Economics and similar, for the sleep-deprived
A subtle change has been made to the comments links, so they no longer pop up. Does this in any way help with the problem about comments not appearing on permalinked posts, readers?
Update: seemingly not
Update: Oh yeah!
Monday, July 31, 2006
Adventures in prediction ...
From back in the dawn of history, when there were still a couple of sane people commenting at Harry's Place (yes I was one of them you cheeky kids), on July 12, I want to preserve this priceless exchange.
Here's a not-so-hypothetical situation submitted for your consideration.
--In May 2000 Israel withdraws all of its forces from southern Lebanon.
--In June 2000 the United Nations certifies that Israel has complied with Security Council Resolution 425, calling for the withdrawal of Israeli forces from Lebanon.
--In July 2006, Hezbollah launches dozens of Katyusha rockets and mortar bombs from Lebanon at the Israeli town of Shlomi and at Israeli outposts in the Shebaa Farms area. Hezbollah forces cross the UN-recognized border from Lebanon into Israel, kill three Israeli soldiers, kidnap two others and take them back into Lebanon.
What should Israel do now?
Cut off their electricity and bomb their bridges?
It was a serious question, dsquared. Do you have a serious answer?
Not 48 hours later, when it turned out that this was indeed the plan, Gene moved to the point of view that this was the rational, indeed the only response. It was so seamless I am not sure if he even realised he was doing it himself.
Of course I cannot really claim any prediction prizes as I certainly did not realise things would get anything like this horrible.
this item posted by the management 7/31/2006 12:53:00 AM
Friday, July 21, 2006
This is why I am not an academic
Apparently the "Journal of Conflict Resolution" is a proper journal and it printed this. (via the CiF comments section).
Meanwhile in the world of option pricing ...
Basically, consider a standard hedge fund charging structure: 2% annual fee and 20% of performance above the high-water mark. One thing you might want to know is what the present value of this stream of performance fees is, out to perpetuity. On the face of it, this looks like it is going to be quite difficult to do, as it is a path-dependent process and in general path-dependent processes are a bugger to value. However, with a bit of ingenuity it isn't. (I apologise for the fact that from here on in, it is going to get a bit incomprehensible for people without a background in finance. I also apologise for just giving cookbook style instructions here rather than showing it rigorously - life is too short to do equations in HTML).
Basically, if you take a lattice approach, it all becomes incredibly easy. The pricing structure is a contingent claim written on the value of the underlying fund assets, so you convert the volatility of those assets to a risk-neutral probability of an up-step and a down-step and draw out (in your mind) the risk-neutral lattice for the underlying.
At every node of that lattice, you either get paid a performance fee or you don't. If you do, then you get paid the value of the underlying at that node, times 2%.
So, you can write another lattice for the payments you get at each node, if you get them at all. You then pick out a copy of this fantastic book and look up the "hitting time theorem". This is an extension of the Bertrand ballot theorem, which just tells you the probability that a discrete random walk will reach some distance d after time t, for the first time. This is exactly what you need to know at every node, because if that value has been reached before for the value of the underlying, then it isn't a high-water mark. So you multiply each node by its first-hit probability and Bob's your uncle.
Except of course he isn't, because if you actually do this, you find that the valuation goes to infinity. This is because as you go out to perpetuity, every time slice contributes a tiny bit of expected value to the overall valuation, and although this gets smaller with every step, it doesn't converge.
This is because, of course, we've ignored the fact that there is an absorbing barrier for the value of the underlying - if the fund goes to zero, it is gone and there will be no more payments. So you have to use the ballot theorem again, to calculate for every note what the probability is of crossing zero before you reach that level, and multiply by one minus that. Obviously the probability of going to zero first gets bigger the further out you go, and this means that the whole thing solves.
This is probably amazingly obvious and has been covered in the literature a million years ago but I felt rather clever when I did it.
this item posted by the management 7/21/2006 07:43:00 AM
Thursday, July 13, 2006
Camden New Journal Readers Say The Damnedest Things
Regular Crooked Timber readers will be aware that the people who write letters to the Camden New Journal are a laugh a minute. However, the stuff about the eliminationist anti-Semitic pizza was not even the funniest letter in the CNJ that week. That honour goes to the following:
I CAN hardly believe that Esther Rantzen could make such an inane remark as "it saddens me that anyone could complain about anyone else's enjoyment (Neighbours relish sounds of silence during concert season, June 29)
Almost all anti-social behaviour from drunkeness and violence to child abuse is someone else's enjoyment. And I thought Esther was the founder of Childline, a charity opposed to child abuse
Well, exactly. Esther thought it was sad that people complained about the concerts at Kenwood House, but when it came to spoiling the paedos' fun, she was just as much of a killjoy herself! Hypocrite!
It might have been a Viz-style Letterbocks joke, but it wasn't marked.
this item posted by the management 7/13/2006 04:08:00 PM
Saturday, July 08, 2006
Can this be true?
I would certainly have thought that some misogynistic arse of a sportswriter would have coined the nickname "Amelie Machismo" before now, but according to Google, not so. Will I be able to claim royalties? I promise to donate them to some sort of charity aimed at stamping out people like me.
Update: what a shame, as well, that Justine Henin-Hardenne never got divorced and then remarried Tim Henman. I would have loved to have heard the commentators trying to get their tongues round "Henin-Hardenne-Henman" under pressure.
Update Update: Would anyone like to hear about my really spiffy pricing model for valuing the "high water mark" fee structure for a hedge fund?
this item posted by the management 7/08/2006 08:17:00 AM
Once more, I must point out that "Daniel Davies" who has a letter in this week's Saturday Guardian (something about Iranians) isn't me. I don't write letters to newspapers and I secretly believe that people who write letters to newspapers are loonies. Having a blog is different of course.
this item posted by the management 7/08/2006 03:27:00 AM