Value of put if underlying stays below strike?
The value at expiration does not depend on the price path for a plain vanilla European or American option. At expiration, the value would simply be: max[K - S_T, 0], where: K is the strike price, and S_T is the underlying price at expiration. $15 - $5 = $10 How did you possibly buy a put for less than the intrinsic value of the option, at $8.25 So we can infer that you would have had to get this put when the stock price was AT LEAST $6.75, but given the 3 months of theta left, it was likely above $7 The value of the put if the price of the underlying asset (the stock ABC) meandered between $5 - $7 would be somewhere between $10 - $8 at expiration. So you don't really stand to lose much in this scenario, and can make a decent gain in this scenario. I mean decent if you were trading stocks and were trying to beat the S&P or keep up with Warren Buffett, but a pretty poor gain since you are trading options! If the stock moves above $7 this is where the put starts to substantially lose value.
I am close to retirement and sell cash secured puts and covered calls on a regular basis.  I make 15 % plus per year from the puts.  Less risky than buying stocks, which I also do.  Riskier than bonds, but several times the income. Example:  I owned 4,000 shares of XYZ, which I bought last year at 6.50 and was at 7.70 two months ago.  I sold 3,000 shares, sold 10 Dec puts @ 7.50 (1,000 shares) for $.90 per share and sold 10 Dec calls at 10.00 for $.20.  Now I had cash from the sale of 3,000 shares ($23,100) plus $900 cash from the sale of the puts, plus $200 cash from the sale of the calls.  Price is now at 6.25.  Had I held the 4,000 shares, I would be down $5,800 from when it was 7.70. Instead, I am down $1,450 from the held 1,000 shares, down $550 on the put and up $200 on the calls.  So down $1,800 instead of down $5,800.  I began buying XYZ back at 6.25 today. "There are two components of option valuation, the value that's ""in the money"" and the ""time value."" In the case of the $395 put, that option was already in the money and it will move less than the stock price by a bit as there will still be some time value there. $22.52 is intrinsic value (the right word for 'in the money') and the rest is time. The $365 strike is still out of the money, but as jldugger implied, the chance of it going through that strike is better as it's $6.66 closer.  Looking at the options chain gives you a better perspective on this. If Apple went up $20 Monday, and down $20 Tuesday, these prices would be higher as implied volatility would also go higher.  Now, I'd hardly call a drop of under 2% ""tanking"" but on the otherhand, I'd not call the 25% jump in the option price skyrocketing. Options do this all the time. Curious what prompted the question, are you interested in trading options? This stock in particular?" The answer provide by @mbhunter is correct, however there are contexts, shorting in spot market and carrying the position over settlement usually does not entail payment of dividend to the broker, one of the reason being post ex-date the price of the share downward adjusts to the extent of the dividend, so practically if you have shorted at 100 and post ex-date (assuming a dividend of 2 and no movement of the stock price), the price would slide to 98, the party who longed the stock @ 100 now is sitting on a price of 98 and received a dividend of 2 which equates to 100. The above is also contextual to the law of the country governing the exchange and the security exchange board regulations. 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. "First, welcome to Money.SE.  The selected page is awful. I don't know the value in listing different expirations at the same strike. Usually, all the strikes are grouped by month, so I'd be looking at Jan '15 across all strikes.  ""In the money"" means the price of a stock is trading above the strike price, if a call, or below it, if a put.  On 10/20 of some year, Intel was trading at $23.34. The January $25 call strike was just $0.70, and April's was $1.82. These were out of the money. The $25 puts were ""in the money"" by $1.66 so you could have paid $1.90 for the Jan $25 put, with $.24 of time premium.  By November, the price rose and the put fell, to $.85, all time premium.  As with stocks, the key thing is to only buy calls of stock that are going to go up. If a stock will fall, buy puts. Curious, what was the class discussion just before the teacher gave you this image?" "But what happen if the stock price went high and then go down near expiry date? When you hold a short (sold) call option position that has an underlying price that is increasing, what will happen (in general) is that your net margin requirements will increase day by day.  Thus, you will be required to put up more money as margin to finance your position.  Margin money is simply a ""good faith"" deposit held by your broker.  It is not money that is debited as cash from the accounting ledger of your trading account, but is held by your broker to cover any potential losses that may arise when you finally settle you position.   Conversely, when the underlying share price is decreasing, the net margin requirements will tend to decrease day by day.   (Net margin is the net of ""Initial Margin"" and ""Variation Margin"".) As the expiry date approaches, the ""time value"" component of the option price will be decreasing." 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 $15.67 each day (assuming no change in stock price or volatility). In reality, the stock price and volatility also change every day, and those are much stronger drivers of the value of your options.  In your case, however, the options are deep out of the money, meaning it's very likely that they'll expire worthless, so all you have left is time premium, which is decaying as time goes on. No, it means what it says. Prices change, hence price of the derivative can go down even if the price of the underlying doesn't change (e.g. theta decay in options). If I sell a covered call, on stock I own 100%, there is no risk of a margin call. The stock goes to zero, I'm still not ask to send in more money. But, if bought on margin, margin rules apply.  A naked put would require you to be able to buy the stock if put to you. As the price of the stock drops, you still need to be able to buy it at the put strike price.  Mark to market is just an expression describing how your positions are considered each day. "According to the book of Hull, american and european calls on non-dividend paying stocks should have the same value. American puts, however, should be equals to, or more valuable than, european puts. The reason for this is the time value of money. In a put, you get the option to sell a stock at a given strike price. If you exercise this option at t=0, you receive the strike price at t=0 and can invest it at the risk-free rate. Lets imagine the rf rate is 10% and the strike price is 10$. this means at t=1, you would get 11.0517$. If, on the other hand, you did'nt exercise the option early, at t=1 you would simply receive the strike price (10$). Basically, the strike price, which is your payoff for a put option, doesn't earn interest. Another way to look at this is that an option is composed of two elements: The ""insurance"" element and the time value of the option. The insurance element is what you pay in order to have the option to buy a stock at a certain price. For put options, it is equals to the payout= max(K-S, 0) where K=Strike Price and St= Stock price.  The time value of the option can be thought of as a risk-premium. It's difference between the value of the option and the insurance element. If the benefits of exercising a put option early (i.e- earning the risk free rate on the proceeds) outweighs the time value of the put option, it should be exercised early. Yet another way to look at this is by looking at the upper bounds of put options. For a european put, today's value of the option can never be worth more than the present value of the strike price discounted at the risk-free rate. If this rule isn't respected, there would be an arbitrage opportunity by simply investing at the risk-free rate. For an american put, since it can be exercised at any time, the maximum value it can take today is simply equals to the strike price. Therefore, since the PV of the strike price is smaller than the strike price, the american put can have a bigger value. Bear in mind this is for a non-dividend paying stock. As previously mentioned, if a stock pays a dividend it might also be optimal to exercise just before these are paid." For a deep in the money, it almost makes no difference because the intrinsic value, the price of the option, is seldom far above the liquidation value, the price of the underlying less the strike price. For an at the money, ceteris paribus, an early exercise would immediately cut the value of the option to 0; however, life is not so simple as JB King has shown. Purely theoretically, for an at or near the money option, an early exercise will be an instantaneous cost because the value after exercise is less than the previously trading or implied option price. The buyer pays $1.99/share for the option of selling a share of AMD to the seller for $10 which is currently $1.94 higher than the price of $8.06/share.  If you bought the put and immediately exercised it, you would come out of the deal losing $.05/share. "What you are proposing is called a ""covered call"" strategy.  It is a perfectly reasonable speculative play on how far the stock will move within a certain amount of time.  If your belief that the stock's volatility is such that it is unlikely to reach the strike price before the maturity is greater than the markets (which it seems it is), then go ahead and sell the call." "When the strike price ($25 in this case) is in-the-money, even by $0.01, your shares will be sold the day after expiration if you take no action. If you want to let your shares go,. allow assignment rather than close the short position and sell the long position...it will be cheaper that way. If you want to keep your shares you must buy back the option prior to 4Pm EST on expiration Friday. First ask yourself why you want to keep the shares. Is it to write another option? Is it to hold for a longer term strategy? Assuming this is a covered call writing account, you should consider ""rolling"" the option. This involves buying back the near-term option and selling the later date option of a similar or higher strike. Make sure to check to see if there is an upcoming earnings report in the latter month because you may want to avoid writing a call in that situation. I never write a call when there's an upcoming ER prior to expiration. Good luck. Alan" 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.