Stan Jonas ''dutch book'' in Aug 7 2007 FT

[Baltazar]

Isn't he launching a HF on that just now? betting on something that just disappeared?



Btw Cheng, ignore my email, you just responded to my question here.



Still some points are not clear for me. In the abstract of his columbia talk he says:



"The existence of actual trading in Arrow-Debreu's has transformed almost all interest derivative trading. As an example, FIMAT's the largest trader in the dominant Eurodollar futures options market place, perhaps the most liquid options marketplace extant. We have not quoted or used a traditional "Greek" in either trading or quoting in almost 2 years.



1. The existence of Digitals on the FED has enabled us to see that Three- Month Eurodollars (Term rates) are nothing more than a basket of digitals.



2. Recognizing Eurodollars (libors) as digitals has revolutionized the Options and Swap marketplace.



3. Traditional "mumbo-jumbo" about skews, vol surfaces, have now become relegated to those that do not trade."



I am intrested in STIR options, so far i did not had the impression that skew was irrelevant, can someone point me to something on that?

[Cheng]

As far as I understood him (no so easy with someone who seems to have a permanent chewing gum implemented in his lower jaw) he is launching a new HF now, but not betting on the stuff he talked about.

[Baltazar]

mm this calls for more in depth searching i think,

i am going to work on this, read all his 300 slides, check the references,..

Damn i have a headache comming just thinking about that



re fdax from what i understand from slide 76:

the puts he buys are not the FF puts but some EUR future puts.



so the analysis is:

t=0 : FF is 96.955

June future on euro is 96.535

may 96.375 put on the june euro future is 1 tick

portoflio is one FF et 4 puts on the euro future (and not on the FF)



t=1 : three cases

case 1 : FF is 96.76 (wich implies but i dunno why yet) that

June future on euro is 96.26

which gives a gain of 42 on the puts on the euro future and a loss of 19.50 on the FF

case 2 : FF is 97 (wich implies but i dunno why yet) that

June future on euro is 96.5

which gives a loss of 4 on the puts on the euro future and a gain of 4.5 on the FF

case 3 : FF is 97.24 (wich implies but i dunno why yet) that

June future on euro is 96.5

which gives a loss of 4 on the puts on the euro future and a gain of 28.5 on the FF





I don't see why two different FF values give the same future euro price, but in either cases the puts are worthless, this does not change the equation.

[AndyM]

I haven't looked at the presentation...



But I guess the gist is something as follows: let's say that there are two possible outcomes (you could add some outliers to this, it doesn't change the basic picture much). Say hike 25bp or do nothing. So your true dbn is bimodal, with very little / zero chance of expiring in between those two outcomes. However, your probability density fn backed out from option prices may well not reflect this very well, since people tend to start with BS, and then faff around with the smile to try to get a more sensible pdf. But there's only so much you can do messing around with BS + smile, and the resultant pdf may not correspond too well to economic reality.



IMO, STIRs just don't tend to lend themselves too well to being modelled as diffusions, which sort of ties in with:



[i]3. Traditional "mumbo-jumbo" about skews, vol surfaces, have now become relegated to those that do not trade."[/i]

[Path Integral]

Maybe a finance equivalent to this and this could rate this guy Wink

[Johnny]

My understanding (without reading the blurb) is about the same as AndyM's. The central idea sounds like a fruitful line of enquiry, regardless of the cro-magnon gum-chewing aspects.

[Cheng]

From what I remember from the presentation AndyM is right. The idea is to use 3 possible outcomes (+25bp, unchanged, -25bp) and forget about more extreme events like +/- 50bps. I don't know enough about futures markets to follow this idea further, however.

[AndyM]

It's not really about forgetting about more extreme events, that would just be selling deep OTM options...it's more an issue of looking at the outcomes as grainy ( not quite discrete, since with ED there is the issue of unstable term premia, and even with FF, actual FF can diverge from target) rather than continuous (eg Fed is vanishingly unlike to move in smaller increments than 25bp). Option pricing for near months should reflect this granularity (whereas back months could be treated more like a diffusion). But for various reasons, this isn't always the case.

[Baltazar]

so it could considered as some kind of model arbitrage, right?:



two models exist: BS-like and a grainy one.

Given the market-prices one can fit the two models.

Except that the no-arbitrage conditions of the two models are different.

Some price may be in the market because from the BS-like point of view no arbitrage is possible, but from the grainy model, there are arbs that he used.



That could be what he refers to when he speaks about proba not adding to 1: Because his grainy model relates prices to discret-move probabilities, arb price implies arb probas. Clever

[Johnny]

Yes. Although the clearest example (to me anyway) is the bimodal example AndyM used previously. With one week to go before an FOMC meeting, and probabilities 50/50 of a rate rise vs no change, there's no way any amount of tweaking with a Normal distribution is going to give you a good approximation to the bimodal distribution required.



btw, a couple of small questions. Obviously these are real world probabilities rather than rn probabilities. Does this matter? My feeling is probably not, as the difference between bimodal and Normal is so much bigger than the difference between rn and real world. Edit: aha! and crucially, this is supposed to be structured as a no-lose "Dutch book", so risk preferences are irrelevant.



Second question (for PJ as this is his specialist subject). What does this all imply for transition probabilities in STIR contracts? Oh, ok, anyone else can answer too if they like. :)