Profitaker
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This thread created for sensible debate and reasoned argument as to whether one side of the fence (buyer / writer) has any inherent "edge" or "advantage".
Best Thread The Options edge (Writing Vs Buying)
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Profitaker
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Correct.JonnyT said:
I'll post something up later as to why this is the case.
Profitaker
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Options trading is often likened to gambling and casinos, with option buyers being labeled the gamblers and option sellers likened to being the casino or “house”. This is a false and arrogant analogy, and I’ll explain why.
Just like in the world of casinos, options trading is a game of probabilities. To illustrate this let’s take a balanced six sided dice, where the probability of any of the numbers 1 thru to 6 coming up is the exactly the same i.e. a uniform distribution. Let’s assume that whatever number comes up is your monetary payout, so if you landed a 5 for example, you’d receive a payout of £5. What would be a fair price to pay for a throw of the dice ? The “fair value” is defined as being the price at which, over many throws, you would neither win or lose but break-even, in other words the expectancy is zero. This “fair value” is easily calculated by adding all the payoffs and dividing by the number of possibilities which in the case of the six sided dice is 1+2+3+4+5+6 / 6 = 3.5. So if you bought (or sold) the bet for £ 3.50 you would neither win or lose but break-even - no edge – no advantage, in the long run. However If you could buy the bet for less than £ 3.50 you’d have an edge, or if you could sell the bet for more than £ 3.50 you’d have an edge. But buy OR sell this bet at fair value (£ 3.50) - no edge – no advantage.
What about a Call option on (say) the number 5, which pays out £ 5 if the number 5 lands. What’s it fair value ? Again, add the payoffs and divide by the number possibilities. In this case the fair value of a Call option on the number 5 is…. 5 / 6 = £ 0.83 3 recurring. So if the number 5 Call option is bought (or sold) for £ 0.83 you’ll neither win or lose in the long run but break-even – no edge – no advantage. If however, you could buy this option for less than £ 0.83 you’d have an edge, or if you could sell this option for more than £ 0.83 you’d have and edge. But buy OR sell this option at fair value (£ 0.83) - no edge – no advantage.
This simple probability concept above applies to pricing options too. However, whereas a 6-sided dice has a “uniform” distribution, stock and commodity asset prices have a “normal” distribution. Simple put, a normal distribution means that the probability of asset price change reduces as we move away from the mean (average) price. In other words a 1% price change is more likely than a 2% price change, and a 2% price change is more likely than a 3% price change and so on.
Calculating probabilities for the “normal distribution” is a rather more complex, but we can use the well known “Black Scholes" model to work them out. I can’t be bothered to explain in any detail the mechanics of the BS equation, but I can simply say that, just like in the dice example above, the equation adds up all the possible payouts and divides by the number of possibilities and calculates the fair value or theoretical value (ThVal) of any option. However, and this is critical, we must input an implied volatility figure into the model. This should be the future volatility of the underlying asset. If we can get that future volatility forecast right and use that figure as the implied volatility in our model, then we can calculate the ThVal of any option. And by selling options trading for more than ThVal and buying those trading at less than ThVal we have an edge, and over the long run will make certain profits.
However, and this is even more critical, future volatility cannot be known in advance. Nobody knows how to calculate future volatility, and they never will. So whenever you look at a particular option trading in the market, you cannot know whether the edge lies in buying or selling it. Only when the option expires can you then look back at volatility in the underlying and comparing that figure with the implied volatility of the option. Then, and only then, can you say with certainty who had the edge.
So in conclusion, where option implied volatility is different from historic volatility (as is almost always the case) one party (writer / buyer) will have had an edge BUT this cannot be known until the option expires.
Sometimes the writer has the edge, sometimes the buyer has the edge, but over the long run neither writer nor buyer has any inherent edge.
A word on “edge”. We all know who has the edge when walking into a casino, but we also know that you can still win a fortune from the casino despite their edge. Similarly if you own a Casino you can lose a fortune, despite your having an edge. Having an edge is no guarantee of profits in the short term, only the long term.
Sensible comments ?
Just like in the world of casinos, options trading is a game of probabilities. To illustrate this let’s take a balanced six sided dice, where the probability of any of the numbers 1 thru to 6 coming up is the exactly the same i.e. a uniform distribution. Let’s assume that whatever number comes up is your monetary payout, so if you landed a 5 for example, you’d receive a payout of £5. What would be a fair price to pay for a throw of the dice ? The “fair value” is defined as being the price at which, over many throws, you would neither win or lose but break-even, in other words the expectancy is zero. This “fair value” is easily calculated by adding all the payoffs and dividing by the number of possibilities which in the case of the six sided dice is 1+2+3+4+5+6 / 6 = 3.5. So if you bought (or sold) the bet for £ 3.50 you would neither win or lose but break-even - no edge – no advantage, in the long run. However If you could buy the bet for less than £ 3.50 you’d have an edge, or if you could sell the bet for more than £ 3.50 you’d have an edge. But buy OR sell this bet at fair value (£ 3.50) - no edge – no advantage.
What about a Call option on (say) the number 5, which pays out £ 5 if the number 5 lands. What’s it fair value ? Again, add the payoffs and divide by the number possibilities. In this case the fair value of a Call option on the number 5 is…. 5 / 6 = £ 0.83 3 recurring. So if the number 5 Call option is bought (or sold) for £ 0.83 you’ll neither win or lose in the long run but break-even – no edge – no advantage. If however, you could buy this option for less than £ 0.83 you’d have an edge, or if you could sell this option for more than £ 0.83 you’d have and edge. But buy OR sell this option at fair value (£ 0.83) - no edge – no advantage.
This simple probability concept above applies to pricing options too. However, whereas a 6-sided dice has a “uniform” distribution, stock and commodity asset prices have a “normal” distribution. Simple put, a normal distribution means that the probability of asset price change reduces as we move away from the mean (average) price. In other words a 1% price change is more likely than a 2% price change, and a 2% price change is more likely than a 3% price change and so on.
Calculating probabilities for the “normal distribution” is a rather more complex, but we can use the well known “Black Scholes" model to work them out. I can’t be bothered to explain in any detail the mechanics of the BS equation, but I can simply say that, just like in the dice example above, the equation adds up all the possible payouts and divides by the number of possibilities and calculates the fair value or theoretical value (ThVal) of any option. However, and this is critical, we must input an implied volatility figure into the model. This should be the future volatility of the underlying asset. If we can get that future volatility forecast right and use that figure as the implied volatility in our model, then we can calculate the ThVal of any option. And by selling options trading for more than ThVal and buying those trading at less than ThVal we have an edge, and over the long run will make certain profits.
However, and this is even more critical, future volatility cannot be known in advance. Nobody knows how to calculate future volatility, and they never will. So whenever you look at a particular option trading in the market, you cannot know whether the edge lies in buying or selling it. Only when the option expires can you then look back at volatility in the underlying and comparing that figure with the implied volatility of the option. Then, and only then, can you say with certainty who had the edge.
So in conclusion, where option implied volatility is different from historic volatility (as is almost always the case) one party (writer / buyer) will have had an edge BUT this cannot be known until the option expires.
Sometimes the writer has the edge, sometimes the buyer has the edge, but over the long run neither writer nor buyer has any inherent edge.
A word on “edge”. We all know who has the edge when walking into a casino, but we also know that you can still win a fortune from the casino despite their edge. Similarly if you own a Casino you can lose a fortune, despite your having an edge. Having an edge is no guarantee of profits in the short term, only the long term.
Sensible comments ?
A Dashing Blade
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Profitaker said:
1) No they're not. They have a leptokurtotic distribution (ie "fat -tailed") which means that extreme events happen far often than a normal distribution would predict.
2) Furthermore, price changes seem to have a "memory" ie sharp moves tend to be followed by further sharp moves. Again, this shouldn't happen (price changes are assumed to be uncorrelated)
3) In practice, when extreme "**** hits the fan" events (crash in '87, Asian meltdown 97/8) occur (which they do) the market rules regarding margin etc change (formally or informally) eg margin requirement are tightened up by the echange, there is a "flight to quality" on the underlying (eg the exact 10 year Bond rather than the 9 year) etc.
So, at the end of the day, I don't think either buyer or writer has an edge . . .
Given Black & Scholes assumptions (uncorrelated and discreet moves, constant interest rates, constant volatility etc) I think the writer has the edge, essentially because
a) the "time value" componant of an optons's premium is a wasting asset and the written premium can always be rolled back if the position goes deeply itm
and
b) (and more contentiously) implied vol componant of an options premium contains the probability that the underlying can move up or down. However, a call buyer for example, only wishes to puchase the probability that the underlying will rise in value.
However, points 1, 2 and 3 imply to me that premium writers will always be caught out by extreme moves sooner or later no matter how deep their pockets.
Chances in a million happen nine times out of ten in finacial markets!
Just my observations for what they're worth.
Profitaker
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DB – good post ! More like that needed.
1) leptokurtotic is not a distribution, it’s a higher moment of the normal distribution. Where the value of Kurtosis is more than 3 it’s said to be Leptokurtic, less than 3 Platykurtic. Kurtosis of 3 describes a normal distribution – and very few distributions are perfectly normal.
2) You seem to be describing increasing volatility ?
3) Good point and agreed. But it’s more of a practical consideration as you say.
a) Being able to buy back a short option position and then simultaneously sell another (roll) has no bearing on edge. An option buyer has the ability to roll too.
b) All probabilities and outcomes are considered in any model. I don’t quite follow what you’re saying ?
1) leptokurtotic is not a distribution, it’s a higher moment of the normal distribution. Where the value of Kurtosis is more than 3 it’s said to be Leptokurtic, less than 3 Platykurtic. Kurtosis of 3 describes a normal distribution – and very few distributions are perfectly normal.
2) You seem to be describing increasing volatility ?
3) Good point and agreed. But it’s more of a practical consideration as you say.
a) Being able to buy back a short option position and then simultaneously sell another (roll) has no bearing on edge. An option buyer has the ability to roll too.
b) All probabilities and outcomes are considered in any model. I don’t quite follow what you’re saying ?
A Dashing Blade
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Profitaker said:
But wouldn't the option buyer would have to go to a higher (call) or lower (put) strike to do it for evens, it seems to me that the writer has far more flexibility . . .
Profitaker
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No it's the other way around - call buyer would move to a lower strike, put buyer would move to a higher strike if the underlying went against him. Buyer is moving his strike towards the underlying, writer is moving his strike away from the underlying - it's exactly the same but in reverse - no edge there. Flexibility (?) don't see how or why.A Dashing Blade said:
A Dashing Blade
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Profitaker said:
It's a point Chick Goslin explicitly and, I believe George Soros implicitly make.
A call buyer, for instance, should only have to pay for the chance that the underlying will rise.
It seems to be that embedded within the volatility part of the premium is also the chance that the underlying will fall as all (ie up and down) price movements are used to calculate implied vol.
Caveat : quants that I explain this to think I'm talking mathematical b*ll**ks but then they are the people who spend months trying to model the smile
Good post both profittaker and BD!
If the market has indeed a normal distribution and let us assume that is does, this
would mean that the chance the market moves up an x amount is exactly the same as the
market moves down an x amount.
Knowing this, we would expect a call option with a strike being x points OTM should be worth
exactly the same as a put being x points OTM. However, in reality, put and call options which are equally OTM are almost always priced differently, especially after a big move up or down.
If the market has a normal distribution I'd say that the buyer of the cheaper priced option and the seller of the higher priced option both have the advantage against the counterparties.
Any comments?
If the market has indeed a normal distribution and let us assume that is does, this
would mean that the chance the market moves up an x amount is exactly the same as the
market moves down an x amount.
Knowing this, we would expect a call option with a strike being x points OTM should be worth
exactly the same as a put being x points OTM. However, in reality, put and call options which are equally OTM are almost always priced differently, especially after a big move up or down.
If the market has a normal distribution I'd say that the buyer of the cheaper priced option and the seller of the higher priced option both have the advantage against the counterparties.
Any comments?
Profitaker
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BD - I need to think about that (struggling so far).
Absolutely agree ! So that then begs the question.... is the vol skew justified ? Or put another way, is the distribution normal ?giodan said:
A Dashing Blade
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Profitaker said:
Sorry, wasn't making myself clear.
Lets say I've purchased a call but that the underlying (and obviously time) have gone against me.
To avoid an injection of new money and to maintain exposure to the underlying, I have to sell the near dated option to finance the purchase of a longer dated. However, the strike of the latter has to be higher than that of the former as, ceteris parabus, the further away expiry, the greater an options premium (apart from deeply in the money european puts where carrying costs are greater than holding benefits).
Thus, the call buyer's choices are limited to always rolling back into a higher strike. Or am I totally missing the point?
A Dashing Blade
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Profitaker said:
Nay, nay and thrice nay!!
And therein lies the rub, my understanding is that even post-Garch modelling is simply a "hack" of the normal distribution model.
Mandelbrot, in his new paperback, makes the point that, assuming a normal distribution, even if one had one been trading every day since the big bang, one would not have anticapted the 10% intra-day move in the Mexican peso (one of the Latins anyway) back in 1998.
Profitaker said:
Interesting... I'm not sure.
The distribution can't be perfectly normal, as it needs to be adjusted a bit for interest.
If the interest is high, then chances are higher that the market moves up more than it moves down over an x period. This can't be the reason for the different pricing between calls and puts which are equally OTM though, otherwise calls would always be higher prices than puts when equally OTM which is not the case in reality.
But what's more interesting is, that even if the distribution is not normal, but it does is symmetrical, the puts and calls equal amount OTM should still be priced equally. That means that even if chances for extreme events at both ends of the scale are higher than normal distribution suggests, it still is no reason why options with an equal probability of becoming ITM should be priced differently.
I think there are 2 possibilities.
1. The price difference is not justible and there's is an advantage for one party
2. The distribution is not symmetrical or fixed and thus changes continually.
What do you think?
Profitaker
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Yes I agree a writer would get a credit to roll, a buyer gets a debit. Perhaps it’s easier to think of it as two separates trades whereby the closing of one trade is the crystallizing of a loss, and has nothing to do with whatever the next trade is going to be.A Dashing Blade said:
Only if he was after a nil debit roll then yes, but in that case he wouldn’t then maintain the same exposure (he would have a lower gamma).A Dashing Blade said:
I see no advantage for a writer in rolling Vs a buyer, except possibly the physiological effect of the writer receiving premium and feeling that he hasn't really lost the trade.
Back soon.....
Profitaker
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Totally agree. Certainly in the FTSE100 options market there is probably a lot of natural hedging with long OTM puts which gives a steeper Vol skew than is really justified. However, you’ve got to go quite away from the money (and lower strikes) to get the real fat IV. And shorting those, with the poor liquidity and massive leverage isn’t for me.giodan said:
I think a lot is down to individual markets, and it’s very difficult to generalize. Certainly stocks and stock indices have a leptokurtotic bias (fat tails) where as I understand that some markets (certain commodities ?) have a Platykurtic bias (thin tails).
As you know, most of the action is ATM, and without any doubt neither writer nor buyer has the edge in that area, IMHO.
DB – re: Mandelbrot. Worth reading ?
=======================================================================Profitaker said:
Mr Profitaker,
Re: Your last point on above post.[ ATM ]
Plz tell us all who has the EDGE ON OTM or DOTM positions? :cheesy:
:cheesy: Mr ChrisW, Perhaps you can help him think of the answer to my question? :cheesy:
Bye BYE and Happy Xmas to all ! Lurkers too!
Bull
A Dashing Blade
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Profitaker said:
The Misbehavior of Markets (paperback, red cover, in all the shops for £6ish)
Well worth reading I'd say.
It's written for the non mathematician
Divided into three parts.
1) A history of financial mathematics.
2) A comprehensive refutation of the efficiant market hypothesis where he actually puts the probability of extreme events (assuming normal distribution) into context. This bit is actually quite jaw-dropping.
3) A final part on fractals and their relevance to todays markets (basically he says that markets are fractal but that they can't be modelled)
Profitaker
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DB
Just ordered it, thanks.
Just ordered it, thanks.
Profitaker
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Bulldozer - Amen
If an ATM option (Put or Call doesn't matter) is correctly priced in the market it will have a delta of 0.50, meaning a 50% probability of expiring OTM (worthless). Is there any material advantage in selling, rather than buying this option ?
Providing the option is correctly priced, I suggest not.
If an ATM option (Put or Call doesn't matter) is correctly priced in the market it will have a delta of 0.50, meaning a 50% probability of expiring OTM (worthless). Is there any material advantage in selling, rather than buying this option ?
Providing the option is correctly priced, I suggest not.
