Risk Latte - Half Lives, Half Wives and Radioactive Libor

Half Lives, Half Wives and Radioactive Libor

Rahul Bhattacharya
March 25, 2011

Since the recent tsunami and the failure of the nuclear reactors in Japan the discussion amongst manyin the technical circles (and by that I mean all those Nuclear Physicists and math Ph.D.sturned quants in sell side banks) these days eventually comes to revolve around half-life of Plutonium or Cesium. I got caught up in one such discussion the other day on the trading floor of a bank. My good friend Jeremy had invited me for lunch on his trading floor. He usually does when the market is quiet and he wants free sandwiches. I love these lunches because Jeremy has one of the most colourful trading teams anywhere in the world.

It all started with figuring out how much salt we should start taking to counter the impact of radioactive iodine that comes out of the nuclear fission reaction when Uranium or Plutonium starts splitting. Apparently, a few traders on the dealing desks of the bank in Tokyo had started taking loads of salt with their lunch. It was obvious that panic was starting to creep into people’s lives in Tokyo.

But the traders in Tokyo needn’t have worried too much. Half life of radioactive Iodine is only about 8 days. Or so, we’re told by Nuke. Nuke is the nickname of Nicolaus, the rates trader in Jeremy’s team who has a Ph.D. in nuclear physics and who’s rumoured to have stumped the legendary quant, Riccardo Rebonato at a Mathematical Finance seminar in Oxford.

So, radioactive iodine was fine but what about Cesium? That’s bad news according to Nuke. Cesium has a half life of 30 years.

A voice from the other side of the floor floated in: “That’s not so bad, Nuke. If you’re lucky you may live to see the 30 year Dollar Yen PRDC notes mature.”

Half life is a very useful concept from Nuclear Physics. Even high school students learn about it these days in their physics class. However, the concept is a mathematical one and is not only associated with a radioactive exponential decay but is also very much part of the study of mean reverting stochastic processes in nature.

In nuclear physics half life measures the time it takes the activity of a given radioactive element like Plutonium, Cesium, Iodine, etc. to decrease by half of its original activity.

Since everything in finance and financial economics is borrowed from physics, the concept of half-life has also entered the finance textbooks and computer models that the quants use to analyze interest rates. The concept of half life is used widely in one area of interest rate modelling in particular where we assume that short rates follow mean reverting Ornstein Uhlenbeck process.Half-life measures the time it takes an interest rate or, an interest rate factor, to move half the distance toward its long term average value. It’s a very intuitive way of looking at the concept of mean reversion.

As we sat around the Bloomberg screens talking about half-life, Kevin, another rates trader pulled up the USD Liborscreen on his monitor andsaid to nobody in particular: “Wellnow there’s true Libor fixing by banks. We’ve finally learned how to fix and game the Libor markets. Now that’s radioactive, mate!ForgetVasicek and the half-life of 6 month USD Libor. This Libor scandal is Hiroshima and Fukushima in one.”

To which someone else in the group replied:“ yeah, why not call USD Libor as L239, for radioactive Libor, like P239 (radioactive Plutonium).” The reference was obviously to the unfolding scandal in the Libor interest rate market.

Jeremy, the most experienced and the least technical member of the group was silent during this light banter. He can somehow, like a fish, sleep with his eyes open. The youngest memberof the team, a Korean, whose first and last names were both “Il”, earning him the nick name of Ill Trader, turned to Jeremy and asked: “what does the guru have to say?”

I have known Jeremy for a long time and he was the reason why I was there on the trading floor of his bankthat afternoon. He usually invites me for lunch on his trading floor, whereby I buy sandwiches from the Starbucks in the lobby and see him just before London opens. Jeremy, who’s been a dear friend of mine for the past fifteen years, has always believed in the dictum that: “there is no free lunch in life, except on the trading floor”.

First, we all thought Jeremy had really fallen off to sleep. He had eaten my portion of the sandwiches as well. Then, slowly, like the movement of earth’s tectonic plates, he moved in his slouched sitting position and looked at Ill Trader square in the eye. Then he said: “You’re in your diapers but one day you’ll understand. A successful man's life is also highly unstable (though it may not be radioactive). As he progresses towards his long term value, he is more and more surrounded by half-wives.”

What the hell was that? Half-wives? To the best of my knowledge Jeremy was happily married to a lovely Welch lady who’s an exceptional cook and a wonderful singer. And he has two great teenage kids. I have known his wife Marcia and his boys for some time now. Why would he talk about half-wives? And what or who is a half-wife anyway?Agirlfriend?A mistress? Then I remembered.

“So, what’s a half-wife, boss?” Ill Trader, can be very persistent sometimes. “You mean a chick? A woman, who’s isn’t your missus?”

Jeremy looked at Ill Trader and smiled. “No, I mean, non-differentiability, Einstein. You got a boner for a chick today, tomorrow it’s gone. You’ve these roadside romances, Friday night drinks with the girl in Independent Valuation Group, one night stands, a weekend getaway to Bali or Phuket. And then what? A non-differentiable memory! Can’t tell one day from the other.Can’t tell one quarter from the other.Profits, losses, bonuses. It’s the same frigging thing.”

I had seldom seen Jeremy so animated. He continued on, “Half-wife, or half-wives, is a measure of how fast your life progresses towards its equilibrium value. But you know want there is no equilibrium value, no frigging mean, only bloody volatility. Equilibrium in life, like in the markets is at best an elusive concept.”

He was unstoppable now. “Life’s the mother of all random walks. And it’s mean reverting. But, we never reach the mean, it’s a meaningless concept. The volatility pushes it far, far away from the mean. All you have are these half-wives and an incessant, drunken walk, from one Friday night to the other.”

Everybody was silent for twenty seconds. Jeremy’s philosophical rants on life and things are well known amongst his team. He could talk about – and mostly did – reflection principle, barrier shift, mean reverting processes and just about anything in quant finance with great eloquence. Mostly it’s bull shit. And the beauty of it all was that most of his team members don’t know, or ever realize, that Jeremy has no math or technical degree.

Finally, Nuke said, “Jeremy, you’re so full of shit. But it’s beautiful.”

Jeremy, the God, the most successful rates trader on this side of the Suez Canal,gave a slight bow of his head and said, with finality:“Life’s the mother of all random walk, fellows. The more money you make, the more random it gets. It’s a journey from one half-wife to another….continuous and random but non differentiable. All right, I got to have a chat with Marcus.” And so the lunch discussion was over.

As I rode the elevator down from the 33rd floor, I couldn’t help but marvel at how adept Jeremy is at bull shitting. What was that, upstairs? He was really talking shit;I guess it was just another non-volatile afternoon.

When Jeremy first moved to Hong Kong from Tokyo about 14 odd years ago to work for the Asian desk of a different bank than where he is now it was rumoured that he had actually followed a Korean girl in his team, a Carnegie Mellon graduate with stunning looks and a totally dead brain who’d moved to Hong Kong a few months earlier. She was Monique something and she was just an intern when she’d joined Jeremy’s desk in Tokyo.

Nobody knows what happened of her but she was very much in Asia somewhere. A trader’s life can be strange.

As I was walking back to my office from Two IFC that afternoon, a curious recollection crossed my mind. I sometimes browse through the myriad brochures of structured products and derivatives conferences that happen in Asia. I think, in most of them I have seen the names of Jeremy Hogan and Monique Choi appearing in the same conference.

© Rahul Bhattacharya
This column is written by Rahul Bhattacharya and reflects his own views about life and business. It does not necessarily reflect the views and opinions of other members of Risk Latte Company Limited, Hong Kong (“the Company”) and the Company accepts no responsibility for any factual errors contained in the column and strongly advises readers not to pay much attention to it.

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