Why Gamma is highest for an option that is at the money
Yes, you've got it right.  The change in price is less meaningful as the instrument is further from the price of the underlying.  As the delta moves less, the gamma is much less. Gamma is to delta as acceleration is to speed.  Speed is movement relative to X, and acceleration is rate of change in speed.  Delta is movement relative to S, and gamma is the rate of change in delta. Delta changes quickly when it is around the money, which is another way of saying gamma is higher.  Delta is the change of the option price relative to the change in stock price.  If the strike price is near the market price, then the odds of being in or out of the money could appear to be changing very quickly - even going back and forth repeatedly. Gamma is the rate of change of the delta, so these sudden lurches in pricing are by definition the gamma.  This is to some extent a little mundane and even obvious.  But it's a useful heuristic for analyzing prices and movement, as well as for focusing analyst attention on different pricing aspects. You've got it right.  If delta is constant (zero 'speed' for the change in price) then gamma is zero (zero 'acceleration').
None of your options seem mutually exclusive.  Ordinarily nothing stops you from participating in your 401(k), opening an IRA, qualifying for your company's pension, and paying off your debts except your ability to pay for all this stuff.  Moreover, you can open an IRA anywhere (scottrade, vanguard, etrade, etc.) and freely invest in vanguard mutual funds as well as those of other companies...you aren't normally locked in to the funds of your IRA provider. Consider a traditional IRA.  To me your marginal tax rate of 25% doesn't seem that great.  If I were in your shoes I would be more likely to contribute to a traditional IRA instead of a Roth.  This will save you taxes today and you can put the extra 25% of $5,500 toward your loans.  Yes, you will be taxed on that money when you retire, but I think it's likely your rate will be lower than 25%.  Moreover, when you are retired you will already own a house and have paid off all your debt, hopefully.  You kind of need money now.  Between your current tax rate and your need for money now, I'd say a traditional makes good sense.  Buy whatever funds you want.  If you want a single, cheap, whole-market fund just buy VTSAX.  You will need a minimum of $10K to get in, so until then you can buy the ETF version, VTI.  Personally I would contribute enough to your 401(k) to get the match and anything else to an IRA (usually they have more and better investment options).  If you max that out, go back to the 401(k). Your investment mix isn't that important.  Recent research into target date funds puts them in a poor light. Since there isn't a good benchmark for a target date fund, the managers tend to buy whatever they feel like and it may not be what you would prefer if you were choosing.  However, the fund you mention has a pretty low expense ratio and the difference between that and your own allocation to an equity index fund or a blend of equity and bond funds is small in expectation.  Plus, you can change your allocation whenever you want. You are not locked in. The investment options you mention are reasonable enough that the difference between portfolios is not critical.  More important is optimizing your taxes and paying off your debt in the right order. Your interest rates matter more than term does. Paying off debt with more debt will help you if the new debt has a lower interest rate and it won't if it has a higher interest rate.  Normally speaking, longer term debt has a higher interest rate.  For that reason shorter term debt, if you can afford it, is generally better.  Be cold and calculating with your debt.  Always pay off highest interest rate debt first and never pay off cheap debt with expensive debt. If the 25 year debt option is lower than all your other interest rates and will allow you to pay off higher interest rate debt faster, it's a good idea.  Otherwise it most likely is not.  Do not make debt decisions for psychological reasons (e.g., simplicity).  Instead, always chose the option that maximizes your ultimate wealth. Differences in liquidity explain why American-style options are generally worth more than their European-style counterparts. As far as I can tell, no one mentioned liquidity in their answer to this question, they just introduced needlessly complex math and logic while ignoring basic economic principles. That's not to say the previous answers are all wrong - they just deal with periphery factors instead of the central cause.  Liquidity is a key determinant of pricing/valuation in financial markets. Liquidity simply describes the ease with which an asset can be bought and sold (converted to cash). Without going into the reasons why, treasury bills are one of the most liquid securities - they can be bought or sold almost instantly at any time for an exact price. The near-perfect liquidity of treasuries is one of the major reasons why the price (yield) of a t-bill will always be higher (lower yield) than that of an otherwise identical corporate or municipal bond. Stated in general terms, a relatively liquid asset is always worth more than an relatively illiquid asset, all else being equal.  The value of liquidity is easy to understand - we experience it everyday in real life. If you're buying a house or car, the ability to resell it if needed is an important component of the decision. It's the same for investors - most people would prefer an asset that they can quickly and easily liquidate if the need for cash arises.  It's no different with options. American-style options allow the holder to exercise (liquidate) at any time, whereas the buyer of a European option has his cash tied up until a specific date. Obviously, it rarely makes sense to exercise an option early in terms of net returns, but sometimes an investor has a desperate need for cash and this need outweighs the reduction in net profits from early exercise.  It could be argued that this liquidity advantage is eliminated by the fact that you can trade (sell) either type of option without restriction before expiration, thus closing the long position. This is a valid point, but it ignores the fact that there's always a buyer on the other side of an option trade, meaning the long position, and the right/restriction of early exercise, is never eliminated, it simply changes hands. It follows that the American-style liquidity advantage increases an options market value regardless of one's position (call/put or short/long). Without putting an exact number on it, the general interest rate (time value of money) could be used to approximate the additional cost of an American-style option over a similar European-style contract. If we assume constant volatility, gamma increases as the stock gets closer to the strike price. Thus, delta is increasing at a faster rate as the stock reaches closer to ITM because gamma is the derivative of delta. As the stock gets deeper ITM, the gamma will slow down as delta reaches 1 or -1 (depends if a call or a put). Thus, the value of the option will change depending upon the level of the delta. I am ignoring volatility and time for this description.  See this diagram from Investopedia: Gamma "Simple answer: Breakeven is when the security being traded reaches a price equal to the cost of the option plus the option's strike price, assuming you choose to exercise it. So for example, if you paid $1.00 for,say, a call option with a strike price of $19.00, breakeven would be when the security itself reaches $20.00.  That being said, I can't imagine why you'd ""close out a position"" at the breakeven point.  You wouldn't make or lose money doing that, so it wouldn't be rational. Now, as the option approaches expiration, you may make adjustments to the position to reflect shifts in momentum of the stock.  So, if it looks as though the stock may not reach the option strike price, you could close out the position and take your lumps.  But if the stock has momentum that will carry it past the strike price by expiration, you may choose to augment your position with additional contracts, although this would obviously mean the new contracts would be priced higher, which raises your dollar cost basis, and this may not make much sense. Another option in this scenario is that if the stock is going to surpass strike price, it might be a good opportunity to buy additional calls with either later expiration dates or with higher strike prices, depending on how much higher you speculate the stock will climb.  I've managed to make some money doing this, buying options with strike prices just a dollar or two higher (or lower when playing puts), because the premiums were (in my opinion) underpriced to the potential peak of the stock by the expiration date.  Sometimes the new options were actually slightly cheaper than my original positions, so my dollar cost basis overall dropped somewhat, improving my profit percentages." He can buy at 69.95 or 69.70 or whatever because he already has all the shares. The HFT bought at a cheaper price earlier. The HFT has all the shares. Now he's testing the guy who won't go above 70.00 with small orders. When he sees that this guy is willing to buy 10 at 70.00 the HFT makes a limit order of all the shares in the market at 70.00 when he got them all already at 69.95.  Whatever doesn't get bought up goes back into the market at the price the HFT originally bought at. The HFT was in line ahead of the guy who won't go above 70.00 as soon as he saw him buying. Like at the horse race, remember? An option is freely tradable, and all options (of the same kind) are equal. If your position is 0 and you sell 1 option, your new position in that option is -1. If the counterparty to your trade buys or sells more options to close, open, or even reopen their position afterwards, that doesn't matter to your position at all. Of course there's also the issue with American and European Options. European Options expire at their due date, but American Options expire at their due date or at any time before their due date if the holder decides they expire. With American Options, if a holder of an American Option decides to exercise the option, someone who is short the same option will be assigned as the counterparty (this is usually random). Expiry is after market close, so if one of your short American Options expires early, you will need to reopen the position the next day. Keep in mind dividends for slightly increased complexity. American and European Options do not in any way refer to the continents they are traded on, or to the location of the companies. These terms simply describe the expiry rules. 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. There are some excellent responses to this question at the time of this post. I have had the greatest success writing 1-month options. The 2 main reasons are as follows: With little time to expiration as stated in the question the implied volatility of the option is dictating the premium. Looking for the highest premiums is a mistake because you are taking a conservative strategy and re-creating it into a high-risk strategy. My sweet spot is a 2-4% monthly return for my initial profit and then mastering management techniques to protect that return and even enhancing it.