Hey guys, I’ve been looking at basic options tables and reading about them, and I wanted to better understand the theory of how the market prices the options and what benefits are being traded. Taking for example basic SPY calls; I was looking at June 2019 expirations, and if you buy an option right at the money, if the market was anywhere from negative to completely flat from here to expiration, you’d be at a 100% loss since the option is worthless at expiry. Then, there would be some sort of partial loss for the range of 0% - 10%--because the premium paid would likely be greater than the (Expiry – Strike) value. A marginally positive return on the underlying still nets a loss because the option doesn’t just provide exposure; you’re also buying leverage, paying cost of carry, and especially buying the possibility of outsized returns if the market were to go further into a positive return. [That’s not because of delta, which decreases when you start to come out from deep ITM. This specific metric means the option value actually fluctuates less when the underlying moves at first because it may expire worthless. The potential of greater returns come from realized gamma? Or just a function of leverage? I’m probably the most fuzzy on understanding gamma.] Tangent aside, I noticed once you get about ~30% ITM the call prices pretty much start to approach [Present Value – Strike]. This is because of increasing delta as the chance of the option expiring OTM becomes less and less. As delta approaches one, do things get simpler and we’re pretty much buying leveraged exposure to the underlying? Is there a premium priced into the value of deep ITM options for the benefit of having a fixed total loss and no direct cost of carry for a leveraged position, which is superior to a leveraged long? In theory, what is the expected value of continually buying a single deep ITM call on the SPY year after year? Should it average out close to the returns of SPY itself? Or greater from the leverage yet with more volatility and the inability to compound because you can/will eventually hit a year where even 30% ITM expires worthless? Or less because you get net returns less the cost of benefits provided from the option? Sorry if this is a bit of a ramble; trying to get my head around some conceptuals and would like to dive into this basic example of SPY calls to understand a few of these components intrinsic to options.

Here are the answers to your questions: https://en.wikipedia.org/wiki/Greeks_(finance)#/media/File:Why_is_long_option_Gamma_positive.png

It depends on how far ITM it is... since that basically determines the leverage factor. If you go all-in, and buy 100 calls @50 or 50 @100... the return on average when SP500 goes up is obviously bigger with the 10 calls@50... since you have more. And if you would compare it to 2x SP500 (since that would be the same value)... than obviously the 2 x SP500 would be returning the least... since it's not leveraged. 100 calls give you 50x the SP500 in this example. 50 calls give you 25x... But that also means the downside is the same (up until a point).

Thanks for the material guys, it was informative to learn gamma is a second order Greek tied to delta, still have more to learn but I think maybe the Greeks were over complicating my questions.. So basically from what you're saying Jack, the leverage factor mostly prevails for the returns given by the calls. I can think of other benefits given by calls such as known and limited downside and having leveraged position but no interest payments, but those are marginal costs for the most part? Or even sort of offset by the risk of OTM expiration buyer is taking on even if it's minimal? Basically though options are deep ITM enough they behave more like a leveraging the underlying, since they move with the underlying and time decay is less relevant because their money was really isn't in question, if I'm understanding correctly. Thanks again for the explanations.

If you have 100.000 to spend and you can put it in SP500 or 20x ITM worth 50, or 5x call worth 200. So most leveraged is the 20x call worth $50. If SP500 goes up 1%, that's 25 points... that's +1k for the index investing (+1%), +50k for the 20x call, since with delta 100 goes up to 75 (+50%) and +12.5k for the other one... So more leverage always mean higher return... but only if you're right. If you're wrong... 2% down and you'll be losing everything in that 20x call... So I guess it comes down to your own skills of predicting the market, please don't think this is a great strategy... it will most definitely cost you dearly at one point in time. So don't over-leverage! Stocks have a known limited downside as well... at zero. Same with your calls... also at zero.. so it depends on how much you put into it... both can go to zero. Regarding the no-interest payments, nope... you're wrong... you're paying interest on those calls because they are priced on the basis of forward pricing with an interest rate component.

Yeah, agreed leverage doesn't make any strategy better per se, just boosts the magnitude of returns in both directions. Also noted about interest costs being priced into options. I figured when we buy options we're paying for a number of different things; not at the point of strategy design yet but mainly trying to understand what those things are and how they fluctuate. Seems deeper ITM is less complex because it behaves more like the underlying.. but as you say options lever up as they go more OTM and your model/strategy needs to be more precise to get good returns. Thanks for taking some time to help me get a grasp on the basics, this discussion will help going forward as I try to keep reading and learning.