We had the pleasure of chatting with Professor Emanuel Derman at his office at Columbia University. Probably best known for his work on option pricing, he introduced, together with Fischer Black and Bill Toy, what was to become known as the BDT, or Black-Derman-Toy model, a popular model used for pricing interest rate derivatives. Following research postings at the University of Pennsylvania and Oxford amongst others, he spent five years at AT&T Bell Laboratories before joining the fixed income department at Goldman Sachs in the mid-80s. After a short hiatus at Salomon Brothers, he re-joined Goldman Sachs in 1990, finally leaving in 2002 as head of the Quantitative Risk Strategies group. He is currently professor, and director of the MS in Financial Engineering Program at Columbia University in New York. He has contributed extensively to the fields of physics and finance, and gained mainstream appeal for his book “My Life as a Quant. Reflections on Physics and Finance”. He was awarded the Financial Engineer of the Year award (in 2000), and was elected to the Risk Hall of Fame in 2002.

CFM: In your memoir, you recall the early days of quantitative finance and what it was like to be “a good quant”, i.e. being “part trader, part salesperson, part programmer, and part mathematician.”11 Reflecting on what the industry looks like today, do you think this still holds?
ED: Yes. I think even more so in some sense. When I first started working in finance during the mid-80s, many of the quantitative researchers weren’t programmers. They were doing the quantitative modelling and IT did the programming – there was a gap which led to mistakes with neither side able to figure out where errors crept in. Now, with nearly universal electronic markets and quants wholly dependent on wrangling large quantities of data, that is necessitating a further closing of this gap.
CFM: Most of the first wave of quants on Wall Street hailed from physics departments and laboratories. Do you think the success of physicists in quantitative finance was owing to this jack of all trades approach?
ED: Yes. Physicists do their own dirty work. At least in my day. You didn’t have somebody who could do your programming for you. When I was running the group at Goldman, we never had a boundary between quants and IT, which I preferred, and which I think worked well.
CFM: Do you think such an interdisciplinary attitude to research in quantitative finance is bound to gain more emphasis, or has the industry become so complex that more specialisation will be required?
ED: I’m a little torn. I think it is important to be an interdisciplinary thinker, but at the same time I notice people becoming ever-more specialised, ever-more pigeon-holed. Often, somebody’s name appears on a research paper having only done a very specific part of the data analysis for example. Being an expert might be very useful for this purpose, but, then again, take for example the excitement of ‘Big Data’, where I feel there is a risk of researchers doing statistics on data without knowing the field they’re working in. And I disapprove of this trend – I believe you not only need to understand the style, but also the content, and the context of what you are doing research on.
CFM: You mention Big Data. Together with Artificial Intelligence (AI) and Machine learning, this trinity of topics are claimed to hold great promise, with many scrambling to employ these tools in their business. Do you think it will revolutionise finance?
ED: I am sure that it will revolutionise medical science, and even fields like media and advertising. For finance it is less clear to me. This scramble has forced many to make bold claims, and that they are actively employing these tools – when it might just be for window dressing. Not talking from first-hand experience, but it may well be that there is some untapped potential in the explosion of alternative data sources, using these new tools in unison. Besides, I have found a lot of students becoming more interested in machine leaning and Big Data, which bodes well for the field.
CFM: This allows me to shift to your current role as director of the MS in Financial Engineering (MSFE) at Columbia. In this role as an educator, how have you seen the academic landscape changing over the past decade, and has it kept pace with what is required from graduates in the workplace?
ED: There is for one, a noticeable shift from sell-side, to buy-side centric education. The needs of the industry, especially since the financial crisis, but even a little before, have been moving away from sell-side research and derivative product design, to serve the demand in the asset management and hedge fund business, where skills for risk management, asset allocation, and alpha generation are prized. A second shift, is the way in which quantitative finance is taught, with a much more Martingale-style approach.12 Something which I disapprove of.
CFM: What is your main criticism against this approach of teaching?
ED: Finance being taught as an axiomatic, mathematical field based on probability theory has become almost standard. People teach the fundamental theorem of finance which is some theorem of changing measures. However, there is no fundamental theory of chemistry or physics, so why – I ask myself: “Why should there be a fundamental theorem of finance?” Even saying there is a fundamental theorem makes it sound like a mathematical science. There are no theorems in Physics, there are laws. Furthermore, none of those intrinsic axioms of finance hold true in the real world, and yet students get taught in this style. The risk is that students and practitioners develop a sense that finance is governed by laws, and you can turn a crank to get the right answer on a problem.
CFM: Do you think this undermines the ability of original thought?
ED: When students do everything the Martingale way, they always get the ‘right’ answer, but they don’t understand the intuition behind what they are computing. When you ask for example “How do you value a forward”, they tell you to go into the risk-neutral measure and you discount it at the riskless rate and you get the price. But they don’t understand that there is, in practice, a trading and a hedging strategy lurking somewhere in there. I used to interview people at Goldman who came out of Math-Finance programs and I would ask them: “Supposing I am an intelligent person, but I don’t know that much about physics, explain to me why we can shoot a rocket to the moon?” Then they would tell me about Newton’s laws and explain dynamics. Then I would ask: “Supposing I am a reasonable person, but I don’t know that much about finance, tell me why people can agree on an option price?” And, invariably, they would say “because of Girsanov’s theorem” as though that was the equivalent of Newton’s laws. But the real answer should be because I can hedge out the risk, or I can make a riskless portfolio by going long the call and short the stock. But they somehow thought the Girsanov’s theorem was a law of nature.
CFM: Short of a universal law in finance, do you think there is a Holy Grail in finance, an ideal equation to model markets?
ED: No I don’t. When I started at Goldman in ‘85, and soon thereafter started working on what was to become the BDT model, I always imagined we would find the one description of interest rates that would allow for the valuation of anything. Fischer Black didn’t have that attitude, although I didn’t properly understand it at the time. He thought there were many parallel ways of looking at different parts of the market – there didn’t need to be one consistent way. Over time, when I started working on the volatility smile, I realised that most finance models are just glorified interpolations – you write down a model with plausible dynamics, fit all the liquid instruments that you can value, because it is calibrated to them, and finally, you try to value the illiquid instruments by interpolation. But! Things change as market behaviour changes. There was for example no ‘smile’ in gold options markets before 1998, but it appeared thereafter.
CFM: Is there anything you are working on, anything you published recently?
ED: I recently wrote an article on the Black-Scholes model that will be in ‘Inference’ – a sort of critical review as to what extent Black-Scholes works, and to what extent it doesn’t.13 In the article I quote Elie Ayache who wrote a book called the “The Medium of Contingency”, in which he argues that derivatives aren’t really derivatives, for, he claims, you can’t really replicate an option, because you don’t know what future volatility is. I’ll explain: I want to hedge an option; but I need the future volatility to hedge it; so, not knowing what future volatility is, I calibrate my model to fit the market; giving me the implied volatility; so, I use the implied volatility to calculate the delta, to hedge the option; but then tomorrow there is a new implied volatility. So, Black-Scholes, being predicated on knowing the future volatility in order to replicate the option, fails, because you can’t replicate an option because volatility keeps fluctuating. Every day your estimate of volatility changes, and so when you hedge an option, what you are really doing, is betting on volatility. So, because volatility is not constant and is stochastic, and different volatility measures change independently (implied and realised volatilities), the failure of the model allows you to trade volatility. In other words, the failure of the model to be correct liberates you to trade the thing the model assumed was going to be constant.
CFM: Do you think, inherently, the structure of volatility has changed?
ED: Certainly compared to twenty years ago, my impression is that volatility mean-reverts much more quickly. Of course, implied volatility has been much lower than historic levels, but, after spikes in volatility seems to revert back to levels prior to the spike, more quickly. It is interesting how the market has developed over the past couple of decades – certainly, 40 years ago, nobody was thinking of volatility as something you could trade. They were just directional when they used options, and now you can trade volatility of volatility instead of the direction of volatility.14
CFM: This is reflective of the culture of the finance industry?
ED: Take credit default swaps – 30 years ago, if you wanted to trade credit, you had to buy a corporate bond and short Treasuries to trade the credit spread and you had to be quite sophisticated. With the invention of credit default swaps, anybody could trade credit. This is dangerous. And I think the same thing has happened with volatility. Today you can trade in VIX futures or options, and I think it may be too easy. It reminds me of research on the ‘anthropology of finance’ by a group at the New School in New York, who observed, perhaps somewhat fancifully, how the world, around the time of Black-Scholes, got more interested in randomness than directionality. Culturally, this was observed in French cinema during the 50s, slightly predating the publication of the Black-Scholes model. These films were often plotless, with a flâneur, strolling around aimlessly, who experiences life without having an aim of where he or she is going, but experiences and enjoys the volatility of crowds. The theory goes that finance evolved in a similar vein, though more quantitatively, in that it became more focussed on the volatility, i.e. by how much the price fluctuates, as opposed to its direction (i.e. either drifting up or down).
CFM: Is there any contemporary research that you find of particular interest?
ED: There is a field of economics called ergodicity economics, which proposes an interesting alternative to certain foundations of economic theory, particularly to the bias approach of behavioural economics. I generally dislike many of the views of behavioural finance for a bunch or reasons. They [behavioural economists] argue human beings act irrationally. They call them irrational, because their simplistic rules for what ‘rational’ should be does not capture human behaviour. Ergodicity economics proposes a competing view of financial values based on time averages, rather than ensemble averages that may explain people’s financial behaviour better.
CFM: So irrationality is just another way of saying the uncertainty of action, or human behaviour that is not captured by a pre-defined set of behavioural rules?
ED: Yes. To use an analogy: in physics, if something does not behave according to your laws, you say “my understanding of the phenomenon is wrong”. In finance, if markets or people don’t obey or behave according to your theory – you say “they are acting irrationally!” – Instead of saying you don’t understand what is driving their particular behaviour. It is unrealistic to imagine there are hundreds of irrational ‘biases’.
CFM: What is the most interesting, or difficult, option you ever had to price?
ED: I won’t claim there is just one of particular interest or difficulty, but, there were options I particularly disliked. Right around my final days at Goldman, French ‘Mountain Range’ options became popular. In the 80s and the 90s, markets were mostly doing interesting pay-offs on single underliers, barrier options, average options, Parisian options and the like. But then during the late 90s, Société Générale introduced options with names like ‘Himalayan’ and ‘Everest’, and they were simple pay-offs on baskets of underliers. They were correlation, rather than structural trades. They were, ultimately, subtle bets on the correlation between winners and losers. Horrible things.

11 From “My Life as a Quant: Reflections on Physics and Finance”, Wiley, January 2016.

12 In probability theory, a Martingale is a sequence of random variables (or, as it is commonly referred to as, a ‘stochastic process’).

13 The article entitled ‘Trading Volatility” is available on the website of Inference: https://inference-review.com/article/trading-volatility.

14 Interested readers are referred to our technical note that investigates the features of volatility and, more specifically the features of the volatility risk premium: Is there a ‘new normal’ in Volatility Markets?


The text is an edited transcript of an interview with Professor Emanuel Derman in May 2019 in New York. The views and opinions expressed in this interview are those of Professor Emanuel Derman and may not necessarily reflect the official policy or position of either CFM or any of its affiliates. The information provided herein is general information only and does not constitute investment or other advice. Any statements regarding market events, future events or other similar statements constitute only subjective views, are based upon expectations or beliefs, involve inherent risks and uncertainties and should therefore not be relied on. Future evidence and actual results could differ materially from those set forth, contemplated by or underlying these statements. In light of these risks and uncertainties, there can be no assurance that these statements are or will prove to be accurate or complete in any way.

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