise?  Sure, but their business is selling the food for slightly more than they pay for it, not speculating on what will happen to its price.  Most option writers are doing the same thing, except what they are buying and selling is sets of cash flows and risk.   As a general rule, the business model of option writers is to profit from the few cents of spread or mispricing, not from aggregate changes in the price of the underlying.  They should and often do maintain balanced portfolios so their option writing activities don't expose them to a lot of risk. Also note that there could be lots of reasons for writing options, even if you do have a particular view.  For example, perhaps the option writer thinks volatility of the underlying will decrease.  Writing a call could be part of an overall strategy that profits from this view. I'm not exactly sure, but it may be due to liquidity preference.  SPY has a much higher volume (30d average of roughly 70m vs. 3.3m, 1.9m for IVV, VOO respectively), and similarly has a narrow bid ask spread of about 0.01 compared to 0.02 for the other two.  I could be wrong, but I'm going to leave this post up and look in to it later, I'm curious too. The difference is very consistent though, so it may be something in their methodology. As other uses have pointed out, your example is unusual in that is does not include any time value or volatility value in the quoted premiums, the premiums you quote are only intrinsic values.  For well in-the-money options, the intrinsic value will certainly be the vast majority of the premium, but not the sole component. Having said that, the answer would clearly be that the buyer should buy the $40 call at a premium of $10.  The reason is that the buyer will pay less for the option and therefore risk less money, or buy more options for the same amount of money.  Since the buyer is assuming that the price will rise, the return that will be realised will be the same in gross terms, but higher in relative terms for the buyer of the $40 call.   For example, if the underlying price goes to $60, then the buyer of the $40 call would (potentially) double their money when the premium goes from $10 to $20, while the buyer of the $30 call would realise a (potential) 50% profit when the premium goes from $20 to $30. Considering the situation beyond your scenario, things are more difficult if the bet goes wrong.  If the underlying prices expires at under $40, then the buyer of the $40 call will be better off in gross terms but may be worse off in relative terms (if it expires above $30).  If the underlying price expires between $40 and $50, then the buy of the $30 will be better off in relative term, having lost a smaller percentage of their money. "The strategy is right. As pointed out by you, will the "" volatility cause the premium on the price of the options to be too high to make this worthwhile"" ... this is subjective and depends on how the markets feels about the volatility and the trend ... ie if the market believes that the stock will go up, the option at 45 would cost quite a bit less. However if the market believes the stock would go down, the option at 45 would be quite high [and may not even be available].   There is no generic right or wrong, the strategy is right [with out without putting dividend into equation] it depends what options are available at what prices."