No, it has to do with probabilities: since the chance for expiring ITM is the same for 1 or more of the same option, then logic tells me that one should get a "rebate" for buying more of the same very thing... But this seems to be possible only with a new, novel option design, not with the classic options.
so it is impossible with current option! what is new in that? You will have to invent a new things for that and then have the market accept it so all this is futile until then is it not
Yeah, this is just mathematical curiosity & research, nothing real yet Imagine this analog situation: in the lotto game you can chose your own numbers on the ticket. You don't increase your chance of winning when you use the same numbers say 100 times, no, the chance is exactly the same like for just one ticket. So, you are paying too much for this constant staying probability, meaning it's unfair and there should be a rebate, ie. a discount. The question is how the mathematical formula for such a discount should be. And of course: if you use different numbers on the said 100 tickets, then of course your chance of winning is 100fold, not 1fold like in the previous case. Just a mathematical question, ie. theory, but IMO an important question.
I think I've found a formula for the options scenario of the OP: Code: For an ATM option with r=q=0 (ie. S=K which also means p=0.5 for UP and DOWN) it gives: leverage_factor discount_(ie._rebate) 1 0% 2 12.5% 3 16.67% 4 18.75% 5 20% ... ... (upto max 25% possible) So, then the broker can advertise "Buy 5 of our newest option product and get 20% discount!" (in reality it's of course just 1 of these new options with 5x leverage) This of course also applies to the option writer side, but of course here the credit the gets is 20% less than with normal options. But since the payoff for the buyer is the same as with normal options, then this means it is the option writer who bears the additional risk (of the rebate he gave the buyer). Can this function? Still testing...
I don't think this is practically possible. 2 identical instruments can't be priced differently unless there is a liquidity advantage of one vs. the other. If both are identical, they should be priced the same or very close to eliminate any potential arbitrage. I remember back in the old days, I believe it was in 2007, CBOT (It was still independent at that time, not part of CME) introduced mini agricultural future contracts (For Corn, Wheat and Soybeans). The standard contract was for 5,000 bushels, the mini-contracts were for 1,000 bushels each. Everything else was exactly the same. On the day those mini-contracts started trading electronically, there was a large discrepancy in their price vs. the standard contract in the overnight electronic trading, i.e. when the pits were closed. It was a clear arbitrage opportunity and that was due to thin liquidity in those minis in the overnight electronic session. I remember very well that I spent almost 2 or 3 weeks arbitraging this until it was gone and prices finally aligned with very narrow differences where it became unprofitable when taking transaction costs into consideration. During those first 3 weeks, it was very normal to see a difference in prices of 5-6 points (That's $250-$300 per 1/5 contracts), i.e. you find ZC (standard) bid at 500 @400 and the XC (mini) offered 20 @395, it was basically free money, you buy 20 @395 and short 4 @400, that during the overnight session, and the next day when the pits open, prices align and you get out booking your profits, and so on. Moral of the story is that as long as there is something fundamental which justifies a difference in price of identical instruments, it can never happen or is not sustainable. Offer me this new option with 5x leverage at 20% discount, I will only buy it if I can offset it with by shorting 5 contracts of the 1x leverage, thus squaring my position and booking those 20% in my pocket, risk free essentially. Change the contract specs and you have a new instrument, in this case, it can be priced differently and based on the changes you do to the contract specs, you have a different pricing formula & a different price (Other things being equal). Sorry for the long post, but hope it helps.
@narafa, thx for your analysis & the anecdote. I must admit I'm not fully through thru my own analysis (b/c of some time constraints here). So, did I get you right that you mean arbitrage would be possible with this leverage construct?
Yes, absolutely. Suppose an option with a 500 shares of the underlying trading at $400 (20% discount from $500) while the same 100 shares option is trading at $100 each (All other things being equal). If the liquidity in both is good enough, anyone would simply buy 1x$400 option and short 5x$100, booking a risk free $100 (less transaction costs). In the real world, this can happen, but it will go away quickly as traders arbitrage this difference out and prices normalize. Identical instruments can only deviate in prices because of factors like liquidity, transaction costs, FX rates, etc...
@narafa, the 5x option trades very normal like 5 times the normal option (but as a 5x set). So, it has a market value of $500. Since it's a (new) special option type, you would need to sell it (the set) with the same discount to another buyer. When done as such then IMO there is no arbitrage possible. I mean: the discount is always an inherent part of such a 5x option at opening as well when closing the position before expiration. Hmm. maybe there is still something missing here... complicated stuff... system error... I need more time to analyze... Let's just try to find a solution that does not create any arbitrage at all.
There are derivative instruments available that have a different multiplier. The multiplier is smaller--not larger. But the underlying is identical. If you look at these products, you should be able to test your ideas using historical market data. Do ND futures trade at five times the price of NQ futures? Or is there some sort of discount because ND is five times the size of NQ? The CBOE has cash-settled index options on the S&P 500 that are one-tenth the contract size of SPX options. The symbol is XSP. Everything is identical except the contract size. Do SPX options trade at ten times the price of XSP options? Or is there some sort of discount because the multiplier is larger? If there is a discount, then why doesn't everyone spend all day buying one SPX contract and selling ten XSP contracts, and pocketing the difference? Don't forget to account for the commisions. You can buy one SPX option and sell ten XSP options, and have a risk-free position, but you'll may get eaten alive by the commissions on the smaller contracts. BMK