x time Leveraged Option

thecoder

thecoder

Mathematical question:
Can there exist options that offer x time leverage over a single unit of that same option, but does cost less than x time of the single unit option?

For example 2x leverage: How to do it other than buying twice of the same option?
Ie. IMO such an option should be cheaper than buying 2 regular options.
How could the maths for this look like?
Is there maybe a synthetic construct possible for this, or maybe a new kind of option?
 
thecoder said:
Mathematical question:
Can there exist options that offer x time leverage over a single unit of that same option, but does cost less than x time of the single unit option?

For example 2x leverage: How to do it other than buying twice of the same option?
Ie. IMO such an option should be cheaper than buying 2 regular options.
How could the maths for this look like?
Is there maybe a synthetic construct possible for this, or maybe a new kind of option?
More...


You could do it locally ... say with call options
... Buy 1 x 100 strike call
... v Buy 2 x 100 - 110 strike call spreads at same price as outright call

Requires 100 - 110 call 1x2 spread to trade at Par or better
 
jamesbp said:
You could do it locally ... say with call options
... Buy 1 x 100 strike call
... v Buy 2 x 100 - 110 strike call spreads at same price as outright call

Requires 100 - 110 call 1x2 spread to trade at Par or better
More...
May I ask you to create that construct online at https://www.optioncreator.com/
and save it and then post the generated link here? Thanks.
 
Technically, options do not provide leverage as they have to be fully paid for. That said, if you buy an ITM call that is a high delta, you can compare the money required to be long to the stock price and get more than 2X. E.g. AAPL closed at 115.35. The Sep 18 100 calls closed around 15.40 and have near 100 Delta. That is 13.3% of the stock price with the same upside and limited downside and about 7.50X leverage.
 
thecoder said:
Mathematical question:
Can there exist options that offer x time leverage over a single unit of that same option, but does cost less than x time of the single unit option?

For example 2x leverage: How to do it other than buying twice of the same option?
Ie. IMO such an option should be cheaper than buying 2 regular options.
How could the maths for this look like?
Is there maybe a synthetic construct possible for this, or maybe a new kind of option?
More...

The leverage you get in options is based on how many units/shares the option controls of the underlying instrument (Typically 100 shares for equity options) and the price you pay for the option itself.

In order to increase your leverage, you need to find an option with a higher multiplier or with a lower price or both. An option with a lower price always exists if you move further OTM. This increases your leverage when compared to the amount you pay per option contract, however, you get worse probabilities, but that's something else.

Since your question is mainly about an identical option giving more leverage at a lower price, so changing strikes is ruled out, leaving you only with finding a higher multiplier option, which for exchange traded standardized options, do not exist as we speak.

One way of achieving a higher leverage through options is to trade options on already leveraged instruments, e.g. option on leveraged ETFs. For example, options on SPXL (3x Bull S&P500 ETF) would typically still control 100 shares of the ETF, but it gives you more leverage because the underlying ETF is leveraged.
 
@narafa, @Robert Morse and all the other responders, thank you very much for your valuable input so far.

I wonder whether one could design such new option types... Just thinking aloud... But since it has IMO to be cheaper than the premium of x times of the normal single option, I don't have any idea yet which mathematical method would best suit this, but I think there should one exist or waiting to be discovered...
 
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I think for this I need to study Game Theory:
https://en.wikipedia.org/wiki/Game_theory

Btw, I think I found a good news article that maybe could help here, but unfortunately it blocks access from Europe :-(
Could someone in the US please copy&paste that article here into a posting, thx :

This is what the search engine shows:

Statisticians question logic of buying multiple lottery tickets as ...
11 Jan 2016 ... Buying multiple $2 tickets in the multistate game may seem logical, but it represents a misunderstanding of the towering odds against claiming the biggest ... "Even after buying 100 tickets, you are still three times more likely to ...
 
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As the world's richest lottery jackpot swelled to $1.5 billion, retailers reported customers trying to improve their odds by buying Powerball tickets in bulk — a practice many statisticians believe defies sound reasoning.

"People are buying five tickets, 10 tickets — one guy bought like 500 tickets," said Indra Katuwal, owner of the BP gas station on Hanover Street in Federal Hill. "People used to buy just one or two."

People are drawn to play against the unfathomable odds by what's become a world record lottery prize. The current Powerball game began Nov. 4 and — despite Wednesday and Saturday drawings — has rolled over since nobody has won.

It's hard not to fantasize about winning. Besides, the thinking goes, someone will win eventually.

The Maryland Lottery's roughly 4,600 retailers sold $11.2 million in Powerball tickets Saturday. That compares with daily sales just two weeks ago of $284,097.

Buying multiple $2 tickets in the multistate game may seem logical, but it represents a misunderstanding of the towering odds against claiming the biggest prize, said Ronald Wasserstein, executive director of the Virginia-based American Statistical Association.

Purchasing 10, 100 or even 1,000 tickets in a game in which the odds are 1 in 292 million "increases your relative chance, but your absolute chance is tiny — so tiny that people don't grasp it," Wasserstein said.

Even increasing your chances 50-fold leaves the possibility of winning "so ridiculously, unimaginably small that it's just a 50-fold waste of money," he said.

In Saturday's drawing, there was one $1 million winner and three $150,000 winners in Maryland (and many lesser prizes), but nobody hit the jackpot even though 78 percent of all possible number combinations were played around the country. That number, called "coverage," is expected to increase to 80 percent for the next drawing on Wednesday night, state lottery officials said.

The jackpot was so alluring that state lottery employees were playing outside the state. They're not permitted to buy tickets in Maryland, so some were buying them in the District of Columbia and Pennsylvania, agency officials said.

The $1.5 billion jackpot resulted in part from some tinkering with Powerball's odds last year by the game's managers. This purse is now so large that many electronic billboards around the state read "$999 million" because the signs aren't configured to reach higher.

Outside a 7-Eleven convenience store in Kensington, a bright-red digital Powerball sign incorrectly read "1 million," but that didn't stop customers from lining up at midday.

Catherine Rasa, a nurse, said she has bought about 30 tickets for herself and her family recently. She seemed to understand that buying so many tickets didn't improve her odds in a significant way.

"I heard that really isn't true, but I do it anyways," she said, smiling.

It's easy to understand why players might splurge on tickets, experts said.

"But if you buy 100 tickets — which will cost you $200 — your odds are still only 1 in 2,920,000," said George Loewenstein, an economics and psychology professor at Carnegie Mellon University. "Even after buying 100 tickets, you are still three times more likely to get killed by lightning in the next year, and about 300 times more likely to get killed in an auto crash."

One problem, Wasserstein said, is that "thinking about large numbers is very unnatural for us. You could imagine yourself at a Ravens game and they're going to pick one seat at halftime to receive a free ticket to the Super Bowl. You could look around and see how likely it is that you're going to be picked. But we can't visualize 292 million of anything.

"From the standpoint of being a statistician, I think there is sort of a fundamental misunderstanding about the probability associated with competition like the lottery," he said.

The current jackpot for Wednesday's drawing has an $930 million cash option. If a Marylander wins and chooses the cash option, they will net $616.1 million. Maryland's share in taxes would be $75.9 million.

The heightened media focus concerns experts helping people with gambling issues, said Loreen Rugle, program director of the Maryland Center of Excellence on Problem Gambling.


"It makes it a challenge for folks in recovery," Rugle said. "It's the buying of hope, and the real benefit is in the place between when I buy that ticket and when they do the drawing," she said. "For folks with a gambling problem, that's where they want to live. It's the fantasy that this will make everything better."

Lottery spokeswoman Carole Everett said the agency "always encourages people to play responsibly. We promote responsible gambling in lots of places."

There is messaging on tickets, a graphic on the website of the Maryland Lottery and Gaming Control Agency and information on the monitors at retail locations around the state.

"The lottery is still all about entertainment," said Dr. Timothy Fong, a psychiatrist who is co-director of the UCLA Gambling Studies Program. "That's what it's supposed to be for. The cautionary tale is if people say, 'This isn't entertainment, it's a way of life, it has to happen.'"

The Powerball jackpot is won by matching the numbers on five white balls — drawn from 69 total — in any order and the red Powerball. The jackpot can be paid over 29 years or in a lump-sum cash payment. Lottery officials say most players use "quick pick," in which their numbers are randomly selected at their retailer.

To increase the game's flagging popularity, Powerball managers tweaked the game in October to boost the chances of producing tantalizing, giant jackpots as well as to offer more wins of secondary prizes.

Under the change, the chances of winning the biggest prize went to 1 in 292 million from 1 in 175 million. But the odds of winning any prize were boosted from 1 in 32 to 1 in 25.

Prior to the changes, Powerball sales had waned in the state, which officials attributed partly to the popularity of instant games, or "scratch-offs," because players don't need to wait for a drawing to learn if they won, and to some so-called "jackpot fatigue." Many players seemed indifferent until the potential payout rose to astronomical levels.

Instant tickets, which cost from $1 to $20, offer relatively high average payouts — from about 59 percent of sales for a $1 ticket to nearly 78 percent for a $20 ticket. That compares to anticipated payouts of 50 percent for Powerball.

But Powerball's big jackpots can be captivating.

"The good reason to buy a Powerball ticket is to give you a cheap license to dream a little bit," Loewenstein said. "If the dream isn't much better when you buy 100 tickets than when you buy one, it probably is a mistake to buy the bunch."

jebarker@baltsun.com
 
thecoder said:
Mathematical question:
Can there exist options that offer x time leverage over a single unit of that same option, but does cost less than x time of the single unit option?

For example 2x leverage: How to do it other than buying twice of the same option?
Ie. IMO such an option should be cheaper than buying 2 regular options.
How could the maths for this look like?
Is there maybe a synthetic construct possible for this, or maybe a new kind of option?
More...

Are you saying that if you buy 2 options of same strike price and expiry instead of 1 the seller should sell them to you for a cheaper price becasue you are buying double the qty?
If so Why would the seller would sell it a cheaper price his risk in selling remains same per unit
may be I got your question wrong!
 
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