Put Option Pricing
Standard options are contracts for 100 shares. If the option is for $0.75/share and you are buying the contract for 100 shares the price would be $75 plus commission. Some brokers have mini options available which is a contract for 10 shares. I don't know if all brokers offer this option and it is not available on all stocks. The difference between the 1 week and 180 day price is based on anticipated price changes over the given time. Most people would expect more volatility over a 6 month period than a 1 week period thus the demand for a higher premium for the longer option.
I use futures options as a sort of hedge to an underwater position that I want to hold onto.  If I am short at 3900 on /NQ and it moves up 3910 then I can sell a put against my position.  For example, I sell this month's 3850 put for 15.00.  If the NQ continues up to 3920, I can probably buy back that put for ~12.00 and sell the 3860 for 15.00. Rinse and repeat if it keeps moving up.     If then the NQ moves down to 3900 then my futures position will be up +10 where my futures options put position will only be down about -3 for a net of +7.    I suppose you could also trade a futures option by itself instead of the future's contract if you didn't want to risk as much $ in a day trade.    Keep in mind that price you see for a future's options relates to the underlying.  For /NQ 1 point = $20  so if a 3850 put costs 15.00 that is really $300.    ES (Sp 500 futures) 1 point = $50 so a 1900 put that costs 15.00 would really be $750. Not necessarily though, since you can simply adjust the premium. I'm thinking an embedded option is just an option with longer maturity, and the increased price of that adjusted option can be reflected (like any other option) in the strike price or the premium. Am I missing something? But if underlying goes to 103 at expiration, both the call and the put   expire worthless If the stock closes at 103 on expiration, the 105 put is worth $2, not worthless. Option prices are computed by determining the cost of obtaining the option returns using a strategy that trades the underlying asset continuously.  It sounds like what you are describing is rapidly trading the option in order to obtain returns similar to those of the stock.  The equality goes both ways.   If the option is appropriately priced, then a strategy that replicates stock returns using the option will cost the same as buying the stock. Because you can't trade continuously, you won't actually be able to replicate the stock return, and it may seem like you are making arbitrage profit (puts may seem abnormally expensive), but you do so by bearing tail risk (i.e., selling puts loses more money than owning the associated stock if an unusually bad event occurs). "Suppose the stock is $41 at expiry. The graph says I will lose money. I think I paid $37.20 for (net debit) at this price. I would make money, not lose. What am I missing? The `net debit' doesn't have anything to do with your P/L graph. Your graph is also showing your profit and loss for NOW and only one expiration. Your trade has two expirations, and I don't know which one that graph is showing. That is the ""mystery"" behind that graph. Regardless, your PUTs are mitigating your loss as you would expect, if you didn't have the put you would simply lose more money at that particular price range. If you don't like that particular range then you will have to consider a different contract. it was originally a simple covered call, I added a put to protect from stock going lower.. Your strike prices are all over the place and NBIX has a contract at every whole number.... there is nothing simple about this trade. You typically won't find an ""always profitable"" combination of options. Also, changes in volatility can distort your projects greatly." /u/NotMyRealFaceBook  As a sniff test, I threw the following assumptions into a Black-Scholes options pricing calculator:  * Stock Price and Strike Price = $200  * Valuation date = 10/31/2017  * Expiration date = 10/29/2027 (European style - no early exercise)  * Volatility = 20% (on the low end for a tech. company - but again see the non-log-normal assumption point above)  * Interest rate = 4% (on the high end - which means the option seller is over-charging you)  * Dividend yield = 0%  The calculator's theoretical call option price results in $82.  Unless the company in question has a materially skewed upside given today's starting valuation, my opinion is the options you are offered are being priced via a Black-Scholes model and are over-priced. I'll just copypasta out of the book for the sake of clarity:   * If you think about it, you see that the only brokers who touch the switch for light bulb number 64 are those whose numbers are divisors of 64. That is, light bulb 64 has its state changed by brokers whose numbers are factors of 64. This means brokers 1, 2, 4, 8, 16, 32, 64. Because light bulb 64 is originally off, it must be after this odd number of switches that it is on.   * You want to be short a put if you expect a price rise. In this case, you expect to keep the option premium when the option expires worthless.   There are a few pages worth of questions for the options, so the explanation for the IBM one is somewhat limited. A few observations - A limit order can certainly work, as you've seen.  I've put in such an order far beyond the true value, and gotten back a realistic bid/ask within 10 minutes or so. That at least gave me an idea where to set my limit.  When this doesn't work, an exercise is always another way to go. You'll get the full intrinsic value, but no time value, by definition.  Per your request in comment - You own a put, strike price $100. The stock (or ETF) is trading at $50. You buy the stock and tell the broker to exercise the put, i.e. deliver the stock to the buyer of the put. Understanding the BS equation is not needed. What is needed is an understanding of the bell curve.   You seem to understand volatility. 68% of the time an event will fall inside one standard deviation. 16% of the time it will be higher, 16%, lower.  Now, if my $100 stock has a STD of $10, there's a 16% chance it will trade above $110. But if the STD is $5, the chance is 2.3% per the chart below. The higher volatility makes the option more valuable as there's a highr chance of it being 'in the money.' My answer is an over simplification, per your request. 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. "One thing I would like to clear up here is that Black Scholes is just a model that makes some assumptions about the dynamics of the underlying + a few other things and with some rather complicated math, out pops the Black Scholes formula. Black Scholes gives you the ""real"" price under the assumptions of the model. Your definition of what a ""real"" price entails will depend on what assumptions you make. With that being said, Black Scholes is popular for pricing European options because of the simplicity and speed of using an analytic formula as opposed to having a more complex model that can only be evaluated using a numerical method, as DumbCoder mentioned (should note that, for many other types of derivative contracts, e.g. American or Bermudan style exercise, the Black Scholes analytic formula is not appropriate). The other important thing to note here is that the market does not necessarily need to agree with the assumptions made in the Black Scholes model (and they most certainly do not) to use it. If you look at implied vols for a set of options which have the same expiration but differing strike prices, you may find that the implied vols for each contract differ and this information is telling you to what degree the traders in the market for those contracts disagree with the lognormal distribution assumption made by Black Scholes. Implied vol is generally the thing to look at when determining cheapness/expensiveness of an option contract. With all that being said, what I'm assuming you are interested in is either called a ""delta-gamma approximation"" or more generally ""Greek/sensitivities based profit and loss attribution"" (in case you wanted to Google some more about it). Here is an example that is relevant to your question. Let's say we had the following European call contract: Popping this in to BS formula gives you a premium of $4.01, delta of 0.3891 and gamma of 0.0217. Let's say you bought it, and the price of the stock immediately moves to 55 and nothing else changes, re-evaluating with the BS formula gives ~6.23. Whereas using a delta-gamma approximation gives: The actual math doesn't work out exactly and that is due to the fact that there are higher order Greeks than gamma but as you can see here clearly they do not have much of an impact considering a 10% move in the underlying is almost entirely explained by delta and gamma." 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. Outside of software that can calculate the returns:  You could calculate your possible returns on that leap spread as you ordinarily would, then place the return results of that and the return results for the covered call position side by side for any given price level of the stock you calculate, and net them out. (Netting out the dollar amounts, not percentage returns.)  Not a great answer, but there ya go. Software like OptionVue is expensive When dividend is announced the stock and option price may react to that news, but the actual payout of the dividend on the ex-dividend date is what you probably are referring to. The dividend payout affects the stock price on the ex-dividend date as the stock price will drop by the amount of paid out dividend (not taking into account other factors). This in turn drives the prices of all options.  The amount of change in the option price for this event is not only dependent the dividend payout, but also on how far these are in our out of the money and what there time to expiration is. The price of a call option that is far out of the money would react less than the price of a put that would be far in the money. Therefore I would argue that these two will not necessarily offset each other. "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."