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JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-06-22 00:02
Are there any option pricing models which make provision for the present quantity of open interest in that contract?

Or backing up a step, considering vol surface modeling - it's commonly stated that demand of an option contracts influences its implied volatility estimate, quoted spreads and transaction prices. In a basic sense, how would a trader account for open interest and/or intraday volume of an option?
...taking this last question a step further, how could demand quantities at other strikes be accounted for on an interdependent basis?

The clouded mind seeks; the emptied mind finds.

Patrik
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Posted: 2015-06-22 16:19
That's a lot of things at once. Try to slow down and form an opinion of some smaller pieces first.

Let's take OI and volumes. You're a market maker and someone calls you up (or RFQs or similar) for a quote on a laid up vanilla structure with 1mm vega worth of risk. I'll normalize figures to be expressed in vega terms to make a point even if that may not be how you'd naturally think about it. How would your quoting be affected if I told you the market trades about 100k vega per day vs if I say i trades about 100mm vega per day? How would it affect your quote if you think/know the OI of similar outstanding strikes to be 10k vega vs 10mm vega?

To add to the situation - let's say you know that 1mm vega of the exact same structure traded 10minutes ago. How does that affect you? If the same structure traded 10 times also yesterday, and you can see the OI was all increases vs if it was all decreases?

I guess my suggestion is break it down to a lot simpler steps and put yourself in the market makers shoes and think about how it'd make you feel. That'll be a good starting point.

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JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-06-26 22:28
Patrik, thanks for your detailed response. You're right - what I'm asking is way more granular in reality, as you allude to, than a few sentences could attempt to sum up.

Thinking on your question, well, I'd price options in the market with 100k vega/day much lower, and the skew much less pronounced, versus the 100mm vega/day where I might get substantially wary and price them with fatter premiums and skew to the OTM puts.

If the average vega in the OI in at any strike works out to ~10k, and the structure is 1mm vega of risk by the model, I'd expect that a lot those positions get closed in short order once risk limits are hit for writers of those options, and likely exacerbates the volatility...I suppose it depends on the distribution of the structure to be quoted, but I'd add more premium due to the IV here...versus if avg vega in OI is 10mm, where I'd understate IV and go further OTM in places, so long as the quoted b/a spreads were agreeable when/where I try to add each.

If 1mm vega in same structure was recently traded, I would perhaps quote on the basis of 1.25mm vega? That's a rough guess of course...it's very situational it seems but I get the motive of the question (I think).

Now, if the same structure traded 10x yesterday, & OI all increases...well, I'd presume that such a structure might have some pull in the fulcrum of the total aggregate of OI, and I could lower the IV component in the pricing model (?)...flipside of that if OI was all decreases, and I'd likely look at a substantially different distribution of strikes/contracts/expirys for this case.


Couple of questions, & asides:
1) quoting vega vs gamma - given the ambitious nature of the question, is your intent to promote precision in my choice of tools for assessing the market so broadly & deeply, or just an industry standard?

2) would structure in this context be synonymous with 'cap' (basket of options)?

3) I've been pondering some papers from academia-land that hit around this 'bird's eye view' consideration of modeling prices in options, mostly from a forecasting standpoint of where the implied aggregate mean may gravitate toward for the underlying instrument...this is of course made more complex when numerous intermarket correlations exist versus some non-indexed, optioned smallcap stock, so the 'implied mean' is just a suggestion like most any other indicator.
Example papers:
http://pages.stern.nyu.edu/~lpederse/papers/DBOP.pdf
http://www.mcgill.ca/files/desautels/OpIntOct04.pdf
http://www.ruf.rice.edu/~yxing/option-skew-FINAL.pdf (e.g. 'volume-weighted implied volatility', whereas most conventional pricing models that I see leave the IV component of the equation as an implied 'black box' of market demand effects on distribution of returns)

The CME Group had a whitepaper on their website titled 'Trading on the Information Content of Open Interest' which was only a rough notion of looking at the open interest broadly...I can't find the link on their site right now for some reason.

4) --> trying to make some forecast from the options on a comprehensive basis in exchange-listed markets certainly assumes that such is the full picture...whereas it seems that OTC markets for similar options can really be the submersed portion of the proverbial iceberg...like what NP member tbretagn alluded to in the recent thread 'Forecasting on open interest' <--

5) I recall reading the paper on dispersion trading published by CSD - very well-written.


The clouded mind seeks; the emptied mind finds.

Patrik
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Total Posts: 1337
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Posted: 2015-06-29 12:03
Your reasoning isn't too sound I'm afraid. I was trying to steer you in direction of thinking about practical risk management if you were a market maker - what makes you concerned or comfortable, and how does that change the way you'd act.

If the current OI is just a fraction of what you're quoting the one big thing that should flash in your head is "I'm about to take on significant risk that I may not easily be able to get rid of". So if you'll need to build in more margin into your quote relative to if you were making a trade that you could lay off in 10sec if you wanted to. You'll also care about what your existing position is, if it's risk reducing or risk increasing etc.

Same goes for the volume hint - if you're quoting something that is insignificant part of daily volume -> you can get rid of the risk, but if you're quoting something that is multiples of daily volume you know you'll be stuck with this position for a while. So you gonna have to charge for that.

About OI increases/decreases for same structure: What I mean is that what you're quoting is clearly in play and you need to think about who it is, why they're doing it, what is their likely total size etc.

1) I just picked a single thing to make you think about something in practical terms. In real life you obv have lots of different dimensions to consider.

2) No. I just meant "linear combination of vanillas"

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JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-06-29 17:21
Yeesh, I'm sorry, that was a real dumb oversight - while entering my response, I overlooked your original statement of quoting 1mm vega of risk, referenced against the different avg daily vega of the hypotheticals. Clearly my answer had some 'flipped' reasoning. So yes, 1mm worth of vega in a market doing 100k vega/day could obviously cause a pronounced vol shift, depending on the progression of entry.

Mea culpa..

The clouded mind seeks; the emptied mind finds.

unsmt


Total Posts: 196
Joined: Jul 2014
 
Posted: 2015-06-29 20:02
It seems that volume of the trade provides more effects on price than open interest.
Implied volatility comes from the option pricing by applying Black Scholes model.
Black Scholes model states: if one uses BS price for option at t than hedged portfolio has risk free instantaneous rate of return at t. It does states that market really uses BS price. If for example a part of the market does not use option for hedging and buy-sell option for speculation then they more focus on P/L then on 'no arbitrage'.
If a model concerns on open interest or volume then these parameters should be presented in the pricing model explicitly. The statement like " it's commonly stated " sounds heuristically. There is rather emotion than a formal evidence.

JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-07-02 04:16
Unsmt, as I've seen it, IV is an assumed/iterated value which is provided by the user of BS to obtain a pricing. Also, the BS model doesn't account for asymmetry of returns due to volatility smile/smirk effects, and also doesn't account for demand effects in further skewing the prices.

The 'commonly stated' reference that I made to demand for an option as an influence of pricing is not emotional in nature, it's in published studies, not something I made up in a bubble.

The clouded mind seeks; the emptied mind finds.

JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-07-02 04:19
Patrik, your input is greatly valued - in attempt to read between the lines here, is it safe to state that you might imply that there is no 'right' model for pricing options based on demand and other effects that I mentioned?

I think that I understand the point of your example in context of a MM, but from a 'top of the mountain' analysis, how does a practicioner get an aggregated glimpse of the market's sentiment so as to try and align with the deep pockets?

The clouded mind seeks; the emptied mind finds.

unsmt


Total Posts: 196
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Posted: 2015-07-02 13:50
JTD, if one provided research which presents explicitly that option price depends on OI then it shows that BS model does not complete and a large effect of the OI on option price justifies that investors do not care about no arbitrage price buying-selling options. It might be true intuitively one can assume that there is many people or institutions want to make money. These participants like people in casino. There almost all want win rather than leave casino with the same money as it was initially.
On the other hand it is difficult to imagine that research which justified OI effect was developed accurately. Accurate research should show market changes of the options prices when only OI changes while all other market parameters are unchanged. Such situation is difficult to observe.
Also it is necessary to specify whether OI relates to options or underlying asset or both.

JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-07-02 16:36
Example reference of this aspect: http://docs.lhpedersen.com/DBOP.pdf

"Intermediaries such as market-makers provide liquidity to end-users by taking the other side of the end-user net demand. If competitive intermediaries can hedge perfectly—as in a Black-Scholes-Merton economy—then option prices are determined by no-arbitrage and demand pressure has no effect. In reality, however, even intermediaries cannot hedge options perfectly—that is, even they face incomplete markets—because of the impossibility of trading continuously, stochastic volatility, jumps in the underlying, and transaction costs (Figlewski 1989). In addition, intermediaries are sensitive to risk, e.g., because of capital constraints and agency."

If a trader is going to buy one measly option contract in a highly-liquid options market with a low- to moderately-volatile underlying, I don't think he need worry about a margin of error due to using BSM versus some more 'sophisticated' pricing model. However, from an analytical viewpoint in gauging sentiment on a comprehensive/aggregate view of the options activity, a highly-liquid and quite volatile market presents a scale which BSM may be insufficient to measure the projected distribution of returns.

The clouded mind seeks; the emptied mind finds.

unsmt


Total Posts: 196
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Posted: 2015-07-02 17:07
Authors of the paper are quite famous experts. Nevertheless reading a few pages in formula (1) one can see that no arbitrage condition of the BS pricing approach is exchanged for " there exists a representative dealer who has constant absolute-risk aversion, that is, his utility for remaining life time consumption " which as it seems to me should be used next to justify option buy. Subjectively I have a feeling that traders do not use utility function or are making a decision to buy options by checking whether their feeling corresponds to their utility function. Intuitively buying options people want to make money over some finite period. If they see that they could not do that they probably think how to sell option. Of course paper could be perfect in all respects

Rashomon


Total Posts: 166
Joined: Mar 2011
 
Posted: 2015-07-02 22:09
Patrik & JTDerp, thanks for these interesting posts. Patrik, I posted a similar question a while ago and would like to verify that I'm understanding you correctly.

Assuming high volume indicates a high general level of interest from both sides. As long as nothing crazy is about to change the environment, you're saying volume means you will be able to ditch a position with minimal price slippage under normal conditions.

But doesn't OI work exactly the other way? Someone is holding rather than trading; maybe that means they would be happy to accumulate a bit more, or maybe that means big size will be trying to ditch at exactly the same time you are. Either way it's not exactly good for you; someone may know something you don't.

It seems to me like (bi-directional) volume should be a better rough indicator of ease-of-exit. Big OI seems like such a question mark. Of course if I'm being asked to put on a Big trade, I should know the product well. But isn't this strictly outside of whether someone else is holding right now?

"My hands are small, I know, but they're not yours, they are my own. And they're, not yours, they are my own." ~ Jewel

NeroTulip


Total Posts: 997
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Posted: 2015-07-03 12:32
OI is bi-directional too: for every buyer there is a seller. So a large OI is a sign that more people have a position in the contract (long or short), and could potentially take the other side of your trade. More OI = more liquid.

Inflatable trader

Tradenator


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Posted: 2015-07-03 13:17
I think of the change in OI rather than OI itself as a backwards looking liquidity measure.

Rashomon


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Posted: 2015-07-03 18:16
Elementary error; my fault. Thanks all.

"My hands are small, I know, but they're not yours, they are my own. And they're, not yours, they are my own." ~ Jewel

JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2015-07-06 04:35
Okay, so as a general point to float here, no one is of the opinion that looking at options OI or volume distribution can be honed into a tool for forecasting a possible increase/decrease in volatility of the underlying, or a probable price range which the UL will be drawn to?

The clouded mind seeks; the emptied mind finds.

unsmt


Total Posts: 196
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Posted: 2015-07-06 15:02
You can try yourself with stock model. A popular model is SDE. One can try to assume that drift , diffusion or these two together constants depend on OI. But it does not look that it will be something reasonable. If OI will not a good factor for stock then it will not good for derivatives too.
One can try to use OI for developing indexes. For example it seems that DJI is calculated using OI as weights. It might make sense to developed 3 other indexes. 1st is arithmetic sum of the DJI stocks, 2nd is weighted by volume, and 3d is weighted by volume/OI. Remarkable difference of one can justify significance of a factor on market though effect on individual stock pricing will be not clear yet.

Patrik
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Posted: 2015-07-06 17:19
@JTDerp:
Well, at a basic level "everything" is priced via "supply and demand", options no exception. If that's going to be helpful for you to fully model the world just based anonymous aggregate data is a different question Smiley Clearly it's relevant information, sometimes more and sometimes less.

As a practitioner you'll have all your mates and brokers in the market to serve you very well for taking the temperature on sentiment. Calibrate a bit with public aggregate data, and if you're buy side your own private knowledge of how people are acting and you're off to a good start. If things don't make sense iterate - work out who may know something about something you can't explain and continue asking questions.

I'd stress that all of this is a very non-mathy part of trading - it's art, gut feel, personal relationships etc. As a practitioner you'll have very practical questions that you attack in a pretty low tech fashion.

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unsmt


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Posted: 2015-07-06 18:03
Patric, it seems that Black-Scholes option price does not a settlement between "supply and demand" though it might be because it is not a basic level? It states that if one is going to have a 'perfect' hedge at moment t for an option the price of the option should be equal to B-S price. It does not tell us what should be the option price if we are not going to apply option for 'perfect' hedge. It is not clear whether adjustments of the hedged portfolio should be added to BS option price because buying option for BS price implies automatically possibility of the risky adjustments over option's lifetime.

unsmt


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Posted: 2015-07-06 18:51
It looks make sense to remark that interpretation of the price as a settlement between supply and demand is good for a fixed (known) price. In stochastic market stock is random at each moment in the future. Hence, supply and demand settlement can be applied for each possible value of the price in the future and therefore any spot price implies profit or loss which depends on market scenario. Such point suggests interpretation of the price in stochastic market as P/L or risk/reward settlement which will imply supply-demand

JTDerp


Total Posts: 42
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Posted: 2015-07-06 19:58
Patrik,
Definitely worth stating this notion as non-mathy...as a lowly 'retail' guy, among other things, I have to question a lot of the approaches pitched around in outdated textbooks and online references to pricing options and analyzing sentiment, and this motive stems from time spent watching the markets, and comparing what I perceive to what the common assumptions in these approaches are (often normally-distributed, Brownian motion, some 'constant'/mean volatility used for input).

Technical analysis can have its uses along with solid risk management, but if we start trying to attain a feel for the 'governing dynamics' of market structure & mechanics, the gut feel as you allude to, for me, is that the big institutional players prefer the options space for its versatility in structuring their positions, and the more vanilla models out there (*cough* BSM) aren't going to frame in their activities to a tight margin.

The notion to seek out more accurate methods of pricing options & estimating volatility comes from the motive to emulate the larger, more established players in the options markets (since I don't personally know any), and might take form in a manner akin to tape-reading (of the options) and building a histogram of where the most active regions along the strike chain are located, and the UL might be drawn to as such. Measuring options activity sentiment by volume or OI alone isn't enough of course, there's moneyness and volatility weightings to consider. Distinguishing institutional order flow vs retail in the options space would involve a good share of tea leaf reading and consideration of market context.

In the context of volatility forecasting for the UL, using a backward-looking method like GARCH, ARMA, etc seems like it may be useful to establish broad relationships...I did read that using the realized variance (sum of squared intraday return) with a standard volatility model proves some accurate results... but, for intraday trading it seems like whale-watching with a sonar that's calibrated to their movement logic would be superior...

The clouded mind seeks; the emptied mind finds.

JTDerp


Total Posts: 42
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Posted: 2015-07-06 21:27
A big shortfall in trying to utilize on-exchange options data like this is that it's not the full picture, like I alluded to in (4) of my 2nd message in this thread...a question in the same ballpark as this discussion was posted here (http://quant.stackexchange.com/questions/7605/changes-in-open-interest-vs-changes-in-underlying-volume?rq=1)

and the reply from user Matt Wolf is informative: "Most market makers do not re-hedge much in the underlying. In many markets the delta is exchanged (off-exchange) alongside the options trade at initiation, making both parties delta neutral at the outset. Re-hedges in large vol books are generally accomplished through other options and only residual delta is hedged in the underlying. But it obviously depends on the specific asset class and market convention as well as individual approach to trading such options. I am just saying that an academic paper will not be able to cover all those ifs..."

So, Patrik, guess you were very diplomatically shooting down my plane, 'cause this is too thick of a layer cake :)

The clouded mind seeks; the emptied mind finds.

Patrik
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Posted: 2015-07-07 16:09
@JTDerp:
It's not about building the perfect model or having the perfect theory. It's about having various tools that are appropriate for the purpose. And knowing how to use your tools. A clean BSM constant vol model can be a great tool - you just need to add in the out-of-model assumptions and know how your position will behave. I.e. if you think prices will accelerate at certain points for some reason (i.e. big pins where only option sellers are likely hedgers), or get sticky (i.e. marginal cost of production of a commodity), or you think vol will go bid/offered in some certain scenarios etc. Use that info for building your position and deciding what you think good value is - and in the end your profitability will be more related to being right or wrong on your views rather than what exact model you choose to observe the world through (given those same views).

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JTDerp


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Posted: 2015-07-07 17:25
Thanks; I'm not trying to make a perfect model, as the amount of 'noise' seen each day in the markets certainly requires a 'factor of safety' built into the logic. In one of Emanuel Derman's papers regarding volatility smile, he states in conclusion that in regard to modelling effects of such, "there is no 'right' model" & I certainly took that to heart.

And like you mentioned in having various & *appropriate* tools, well that's my aim - getting ones that are more relevant to the realities of volatility than, say, a model which assumes mean and variance of returns are roughly constant, or normal distributions.

Your point is noted on using BSM with additions...I assumed that for options, the Heston-Nandi & GARCH models, among others, took the core framework of BSM and modified for additional sensitivities of the inputs.

I just figured that building out a more comprehensive model for observing the world, with correlation & cointegration studies, non-constant volatility, etc. needs a close look and not to choose the first tool that I see on the shelf.


In closing, I get what you're stating here, Patrik...it's far better to have a tool that 'satisfices' and be very insightful & proficient using it, than a tentative, impractical oaf of a trader with some "holy grail" model. :)

The clouded mind seeks; the emptied mind finds.

JTDerp


Total Posts: 42
Joined: Nov 2013
 
Posted: 2016-12-02 17:49
Patrik,
A very belated follow-up here, but I think the finer points of your responses here are finally clicking in my thick head. Got a few rough notions to ponder still-yet:

1) Would logging all activity in an option chain, from first listing date until the time where that expiry becomes the 'front' month, offer a more vivid picture and maybe leading indication of potential 'pinning' effects (and hence near-term UL price direction) until that chain expires?

2) As a general rule-of-thumb, should a market maker focus more on certain Greeks than the others, as a function of which 'volatility regime' (a relative measure to the longer-dated/historical norms) is observed in the underlying? E.g. if realized vol has been high for the past several days, and IV is abnormally high, should theta and vega get more attention than just delta & gamma?


The clouded mind seeks; the emptied mind finds.
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