I am still in shock and unable to post coherent thoughts about losing Peter. However, there have been some rumors floating around, fortunately not in this thread. Peter’s wife has requested privacy and I pray I do not breach Carol’s trust by reporting some brief facts. Peter had an acute medical condition that was quickly diagnosed. His doctors believed it was treatable and he would recover to full health. Sometime during the night after his first operation his heart stopped. He went into a coma and never regained consciousness. Hopefully this will put an end to speculation.

Allow me try and cobble together a few thoughts. I met Peter at Morgan Stanley when I went to a talk (that he arranged, of course). He button-holed me after the talk about a question I asked. He said he also thought the speaker did not understand the difference between real-world and risk-neutral measure. Looking back, I’m sure he was just too polite to ask in order not to embarrass the speaker; a quality I utterly lack. We have been on the same wavelength ever since.

I was his first hire when he moved to Banc of America Securities at the end of the Glass-Steagall era when banks trading equities still required a ‘c’ fig leaf. It was an honor I cherish far more than any Quant-of-the-Year award handed out by a company selling overpriced magazine subscriptions. (Peter’s politeness never rubbed off on me, unfortunately.) The first model we delivered made the bank 9 bucks, as they say in the business. It was an early-ending barrier option that Peter, literally, wrote the article on. We eventually assembled a team of quants that could also write production quality C++ code and took over responsibility for the Excel add-ins used by the traders. The IT group was quite adamant about not using our libraries but they could not make the business case that they should rewrite our code that traders were already using. Our group worked hard to earn their trust and it paid off for the business.

Peter was not just a mentor, friend, and constant source of inspiration, he was also my neighbor. A few years back he moved to Carroll Gardens and we would often meet to check out the latest coffee shop opening on Smith Street and talk math. He always bubbled over with excitement getting me up to speed on his latest discoveries, and did most of the talking. It was only fair. He had 10 times more ideas than I did. When he listened to my ill-formed thoughts he used his vast knowledge of the literature to point out things I might not be aware of. Not to prove he was smarter than me, but to help me improve my research. Peter wasn’t just nice, he was Canadian nice.

Over the past month I’ve used gallows humor to deal with the uncertainty. Peter enjoyed a joke I used to tell that is too racy for LinkedIn so this might only be amusing if you already know it. I joked that Peter was just fooling us so he had some peace and quiet to think about math.

If there is a Mathematical heaven I am sure he is enjoying an espresso while jotting in his ever-present notebook. If we ever meet again I can see in my mind’s eye the excited look on his face in anticipation of sharing his latest ideas. I’m not ashamed to admit I’m having trouble seeing the words I write now. So I will just stop.

MoMath

Met Peter at MS at a talk he organized, of course.

The speaker did not understand the difference between risk-neutral and real-world probability.

Peter was too polite to point that out. I wasn’t.

He button-holed me ater the talk, and we started talking.

My guilty pleasure was sneaking out from my technology job on the swaps desk to go to his office and geek out about mathematical finance. I “proved” the value of a call option is equal to its intrinsic.

Peter just giggled and said “that’s impossible.” He was right. I showed him how \int_0^t 1(X > K)\,dX_t is the P&L and it is equal to \max\{X_t - k, 0} + \int_0^t A_s\,ds. where A_s is the local time. I was surprised when he turned that into a paper that actally got published.

Protter’s “Stochastic Integration and Differential Equations” is one of those books, like Artin’s, “Algebra” that cannot be improved on. The only possible person to write a second edition is Philip Protter.

He left for Banc of America Securities. (Banc)

I was his first hire.

Nationsbank, Bank of America, Montgomery Securities.

John Sandelman came from Saloman Brothers pitching capital structure arbitrage.

He didn’t think quants were necessary and ran his business for 6 months without them.

Walter, the BofA head of risk management, was shutting him down.

Sandleman found out Walter had a PhD in Finance so he figured that all he needed to do was hire the top Finance PhD on Wall Street to give him a secret handshake.

It doesn’t work like that. Trading models have to be vetted by risk managers.

He bought a turn-key system, Imagine, and found out it was missing a few keys.

Very heady days. 9 building on W 57. Got in trouble for writing on glass because Kevin Beauregard couldn’t provide white boards.

The first model I built was an early ending barrier option. Peter wrote the paper on that.

When I implemented that I noticed the numbers seemed wrong. I put together a Monte Carlo simulation that indicated there was a problem.

I found the mistake in the math and fixed it.

I was so nervous approaching him about this. It could have been an early ending carrer option to tell your boss he was wrong.

To Peter’s credit, he immediatley recognized the mistake and thanked me. “Can you imagine what would happen if we gave them the wrong numbers?”

Yes. Yes I could. I had seen what happens.

We made 9 bucks, as they say in the business.

Every function is linear when plotted with a magic marker with a fat pen.