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OTM (out-of-the-money) options are cheap but even decent move can yield dramatic returns that eclipses ATM (at-the-money) or ITM (in-the-money) options, but what I don't understand is that delta and gamma is supposed to be low for OTM so what causes the giant leap in returns when price approaches the strike? Often, it doesn't even need to touch the strike but a large swing can drive up the premium.

Near expiry options (1 week let's say) are also priced cheaper, but does it contribute to the high leverage?

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    they are so thinly traded it is meaningless. try it a few times (it will cost you maybe 50, 200 bucks) and you will be massively more informed. – Fattie Feb 24 '18 at 19:13
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I have a feeling you're looking at large percentage increases which is very different that absolute increases. Delta and Gamma measure absolute changes in value per dollar of change in the underlying, not percentage changes. If a option that costs 5 cents goes up another 5 cents, that's a 100% increase, but a $1 option that goes up 5 cents is only a 5% increase. If the 5 cent option goes down 2 cents, though, it's a 40% drop.

So yes, you can see huge swings in relative returns just because the prices are so small relative to ITM options, but those swings go both ways.

The other problem is that the reason those options are so cheap is because there's very little chance that they'll be worth anything at expiration.

Note that this has nothing to do with leverage, where returns are multiplied because you borrow money to multiply the amount of money invested, it's just the mathematical phenomenon of larger percentage changes when the denominator is smaller.

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    Margin borrowing applies equities, ETFs, futures, etc. Long standard options (not LEAPs) must be paid for in full. Buying a long option does indeed provide leverage since you control 100 shares for a fraction of the cost. Even many more times so if you consider an equi-dollar purchase. – Bob Baerker Feb 25 '18 at 23:48
  • @BobBaerker No, you control the option to buy 100 shares for a small premium. You still need to buy the shares at the strike price if the option expires in the money. – D Stanley Feb 26 '18 at 2:32
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    @D Stanley: Huh? You bought the option in the option market and you can sell it in the option market. You don't have to go anywhere near the underlying. The only time you would have to buy the underlying would be if you were foolish enough to let the it expire ITM and face "exercise by exception" by the OCC. One could avoid this by designating one's broker not to exercise the contract but that would make no sense if the position's value exceeded the closing commission. – Bob Baerker Feb 26 '18 at 5:17
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but what I don't understand is that delta and gamma is supposed to be low for OTM so what causes the giant leap in returns when price approaches the strike

yeah delta and gamma and absolute returns don't exist in a vacuum

gamma is a measurement of the rate of change of the delta, and delta is the measurement of rate of change of the option price relative to the underlying asset. gamma increases the closer in the money you get, and so does delta (because of gamma) until it gets to a value of 1

I guess thats the answer?

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This is the option table for a stock that closed Friday at $175.50. These options expire this coming Friday, i.e. 5 trading days left.

enter image description here

I've been trading options for over 35 years, and never took the time to study "the greeks." What I know from this table is that the market is telling us this stock is not likely to move $5 in 5 days. If it did, your $2.15 bet on the $175 strike would go to $5.50, or a $0.95 bet on $177.50 would be a $3 return. The former is a 2.6X return vs 3.2X return for the latter. Stocks can and do move 10% in a week, but it's most often as a result of remarkable news, or earnings.

In the case of this particular stock, it's not hard to find times where a return of 10X was available for a 50% move in the stock over a longer period, 18 months.

If the current answers don't really address the question as you asked it, you should study the Black Scholes options model for the effects of time and volatility on the options price. It's all about risk, reward, and the bell curve.

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AFAIC, understanding the statistical underpinnings of Black Scholes etc. and the Greeks (other than delta) isn't relevant for most retail option traders. It's like asking someone for the time and they tell you how to build a watch :->). In this case, all you need to grasp is that options near the money benefit the most percentage wise from price change.

Let's use Joe Taxpayer's option prices for stock XYZ. Suppose one second after his pricing, XYZ jumps $2.50 with no change in implied volatility. Take the option prices and shift them down one row. I priced the missing ones. Column 1 is the strike price. Column 2 is his original call premiums. Column 3 is the new option price after a $2.50 rise in XYZ. Column 4 is the call's gain in dollars. Column 5 is the call's gain in percent. I hope this uploads properly.

XYZ = $178

175.00 2.15 3.70 $1.55 72%

177.50 0.95 2.15 $1.20 126%

180.00 0.35 0.95 $0.60 171%

182.50 0.14 0.35 $0.21 150%

185.00 0.07 0.14 $0.07 100%

187.50 0.04 0.07 $0.03 75%

190.00 0.03 0.04 $0.01 33%

As you can see, the ITM options have the larger dollar gain and the near the money have the larger percent gain.
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Suppose XYZ jumps another $2.50 (total of $5). Again, the same holds true.

175.00 2.15 5.75 $3.60 167%

177.50 0.95 3.70 $2.75 289%

180.00 0.35 2.15 $1.80 514%

182.50 0.14 0.95 $0.81 579%

185.00 0.07 0.35 $0.28 400%

187.50 0.04 0.14 $0.10 250%

190.00 0.03 0.07 $0.04 133%

Options provide leverage because you control 100 shares with a small premium, compared to the cost of the underlying. And if you compare an equi-dollar investment, it offers multiples of that (compare the returns from buying one $175 call with buying six $180 calls).

And yes, near expiry options contribute to the leverage because they have less time premium to lose as time premium decreases and intrinsic value increases as share price increases.

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