Why do deep in the money options trade below their intrinsic value?
You made 94$ on an investment of 554.80 *100 = 55480$ for an approx holding period of 1 year. So the % return is ~0.16%, which is not much better than the short term us treasury rate. The current 1 year treasury rate is 0.27%: http://ycharts.com/indicators/1_year_treasury_rate So yes, you have a risk free portfolio, so you make the risk free rate. Remember this is an European option, so you are stuck for 1 year. if you found the same mispricing in an American option, then you found an arbitrage.
"When you buy a put option, you're buying the right to sell stock at the ""strike"" price. To understand why you have to pay separately for that, consider the other side of the transaction. If I agree to trade stock for money at above market rates, I need to make up the difference somewhere or face bankruptcy.  That risk of loss is what the option price is about. You might assume that means the market expects the price of AMD to fall to 8.01 from it's current price of 8.06 by the option expiration date. But that would also mean call options below the market price is worthless. But that's not quite true; people who price options need to factor in volatility, since things change with time. The price MIGHT fall, and traders need to account for that risk. So 1.99 roughly represents the probability of AMD rising to 10. There's probably some technical analysis one can do to the chain, but I don't see any abnormality of AMD here." You'd likely be most familiar with them with respect to options and futures on commodities but they're used for credit/interest as well. The intrinsic value of an option is *derived* from the spread between call/put price and strike price; the value of the contract I've paid for or sold is derived from the current market value of the underlying asset, be it rice, platinum, or the Swedish kroner So, this isn't always the case, but in the example provided the option is most likely in the money or near the money since the delta is nearly 1 - indicating that a $1 move in the underlying results in a $0.92 move in the option - this will happen when the expiration is very far out or the option is in the money. As expiration gets closer, movements in the underlying become more pronounced in the options because the probability of the stock price moving from its current position is lower.    As the probability of the stock price moving goes down, the delta of in the money options approaches 100, eventually reaching 100 at expiration. Another way to word this is that the premium on in the money options shrinks as expiration approaches and the intrinsic value of the option increases as percentage of total value so that movements in the underlying stock price become a greater influence on the option price - hence a greater delta. Again, if the option is out of the money, this is not the case. "Seems like you are concerned with something called assignment risk. It's an inherent risk of selling options: you are giving somebody the right, but not the obligation, to sell to you 100 shares of GOOGL. Option buyers pay a premium to have that right - the extrinsic value. When they exercise the option, the option immediately disappears. Together with it, all the extrinsic value disappears. So, the lower the extrinsic value, the higher the assignment risk. Usually, option contracts that are very close to expiration (let's say, around 2 to 3 weeks to expiration or less) have significantly lower extrinsic value than longer option contracts. Also, generally speaking, the deeper ITM an option contract is, the lower extrinsic value it will have. So, to reduce assignment risk, I usually close out my option positions 1-2 weeks before expiration, especially the contracts that are deep in the money. edit: to make sure this is clear, based on a comment I've just seen on your question. To ""close out an options position"", you just have to create the ""opposite"" trade. So, if you sell a Put, you close that by buying back that exact same put. Just like stock: if you buy stock, you have a position; you close that position by selling the exact same stock, in the exact same amount. That's a very common thing to do with options. A post in Tradeking's forums, very old post, but with an interesting piece of data from the OCC, states that 35% of the options expire worthless, and 48% are bought or sold before expiration to close the position - only 17% of the contracts are actually exercised! (http://community.tradeking.com/members/optionsguy/blogs/11260-what-percentage-of-options-get-exercised) A few other things to keep in mind: certain stocks have ""mini options contracts"", that would correspond to a lot of 10 shares of stock. These contracts are usually not very liquid, though, so you might not get great prices when opening/closing positions you said in a comment, ""I cannot use this strategy to buy stocks like GOOGL""; if the reason is because 100*GOOGL is too much to fit in your buying power, that's a pretty big risk - the assignment could result in a margin call! if margin call is not really your concern, but your concern is more like the risk of holding 100 shares of GOOGL, you can help manage that by buying some lower strike Puts (that have smaller absolute delta than your Put), or selling some calls against your short put. Both strategies, while very different, will effectively reduce your delta exposure. You'd get 100 deltas from the 100 shares of GOOGL, but you'd get some negative deltas by holding the lower strike Put, or by writing the higher strike Call. So as the stock moves around, your account value would move less than the exposure equivalent to 100 shares of stock." "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." 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). "Consider the futures market. Traders buy and sell gold futures, but very few contracts, relatively speaking, result in delivery. The contracts are sold, and ""Open interest"" dwindles to near zero most months as the final date approaches. The seller buys back his short position, the buyer sells off his longs.  When I own a call, and am 'winning,' say the option that cost me $1 is now worth $2, I'd rather sell that option for even $1.95 than to buy 100 shares of a $148 stock. The punchline is that very few option buyers actually hope to own the stock in the end. Just like the futures, open interest falls as expiration approaches." There are a few situations in which it may be advantageous to exercise early. Wikipedia actually has a good explanation: Option Style, Difference in value To account for the American's higher value there must be some   situations in which it is optimal to exercise the American option   before the expiration date. This can arise in several ways, such as: An in the money (ITM) call option on a stock is often exercised just   before the stock pays a dividend that would lower its value by more   than the option's remaining time value.  A put option will usually be   exercised early if the underlying asset files for bankruptcy.[3]  A deep ITM currency option (FX option) where the strike currency has a   lower interest rate than the currency to be received will often be   exercised early because the time value sacrificed is less valuable   than the expected depreciation of the received currency against the   strike.  An American bond option on the dirty price of a bond (such as   some convertible bonds) may be exercised immediately if ITM and a   coupon is due.  A put option on gold will be exercised early when deep   ITM, because gold tends to hold its value whereas the currency used as   the strike is often expected to lose value through inflation if the   holder waits until final maturity to exercise the option (they will   almost certainly exercise a contract deep ITM, minimizing its time   value).[citation needed] "As already noted, options contain inherent leverage (a multiplier on the profit or loss). The amount of ""leverage"" is dictated primarily by both the options strike relative to the current share price and the time remaining to expiration. Options are a far more difficult investment than stocks because they require that you are right on both the direction and the timing of the future price movement. With a stock, you could choose to buy and hold forever (Buffett style), and even if you are wrong for 5 years, your unrealized losses can suddenly become realized profits if the shares finally start to rise 6 years later. But with options, the profits and losses become very final very quickly. As a professional options trader, the single best piece of advice I can give to investors dabbling in options for the first time is to only purchase significantly ITM (in-the-money) options, for both calls and puts. Do a web search on ""in-the-money options"" to see what calls or puts qualify.  With ITM options, the leverage is still noticeably better than buying/selling the shares outright, but you have a much less chance of losing all your premium. Also, by being fairly deep in-the-money, you reduce the constant bleed in value as you wait for the expected move to happen (the market moves sideways more than people usually expect). Fairly- to deeply-ITM options are the ones that options market-makers like least to trade in, because they offer neither large nor ""easy"" premiums. And options market-makers make their living by selling options to retail investors and other people that want them like you, so connect the dots. By trading only ITM options until you become quite experienced, you are minimizing your chances of being the average sucker (all else equal). Some amateur options investors believe that similar benefits could be obtained by purchasing long-expiration options (like LEAPS for 1+ years) that are not ITM (like ATM or OTM options). The problem here is that your significant time value is bleeding away slowly every day you wait.  With an ITM option, your intrinsic value is not bleeding out at all. Only the relatively smaller time value of the option is at risk. Thus my recommendation to initially deal only in fairly- to deeply-ITM options with expirations of 1-4 months out, depending on how daring you wish to be with your move timing." A long straddle using equity would be more akin to buying a triple leveraged ETF and an inverse triple leveraged ETF, only because one side will approach zero while the other can theoretically increase to infinity, in a short time span before time decay hits in. The reason your analogy fails is because the delta is 1.0 on both sides of your trade. At the money options, a necessary requirement for a straddle, have a delta of .5 There is an options strategy that uses in the money calls and puts with a delta closer to 1.0 to create an in the money strangle. I'm not sure if it is more similar to your strategy, an analogous options strategy would be better than yours as it would not share the potential for a margin call. If you are in the money at expiration you are going to get assigned to the person on the other side of the contract. This is an extremely high probability. The only randomness comes from before expiration. Where you may be assigned because a holder exercised the option before expiration, this can unbalance some of your strategies. But in exchange, you get all the premium that was still left on the option when they exercised. An in the money option, at expiration, has no premium. The value of your in the money option is Current Stock price - Strike Price, for a call. And Strike price - Current Stock price, for a put. Thats why there is no free lunch in this scenario. First, in the money options are scarcely created because most options trade at the money with the rest evenly distributed between in and out, so they are at best half the market when created. They are also closed before expiration. The reason is still unknown, but one theory is: Barely in the money options carry enormous exercise risk because the chance that could be turned into a potentially solvency threatening unhedged liability is great; therefore, option sellers prefer to close barely in the money options so not to take on unhedged liability risk. Statistically, option sellers are risk avoiders. I think it depends on your broker. Some brokers will not try to auto exercise in the money options. Others will try to do the exercise it if you have available funds. Your best bet, if find yourself in that situation, is to sell the option on the open market the day of or slightly before expiration. Put it on your calendar and don't forget, you could loose your profits. @#2 Its in the best interest of your broker to exercise because they get a commission. I think they are used to this situation where there is a lack of funds. Its not like bouncing a check. You will need to check with your broker on this. @#3 I think many or most options traders never intend on buying the underling stock. Therefore no, they do not always make sure there is enough funds to buy. 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. 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?