Option Theta: What conditions are needed for Theta > P/N, where P = option price, and N = days to expiration?
"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."
I'm sorry, but your math is wrong.  You are not equally likely to make as much money by waiting for expiration. Share prices are moving constantly in both directions.  Very rarely does any stock go either straight up or straight down.  Consider a stock with a share price of $12 today.  Perhaps that stock is a bad buy, and in 1 month's time it will be down to $10.  But the market hasn't quite wised up to this yet, and over the next week it rallies up to $15. If you bought a European option (let's say an at-the-money call, expiring in 1 month, at $12 on our start date), then you lost.  Your option expired worthless. If you bought an American option, you could have exercised it when the share price was at $15 and made a nice profit. Keep in mind we are talking about exactly the same stock, with exactly the same history, over exactly the same time period.  The only difference is the option contract.  The American option could have made you money, if you exercised it at any time during the rally, but not the European option - you would have been forced to hold onto it for a month and finally let it expire worthless. (Of course that's not strictly true, since the European option itself can be sold while it is in the money - but eventually, somebody is going to end up holding the bag, nobody can exercise it until expiration.) The difference between an American and European option is the difference between getting N chances to get it right (N being the number of days 'til expiration) and getting just one chance.  It should be easy to see why you're more likely to profit with the former, even if you can't accurately predict price movement. Options reflect expectations about the underlying asset, and options are commonly priced using the Black-Scholes model:  N(d1) and N(d2) are probability functions, S is the spot (current) price of the asset, K is the strike price, r is the risk free rate, and T-t represents time to maturity.  Without getting into the mathematics, it suffices to say that higher volatility or expectation of volatility increases the perceived riskiness of the asset, so call options are priced lower  and put options are priced higher. Think about it intuitively. If the stock is more likely to go downwards, then there's an increased chance that the call option expires worthless, so call options must be priced lower to accommodate the relative change in expected value of the option.  Puts are priced similarly, but they move inversely with respect to call option prices due to Put-Call parity. So if call option prices are falling, then put option prices are rising (Note, however, that call prices falling does not cause put prices to rise. The inverse relationship exists because of changes in the underlying factors and how pricing works.) So the option action signifies that the market believes the stock is headed lower (in the given time frame). That does not mean it will go lower, and option traders assume risk whenever they take a particular position. Bottom line: gotta do your own homework! Best of luck. Looking at the SPY option chain you posted, all of the call options with a strike price of 199.50 or higher have a bid of N/A.  That's because the ask price for all of those options is 0.01, and the bid price has to be less than the ask price, but buyers are not allowed to bid 0.00.  It's not accurate to say that no one wants to buy those calls - anyone who wanted to buy one of those calls would just buy it at the ask price of 0.01. So why are people selling those calls for just 0.01?  The further out of the money you go as you get closer to expiration, the less likely the underlying stock or ETF (SPY in this case) will go over the strike price, and the less you can sell it for.  SPY closed yesterday at about 195, and it would have to go up almost 2.5% today for the 199.50 calls to be in the money, and a 2.5% move in one day is extremely unlikely. I understand that ITM have little time value, so they will have small time decay(theta), but why OTM has a lesser theta than ATM? The Time value represents uncertainty.  That uncertainty decreases the farther away from ATM you get (in either direction).  At-the-money, there is roughly a 50% chance that the option expires worthless. As you get deeper in-the-money, the change that is expires worthless decreases, so there is less uncertainty (there is more certainty that the option will pay off).  As you go deeper OTM, the probability that the option expires worthless increases, so there is also less uncertainty. At the TTM decreases, the uncertainty (theta) decreases as well, since there is less time for the option to cross the strike from either direction.  Similarly, as volatility decreases, theta decreases, since low-volatility stocks have a less change of crossing the strike. "SELL -10 VERTICAL $IYR 100 AUG 09 32/34 CALL @.80 LMT 1) we are talking about options, these are a derivative product whose price is based on 6 variables. 2) options allow you to create risk out of thin air, and those risks come with shapes, and the only limit is your imagination (and how much your margin/borrowing costs are). Whereas a simple asset like the shares for $IYR only has a linear risk profile. stock goes up, you make money, stock goes down, you lose money, and that risk graph looks linear. a ""vertical"" has a nonlinear risk profile 3) a vertical is a type of ""spread"" that requires holding options that expire at the same time, but at different strike prices. 3b) This particular KIND of vertical is called a bear call spread (BCS). Since you are bearish (this makes money if the stock goes down, or stays in a very specific range) but are using calls which are a bullish options product. 4) -10 means you are selling the vertical. +10 means you are buying the vertical. A ""long"" vertical is initiated by buying an option closer to the money, and selling an option at a higher strike price. This would be +X A ""short"" vertical is initiated by selling an option closer to the money and buying an option at a higher strike price. The quantity would be -X 5) 32/34 stands for the strike prices. so you would be selling 10 call options at the 32 strike price, and buying 10 call options at the 34 strike price, both options expire in August 6) LMT stands for limit order, and $.80 is the limit order price that is desired. OPENING a vertical spread requires knowledge of options as well as how to send orders. MANAGING a vertical requires even more finesse, as you can ""leg-in"" and ""leg-out"" of spreads, without sending the entire order to the exchange floor at once. There is much to learn." One way is to compare the implied volatility with the realised volatility over a period similar to the time left to expiry. However there are plenty of reasons why the implied may be higher than the historical, for example because the market volatility has increased overall or because the underlying company is going to report their results before the option expires. An expiration 2 years out will have Sqr(2) (yes the square root of 2!) times the premium of the 1 year expiration. So if the option a year out sell for $1.00, two is only $1.41.  And if the stock trades for $10, but the strike is $12, why aren't you just waiting for expiration to write the next one? Short answer: Liquidity. Well, you have to see it from an exchange's point of view.  Every contract they put up is a liability to them.  You have to allocate resources for the order book, the matching engine, the clearing, etc.  But only if the contract is actually trading they start earning (the big) money. Now for every new expiry they engage a long term commitment and it might take years for an option chain to be widely accepted (and hence before they're profitable).  Compare the volumes and open interests of big chains versus the weeklies and you'll find that weeklies can still be considered illiquid compared to their monthly cousins. Having said that, like many things, this is just a question of demand.  If there's a strong urge to trade July weeklies one day, there will be an option chain.  But, personally I think, as long as there are the summer doldrums there will be no rush to ask for Jul and Aug chains.