Remembering Mark Rubinstein

MENACHEM BRENNER

I met Mark on my first visit to the UC Berkeley Finance Department in 1974 and was impressed by his detailed knowledge of the history of the Middle East back to the Roman and Greek times. Over the years whenever we met, we mostly talked about finance, especially about the options markets. I was fortunate to be at Berkeley in the late 70s, having numerous discussions with him while he was writing his Options Markets book with John Cox. In the following years, his creative mind, vast knowledge, and skills produced some of the great contributions to financial economics.

The 80s and 90s were exciting years in the financial markets, especially in the derivatives markets where academia and industry worked hand in hand. Mark was at the center of it, making his mark in both domains.

For a while, after the burst of the high-tech bubble, we met a couple of times in New York. Then, in 2008 I received an e-mail from Mark noting that he was about to retire, but would continue to work on religion, his old passion. “I am working on a book on Christianity and now have a full chapter on the Hebrew Bible,” he wrote. Over the next six or seven years, we were corresponding, occasionally meeting, and discussing religion and faith. I was mostly a passive recipient, a sounding board for his scholarly analysis of the Christian gospel. He was trying to apply a scientific approach to many of the common (and uncommon) stories and hypotheses concerning the birth of Christianity, the crucifixion, the morality of religious faith, and so forth. In his essay, “Faith: A Disappearing Concept,” Mark discussed the concept of probability, which is often used in science, but in fact is non-existent in religion, which makes religion harder to deal with in a scholarly manner.

Mark was very persistent, sometimes checking in to see if I was reading his book. “My book is not Christian, it is secular humanist,” he said once. “If you haven’t read it yet but might read it, I would like to send you the significantly revised version of it that I have. The new title is: The New Gospel: A Humanist Appraisal of Christianity.”

At some point, I felt I needed to involve a couple of my friends who were perhaps more knowledgeable than I and could be more critical of his hypotheses. One of these friends suggested that Mark was missing some facts and stories about Jesus. Mark’s response was, “You should realize that I know almost everything you are writing about, since I have read perhaps 200 books about this subject over the last 5 years. It will not be easy to teach me something about Jesus that I don’t know.” Still, he was open to criticism “…as you read the book, if you hear me say something that you disagree with, then I would very much like to know what you think.”

His vast knowledge and scholarly approach were manifested in drawing from ancient and not-so-ancient history. “I quote from Plato in the book of mine that you have, who wrote this 400 years or so before Jesus lived,” he said once. And another essay entitled “What Paul Revere’s Ride Tells Us about Jesus” draws from more recent American history.

In another note, he concludes: “It seems that anything to do with Christianity is just too much of a turn-off, and even a new non-Christian gospel has a bad odor about it. The incuriosity of people about other people’s religions is an interesting fact of life, and probably one of the reasons we have problems with each other.”

As a true scholar, he wanted his message to get out into the public domain: “There is one group that may be interested: secular humanists,” he stated once. “Their leading journal is called Free Inquiry and I have been submitting essays for publication. At this point, I am batting 75/100: 3 accepted out of 4 submissions. So, I seem to have found a home for some of my stuff.”

Not only did I have the privilege of friendship and scholarly discussion with Mark, I also enjoyed his great sense of humor. Two of his best professional (and PC) stories and jokes, told in “old” days, are still relevant today and I continue to use them in my classes. He will be missed.

EMANUEL DERMAN

I first heard of Mark Rubinstein when I started work at Goldman Sachs in late 1985. Within a few days of my arrival, I was assigned to the bond options trading desk, given a copy of the famous Cox–Ross–Rubinstein paper on the binomial options model, told to read it over the weekend, and then work on bond option valuation models. It was an immensely lucky opportunity that influenced everything that happened to me afterwards.

Since then I’ve had lots of interaction with Mark. I first heard him speak at the 1986 annual derivatives meeting organized by the Amex. I wandered around town with him during the 90s, in Paris and Barcelona and Juan-les-Pins, and other locations where Global Derivatives held their annual conference that brought together practitioners and academics, eating and talking about everything from models to life in general between and after sessions. I worked on explaining the volatility smile by using methods similar to the ones he pioneered. I read his papers on the apparent paradoxes in option theory. I went to visit him at his house outside San Francisco when I gave a talk several years ago at the Berkeley MSFE program’s commencement.

Mark had boundless curiosity and willpower and took life seriously. Soon after I met him, he told me that he had decided, while young, that he wasn’t going to read any imperfect modern books until he had read all the classics. I believe he did that. He also once told me that he believed he was a mechanism (without free will) that was built to want to find the truth. I didn’t believe he was an automaton, but he really was interested in finding the truth and in experiencing the best of everything. He had photos of classic artistic masterpieces revolving on a large screen in his house.

The last time I saw him was by accident while I walked on Madison Avenue, one late afternoon a few years ago. I had been wondering about how the concept of implied volatility had arisen (it was an invention that appeared several years after Black–Scholes–Merton) and Mark told me where to find the first paper that used it. Mark also wrote a wonderful book about the history of financial concepts.

Mark was one of the last of a generation of finance theorists who still thought and taught about the ideas rather than about the mathematics. Someone once commented somewhere that Feynman did all the astonishing things he did with only nineteenth-century mathematics. Mark did too, and binomial trees became a kind of Feynman diagram, bringing intuition and calculation to the unwashed masses, myself included. Everything I feel I know about how to think about the randomness of security prices and the valuation of derivatives I owe to his papers on the binomial model. And every time I encounter a new problem, that’s the way I start to think about it. With Mark Rubinstein and Steve Ross gone, it’s very sad.

ROBERT JARROW

I had the pleasure and honor of knowing Mark starting after I graduated from MIT with a PhD in 1979. His insights and writings have always had a profound impact on my career. This influence began when I took my first job at Cornell University. On the faculty at that time was one of Mark’s former PhD students, Andrew Rudd. Andy was teaching an options course at Cornell prior to my arrival. After I started teaching there, I took over his options course so that he could teach investments.

To prepare my course materials, Andy shared with me his teaching notes and a preliminary options manuscript using the discrete time model, written by Mark and John Cox. This manuscript was the precursor to their famous textbook: Options Markets (Prentice Hall 1985). Since I was trained at MIT under Bob Merton and Fischer Black, I wanted to teach options using a continuous time approach. So, out of necessity, I created my own set of teaching notes using the continuous time mathematics. However, although I created my own lectures, Mark’s manuscript influenced the way I structured my material.

Mark was always open to frank, intellectual, and friendly discussions. I remember one time talking to him about continuous time models in finance. Unlike myself, Mark didn’t really like these models. He believed that almost everything one could do with a continuous time model, he could do in discrete time. Although we disagreed, he respected my differing opinion. And, of course, I respected his. To this day, I have always thought of Mark as the master of discrete time finance models. Whenever I needed a reference for these models, I used Mark’s publications. And, there were many such insightful and important papers.

Mark was a true scholar, interested not only in the theory and practice of finance, but its history as well. His love of history was contagious, and because of him, I now share this passion. Whenever I teach or write, I always try include some history of finance to enhance and to clarify the relevance of the material. I am grateful to Mark for his influence on the profession and my own writings. We will all miss him.

ERIC REINER

(This is a lightly edited version of comments made at Mark Rubinstein’s memorial Service in Mill Valley, California, on June 9, 2019.)

Friends of Mark Rubinstein, lend me your ears!

Unlike Marc Anthony, I make no pretense about my objective today: I DO come to praise Caesar. And while, like Polonius in another play, I promise to do my best to be brief and stay on point, I don’t think I can offer to accept banishment to a life of farming (or worse) if, almost inevitably, I don’t entirely succeed.

One of the first things I learned about Mark was his love of Shakespeare, something we shared. It was telling for me that, in our few conversations during his recent illness, Mark would revert to flawless quotation of Will S. to reassure me (and himself) that he still had command of his ample faculties. It goes without saying that, even though I belonged to a Shakespearean acting troupe in college, Mark’s knowledge of the Bard was far beyond mine—even toward the end.

It seems particularly fitting that we come together this weekend to remember Mark. Yesterday would have been his 75th birthday, so our gift to him today is to celebrate a truly full, memorable, and accomplished life. I thank Diane Rubinstein for allowing me to participate in that gift.

Before sharing a few personal anecdotes, I’d like to relay some comments from members of the financial economics and financial engineering communities, as well as colleagues and former students.

From a leading financial economist: “He was one of the greats, in terms of creating interesting and useful theory, implementing it himself, and also communicating to practitioners.”

From a past Financial Engineer of the Year: “[I’m saddened] to learn of Mark’s passing. Finance has lost one of its giants.”

From a senior managing director at a leading Wall Street firm: “Mark was truly a giant in finance. We will never forget his academic excitement, inspiration, and mentorship to all of us.”

From a leading administrator at the Haas School of Business: “Mark had a huge impact on me. First, obvious to anyone, any conversation with Mark was always enlightening. Mark… never threw a temper tantrum, was always smiling, respectful, and kind… and so funny!”

From a former student: “I was very sorry to learn of the sad news about Prof. Mark Rubinstein, at such a nowadays rather young age. He was such a tough, stimulating, demanding, and enlightening teacher. His courses stand out to me as the bedrock of the MFE program when I did it. Looking back on it, his problem sets were extremely challenging, forcing us to dig deeper and deeper into the subject at hand, but a challenge I would relish getting stuck into… He knew he was tough and seemed to feel both good and bad about it at the same time; cognitive dissonance, an essential tool for survival.”

From a former research assistant at LOR¹: “My deepest condolences to Mark’s family. Mark was always a gentleman and a brilliant man. Proud to work under his influence.”

From another Haas MFE alumnus: “Please pass my sincere condolences to his wife & family… I was actually thinking about him just last week hoping that we could meet again. Now the Irish blessing John O’Brien gave at the end of our graduation ceremony resonates strangely:

May the road rise up to meet you.

May the wind always be at your back.

May the sun shine warm upon your face,

and rains fall soft upon your fields.

And until we meet again,

May God hold you in the palm of His hand.”

For me, the most important takeaway from the tidal wave of responses and condolences of the past few weeks is not just the wide admiration and love for him that we all know of and share, but also—in a manner reminiscent of Richard Feynman—that Mark’s way of interacting with people, in particular his openness, his curiosity and interest, his intellectual honesty, his kindness, and his generosity were the same no matter who you were—whether Nobel Prize short-lister, Financial Engineer of the Year, or junior student. This may have been of little solace to seminar presenters who experienced first-hand his uncanny, almost unerring skill at homing in on the scent until he uncovered the key point or critical assumption in almost any paper: always driven by his curiosity, excitement, and love for intellectual engagement, never tainted by even a hint of malice, and often accompanied with ample mirth and humor.

I’ve been the beneficiary of those traits many times over. Nearly 30 years ago, an unknown 25-year old chemical engineer decided to audit Mark’s BA 236 course—the one subject on options and derivatives offered by the Haas business school at the time—and turned up at his office hours the first week purporting to have not only already completed most of the semester’s homework assignments by that point, but also questioning whether some of the problems were correctly posed. Many instructors—certainly many of those of Mark’s standing—would be dubious, perhaps a bit dismissive, and wary or defensive. Not Mark. With his usual curiosity, he invited me to sit down and walk him through my thinking process. Thus began a decades-long mentorship, colleagueship, and friendship.

I’d like to relate a couple of other anecdotes that reflect on the aspects of Mark’s character that I’ve mentioned and that, I think, we all recognize, admire, and hope to emulate. I’m conscious that, because they’re personal recollections, they contain significant self-reference. I ask your indulgence and forgiveness for that.

The context is that, in early 1991, RISK Magazine had asked Mark to author a series of articles on Exotic Options, a particularly trendy area at the time, in which most of the underlying theoretical and computational results had been quietly obtained by the major banks and brokerages and held closely by them as proprietary information.

LOR had planned a two-day seminar on the topic as a potential route to new business, and Mark, Hayne Leland, other LOR team members, and I divided up the subject matter, with me taking on the path-dependent options that had been of particular interest to me. When it came time for Mark to submit articles on barrier and binary options to RISK, even though he had no need of any assistance and had completed drafts on his own, not only did he offer co-authorship, he also volunteered to list me as first author. I couldn’t countenance the latter since I hadn’t earned it, but I did feel I could contribute enough—and was grateful for—the opportunity to make them a joint effort. As of today, “Breaking Down the Barriers” has over 500 citations on Google Scholar, while “Unscrambling the Binary Code” has 150. Not amongst the absolutely most cited of Mark’s publications (some of which have many thousands of references), but a reason to be proud nevertheless.

But there is one paper that isn’t included in the widely distributed compendium of RISK articles and the story around that is, I think, instructive and enlightening. Mark had examined the valuation of so-called quanto options, in which the payoff of a stock option that is normally expressed in one currency is actually paid in another. Mark’s RISK article argued that the valuation could be broken up into two steps: one in which the probability-weighted stock option outcomes were averaged in the original currency and then a second, independent step in which that expected outcome was discounted to today’s present value in the payoff currency. Shortly after the article appeared, a prominent industry researcher took me aside at a conference and told me that he thought the result wasn’t correct. This was a matter of honor and pride: how could he be right and Mark not?! For my next talk, I found what appeared to be a water-tight way of getting at a corrected formula and a hedging strategy to implement it. What happens is that the generation of outcomes and the discounting process can’t be treated as independent, because of correlated moves between the stock price and currency. The result is a small, but conceptually important, modification: a kind of covariance or cross-convexity correction somewhat reminiscent of the difference between forward and futures prices. I informed Mark about what I had been told and about what I (and, as I learned later, others) had worked out. When it came time to write up those results for the RISK series (this time, at Mark’s suggestion, I took the lead), Mark refused to allow me to include him as a co-author (which would have repaid, at least in part, his courtesy with respect to the earlier papers) and insisted that I publish alone. Given the opportunity to own the correction of an error (and thereby redeem it for himself) or allow a junior colleague to receive all the credit, he demanded the latter.

I’ll miss Mark. I’ll miss his intellect, his charm, his modest eccentricities, his equanimity, and the twinkle in his eye accompanying his wit. But above all, I will miss his openness, his egalitarianism, his generosity, and his absolute integrity toward all the people and ideas he encountered.