Peter Christoffersen

Reading time :
17 Jan 2022

"I love the combination that the students have: they are very technically skilled on average and also have all a wealth of practical experience. The biggest challenge for the traditional PhD student is to come up with ideas, whereas the EDHEC PhD students typically have lots of ideas from their work and their challenge is finding time to execute them. So it is fun to be around students who have ideas and different challenges."

Could you tell us a bit about your background and what your research focus is?

I finished my PhD in Economics in 1996, having focused on time series econometrics and forecasting with applications to finance. My first job was at the International Monetary Fund in Washington DC and I was fortunate enough to work for a year in the Capital Markets division of the Research Department. There, I got exposed to all the current issues in international regulation and supervision of the financial markets. These were particularly “interesting times” as, over the course of my two-year tenure there, the Asian financial crisis broke and Russia defaulted. All of a sudden, the whole world started to realise that finance was much more important for everyone than previously thought. So I got more and more interested in moving my focus of work from straight econometrics and into more finance, using my econometrics background. I started working on option valuation and on various issues surrounding emerging financial markets. In 1998, my wife finished her PhD and we went on the job market together and we ended up in Montreal at McGill University, where we both started as assistant finance professors. That completed the transition to finance for me. I was very fortunate to meet Kris Jacobs at McGill, with whom I have had a very productive research relationship. My earlier work had been on back-testing risk models. Over the first ten years of our collaboration, Kris and I worked on a bunch of different papers surrounding empirical research in option valuation. Much of the early option work had been quite theoretical in nature and there was not much large scaling empirical work that compared models – what kind of model is better, what kind of volatility dynamics do we need, what kind of distribution do we need, etc. Our angle was to test empirically motivated discrete time models, whereas the extant literature was focused on continuous time models. We ended up publishing quite a few papers on GARCH option pricing. We started working with Steven Heston from the University of Maryland on new model development and their implementation on large-scale option data sets. Our early research was focused on finding a better volatility model, but the work we have been doing more recently I believe is in some sense even more interesting: we look at what option prices tell us about the pricing kernel (the transformation from the physical distribution that the underlying asset follows to the pricing measure that we use to price derivatives), which in turn tells us something about the manner in which different aspects of risk are rewarded. As options are not linear assets, it turns out you can get a lot of information from options that is not immediately available if you just try to estimate the pricing kernel from prices on the underlying asset. What I told course participants is that are many econometricians who work on estimating the physical distribution and financial engineers who work on estimating the pricing measure, but really a lot of the interesting work is on how those two are related, which is the pricing kernel. In order for us to get a handle on what the pricing kernel looks like, we need to jointly estimate the models for returns on the underlying asset and option prices. We recently published a paper in the Review of Financial Studies on this topic, but there have only been a few papers and we still have a lot to learn about what the optimal pricing kernel specification is. The fascinating thing is that a lot of people have this Black-Scholes mindset where the markets are complete and there is no choice to be made for the pricing kernel, but of course, now that we realise since Hull and White’s and Heston’s work that volatility is scholastic and option pricing very much reflects that, we are not longer in a complete market setting: we are in an incomplete market world where the pricing kernel is not unique and it is very much a task for the financial econometrician or economist, to specify the pricing kernel along with the physical distribution for the underlying asset, so it is an important as well as a fun task from an economic perspective.

This is closely related to the elective you taught in the programme. Could you tell us more about the objectives of this course and the way you organised it?

The course looked at different aspects of financial risk management and was split into five sections. The first section was a recap on volatility modelling, the second section was on modelling correlation dependence across assets, the third section was on option valuation, including pricing kernels and the fourth section looked at the use of highfrequency information in portfolio allocation and risk management, which is how we can harness the all the information we see intraday investment management. The most obvious application is volatility forecasting and that has been done by many people over the years. I know Torben Andersen has taught a realised volatility elective in the EDHEC-Risk Institute PhD in Finance, covering that whole aspect. My focus is how to go beyond volatility, what else the intraday data tell us and what it can be used for. This is still a new field and I encourage students to go and look for ideas and topics in this area. The final section of the course surveyed the use of optionimplied information for better portfolio allocation and risk management. There is very recent literature on this topic, which started with a paper by Ang, Hodrick, Xing and Zhang in the Journal of Finance in 2006, in which they showed that a stock’s exposure to the VIX (the option-implied volatility index from the Chicago Board Options Exchange) helps explain the expected return on the stock. I became fascinated by this paper and have since done some work with Kris Jacobs and PhD students on stock exposure to option-implied skewness, finding that it too is priced. More recently, I started looking at option-implied oil volatility and found that stock exposure to oil volatility has been priced in the cross-section for the last ten years. There appears to be a structural break in 2004/2005 when a lot of things changed in commodity futures and options markets, with a move towards financialisation.

I try to encourage the students to be creative in terms of what kind of information we can get out of the stock prices that people have not yet had a look at. I told the students at the beginning of this course that my goal for the course is for each of them to get an idea for a paper during the course. So, I tried to give them some tools that I found useful both in terms of high frequency data and options and large-scale multivariate models, but I also tried to show them a bunch of applications. I also very much tried to emphasise that they should all be doing empirical work as part of their dissertations. I find that the EDHEC PhD programme has some extremely quantitatively strong students, who would naturally tend to focus a lot on their strengths, so when it comes to discussing their dissertations, I tell them I want to see what the data has to say before they show me their models. To push them in that direction, I asked all participants to present a current research idea or topic of interest before I formally began the class, and gave each of them only eight minutes to do that, asking them to focus on ideas they had not presented before. This also allowed me to identify topics that were related to the elective and that I was able to refer to in the context of the course, which made the lectures more interactive.

This is your second time teaching in this programme. What is your impression of the participants?

I had a lot of fun teaching here in Singapore, as well as in Nice two years ago. I was extremely happy when EDHEC invited me to come back and do it again. In Nice, my motivational introduction to the course described two traders who had used two different risk models and as a result, had two different VaR limits, were not able to take the same positions, and had different P&Ls as a consequence. I remember there were several students in the class who were in the situation that my fictional traders were in, so right away there was a connection with the students; once some students can see that other students are interested, then they become interested too and that becomes a lot of fun. I love the combination that the students have: they are very technically skilled on average and also have all a wealth of practical experience. The biggest challenge for the traditional PhD student is to come up with ideas, whereas the EDHEC PhD students typically have lots of ideas from their work and their challenge is finding time to execute them. So it is fun to be around students who have ideas and different challenges.

The paper you presented for the research workshop, while also related to the pricing kernel, explores a topical area that you did not approach directly in the seminar. Could you tell us more about this work?

Yes, I presented a working paper titled “Illiquidity Premia in the Equity Options Market”. In the wake of the financial crisis, there has been an increased focus on illiquidity premia, how illiquidity is priced, how illiquidity changes in different markets or how funding and market illiquidity differ. A lot of papers have dealt with the equity markets and there has also been some work on the bond markets, but very little has been done on illiquidity premia in derivatives markets. Most of the existing option papers look at illiquidity across time and underlying assets, but do not really address the question of premia. So how expected returns on different derivatives are related to illiquidity is what we look at in this paper. We use US equity options and document illiquidity premia using a large cross-section of firms. An increase in option illiquidity decreases the current option price and predicts higher expected delta-hedged option returns. This effect is statistically and economically significant, and it is consistent with existing evidence that market makers in equity options hold net long positions. The illiquidity premium is robust across puts and calls, across maturities and moneyness, as well as across different empirical approaches. It is also robust when controlling for various firm-specific variables. The link with my other work is that none of the models we designed for option pricing has illiquidity in them, so we are starting afresh, looking at the data and what it tell us, wondering what an option pricing model that includes illiquidity should look like. The data exploration exercise is a first step helping us learn how illiquidity and option prices are related. There has been some research done on the pricing of options on illiquid stocks. Here, we look at illiquidity in the option itself. There is not yet a model for that. I would love to say we have one, but we do not; we just have ideas of avenues to explore. For example, in an incomplete market with stochastic volatility, there could be an illiquidity premium driven by the option’s sensitivity to volatility as well as by its sensitivity to the underlying stock… So that is sort of the way that we are headed with our work, but for now, it is only an empirical investigation.

You mentioned that the difficulty for the usual PhD student is to come up with an idea. What would be your recommendations for the participants of the EDHEC programme?

I saw 10 eight-minute presentations this week in the context of my course, as well as a couple of halfhour presentations that PhD candidates gave to the programme at large as part of their annual research presentation series. I was impressed by the quality of the ideas and the diversity of the areas of interest, so it seemed they were definitely doing something right. In general, I encourage students to read something other than academic research. In my experience, if you simply read a bunch of working papers, your brain starts thinking that everything has been done. You need to read something else, like The Economist or the Financial Times. You do not want to spend all day reading the news of course; the weekly frequency works fine with me. Another recommendation is to just explore data and get motivated by some interesting empirical finding that is puzzling from an economic perspective.

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