The World According to Eric Reiner
Derivatives Strategy: The focus of your research seems to be trying to rationalize the theoretical basis for trading vanilla and exotic options. Is that how you'd characterize it?
Eric Reiner: Yes, with a view to ensuring the consistency of the two. Typically when we do exotic, structured transactions, we do them on underlyings with an established, stable market for vanilla options. So there's usually a fairly transparent term structure of volatility and a term structure of skew (strike dependence of volatility) for European calls and puts, and our job is to make sure that we can mark and hedge our exotics consistently with our vanillas. We don't usually try to model or predict the realized volatility of the underlying. Instead, we try to get a handle on what the matrix of available vanilla prices—vs. strike and maturity—tells us about how we should treat our exotics.
DS: The goal is to value things more accurately?
ER: Valuation is only part of the game. We also try to advise traders about their hedges. To be able to do that, we have to understand the dynamics of implied volatilities. If the market moves up or down, what happens to option prices and what happens to the volatilities implied by those option prices?
Let's say I'm looking at a oneyear option on the Standard & Poor's 500. Let's say it's atthemoney with a spot and strike of 1300. If the market trades up 10 points, will the value of that option increase proportional to its BlackScholesMerton delta, which assumes that its implied volatility will remain constant? Or will it go up by more or by less, based on other factors?
The answer to that question is important for hedging purposes, but it's also important because it can tell us something about volatility structure and dynamics, which we can then use—or ought to use as much as possible—in pricing more exotic options.
DS: Different people will have different answers to that question.
ER: Right, but they basically fall into three camps, each supporting a different viewpoint. The first is represented by implied diffusion theory, or what one member of my group has named volatilitybyspot. The second is called volatilitybystrike. The third is known as volatilityby"moneyness,” or volatilitybydelta.
"When you put 10 traders in a room and talk about models and market dynamics, you'll get 20 different opinions.” 
Quants and other people who follow the technical literature will be most familiar with—and will use—the implied diffusion approach. This theory is associated with Bruno Dupire, Emanuel Derman and Iraj Kani, and Mark Rubinstein. It says, start out in the BlackScholesMerton world, but instead of simply letting volatility be a function of time, make it a function of asset price as well. It contains a prediction that the underlying stock or index will generally realize smaller volatilities at higher prices than at lower prices.
That prediction also has implications for how implied volatilities should behave. For example, when the S&P 500 trades up from 1300 to 1310, the theory says that the 1300strike option will trade on a lower volatility, roughly the same implied volatility the 1310strike option was trading on before the upmove. The 1310strike option's volatility will decrease by roughly the same amount, call it X, so if we look at the world in relative rather than absolute strike terms, the atthemoney volatility decreases by 2X.
That's the theory quants are extremely fond of. Most of the models that quants build for exotics are based on this implied diffusion approach. The mathematics are attractive, but if you ask a trader, "What do you think?” he'll say, "I don't think markets do that at all. At least not most of the time.” This brings us to the second camp. Most traders will say that, on average, the 1300strike option will trade on pretty much the same volatility, regardless of whether the market moves up or down.
DS: This is based on their own memory?
ER: Institutional experience.
DS: So there's some accuracy to it.
ER: There's got to be something to it. Recently, Emanuel Derman took a look at the empirical data and saw that there are long periods in the market where it does seem to be true. If anything, it's a selffulfilling prophecy—if most traders believe that's how the market should trade, then how else will it behave?
DS: If that were the case, you'd think there would be some way to take advantage of that gap between models and trader intuition.
ER: That's an interesting point. The problem is this: It's quite difficult to build models that respond to the market in the same way that traders think, to find mathematics consistent with that kind of trader intuition.
DS: Why? Because it's not mathematical? Because it's essentially irrational?
ER: It might be. Markets are driven by psychology, by supply and demand, by consensus, and not by simple diffusion processes. It's difficult to build that kind of behavior into models. If the math were relatively easy, such models would be available, but it's not so easy. What you frequently see is people using a model that calculates values based on an implied diffusion approach and then jerryrigging it a bit, trying to get it to line up a little bit better with trader intuition. The problem is you don't really have a selfconsistent model, selfconsistent dynamics. Internally, you're building the model so that if the S&P 500 goes up to 1400, the volatility is going to decrease. But external to the model, you're tweaking things so the volatility stays essentially flat. Sometimes, the lack of selfconsistency can come back and bite you.
DS: I suppose the other way is to have traders actually construct the models.
ER: You need to have traders and quants working together. That's the only way you'll reflect any degree of market reality. You need to have traders understand and be reminded of—frequently—the assumptions that are built into the models. And you need to give them as much insight as possible—qualitatively and quantitatively—about where those models break down and about the potential errors associated with the models. I don't simply mean technical considerations like Monte Carlo error bars, but more literally: What is my model risk, and how much am I exposed to the assumptions built into the model?
DS: Do you find yourself talking to traders and saying, This is what we've come up with and it differs from your own perception of the market?
ER: I have those dialogues, those "polylogues,” frequently. Inevitably, when you put 10 traders in a room and talk about models and market dynamics, you'll get 20 different opinions. You need to have those conversations on an ongoing basis, because you want traders to be comfortable with what the models are doing—and you want them to share responsibility for and ownership of the pricing tools.
DS: A lot of people who have criticized modelbased derivatives trading have argued that the key problem is its failure to take market dynamics into account.
ER: At this juncture in the evolution of tradingland and quantland, there's probably some truth to that. It's a difficult, certainly not wellunderstood problem, yet we have to live with it and try to do something about it.
"A good correlation product that really isolates correlation has yet to make its way into the market.” 
Things get particularly tough when you go beyond a single underlying into areas such as correlation products, where you have to make assumptions about two or more markets' dynamics. Can you characterize the relationship between them by a single number, a correlation coefficient? I don't think so. There's a lot more richness to the dynamics than that, and I think it's difficult to build models that represent that richness.
DS: So are the people trading correlation and volatility products skating on thin ice? Is there enough pricing security to give confidence to the market?
ER: What good traders will do—on a correlation product, for example—will be to put upper and lower boundaries on the correlation. That's usually a good approach, except when things get difficult…
DS: So it's worthless. Or worse than worthless, if the models give you undue confidence.
ER: Most traders would tell you that if you rely on models in a time of crisis, you won't be very successful.
DS: Let's get back to your three camps. There's the implied diffusion theory or volatilitybyspot. Then there is the trader's view of things.
ER: That approach is called volatilitybystrike, or "sticky volatility,” because as markets trade up and down over the course of a day or over the course of a few days, traders believe the implied volatility for a particular option will stay roughly the same.
What does that imply? Let's look at our atthemoney S&P 500 option when spot goes from 1300 to 1310. The 1300strike option will trade on the same volatility regardless of spot and the 1310 strike on a corresponding, smaller volatility. If we switch again from absolute to relative terms, the atthemoney option's implied volatility will go down by the difference in volatilities between the two strikes. That's a prediction in contrast to what the implied diffusion theory says. According to implied diffusion, holding strike constant, option volatility goes down. Holding moneyness (the ratio of spot to strike) constant, option volatility goes down by roughly twice as much. Volatilitybystrike says that for fixed strike, implied volatility stays flat, and for fixed moneyness, it decreases.
We've known for a long time how to build tools to tell us what the implied probability distribution looks like in a world with strikedependent implied volatilities. But we have yet to build a good model to represent the market dynamics that volbystrike implies, because such a model necessarily incorporates both diffusion and complicated jump components.
In some sense, trying to fit traders' intuition and beliefs into models is actually leading us toward representing more of the real characteristics of returns processes. But it's still a tough problem.
DS: What's the third approach?
ER: The third approach is somewhat popular with traders on the long end of the maturity curve. If you look at options on some of the major indices that are three or five years out, there's reason to believe that as spot moves, options of the same moneyness will tend to trade on the same volatility. Hence, this view is called "volatilitybymoneyness.” With spot at 1300, if an S&P 500 atthemoney option one year out with a 1300 strike is trading on a 20 volatility, and the market moves to 1310, then the 1310 option will now be trading on a 20 volatility.\
Some people like to use a rule that was popular in the foreign exchange market for a while. To find the implied volatility for a particular strike, they add to the atthemoney volatility a constant times the delta of the given strike minus the delta of the atthemoney, both evaluated at the atthemoney volatility. Hence, this approach is sometimes called volatilitybydelta. There's some evidence, at least for longerterm options, that this works well for options on major stock indices.
"Financial engineering of products for corporate customers is much healthier than it was five years ago.” 
We've looked at what this set of traderbeliefs implies and built some dynamic models around it. It implies that as the S&P 500 moves from 1300 to 1310, the 1300strike option will now trade on a higher volatility. This is a distinctly different prediction from that produced by either of the other two approaches.
So you have three completely different sets of predictions. If you go to any particular trader and ask him which one of these is right, he'll tell you: "Well, this arbitrary one most of the time, but not always.”
DS: Does any of this vary by asset class?
ER: I live mostly in a world of equities. A lot of research has been based on equity indices, because the volatility patterns for these markets are relatively stable. If I tell you that the difference in volatility between a 1310 strike and a 1290 strike oneyear option is half a volatility point today, chances are good that something similar will be true tomorrow and a week, a month or six months from now.
DS: Whereas in the currency markets...
ER: The risk reversals can sometimes trade up or down, depending on supply and demand, or on the outlook for interventions from central banks. Foreign exchange markets are twoway markets. On dollar/yen, I can apply pressure from either side. Whereas with the S&P 500, I've only got one tradable product.
The implied dynamics seem less stable in the foreign exchange markets. In the equity markets, the strike dependence of volatility follows a consistent, regular pattern. The skew may trade up a little bit in times of crisis or trade down a little bit in times of stability, but it's not simply an artifact. It's there and, as a quant, I should try to build models consistent with it and mark all instruments consistently with it.
DS: So what are the implications of all this for trading?
ER: The easiest implication to see is that, even if you're trading a vanilla option, you'll get a different delta from each of the volatility camps.
To see this, let's go to the second case first: If you believe that your implied volatility will be the same BlackScholesMerton volatility no matter where spot trades, you should be hedging on a BlackScholesMerton delta.
Now let's go back to the first case. If you're actually hedging on this volatility surface, with smaller volatilities at higher spot levels and larger volatilities at lower spot levels, then your delta should be a little bit lower. You can think about adding to the BlackScholes delta a correction term, which is just the change in the implied volatility as spot moves times the option's vega. In the third case, this simply works the opposite way around: Your delta will be a little higher.
DS: What do you think of using secondorder derivatives like vomma and vanna?
ER: In some ways, they're a good idea, and they appear pretty naturally when you're looking at volatility dynamics such as those we've been discussing. But you shouldn't think that knowing a few higherorder local derivatives tells you all you need to know about your risk. It doesn't replace knowing what your book looks like. Where are your strikes concentrated? If volatilities shock up significantly, how is your long or short vega going to change? And by how much? What will happen if you're short a lot of outofthemoney strikes, and volatilities suddenly go up? You may be comfortably within risk limits when the markets are quiet, but when things get a little more excited, you may find that you're suddenly short volatility—and all of those outofthemoney options suddenly have a lot of vega. Now you're short lots of volatility and the risk managers want to know why—and what you're going to do about it.
DS: What do you think about the future for exotic derivatives? Is the era of innovation behind us?
ER: The markets for interesting newfangled stuff have been fairly quiet over the last year or so. People are trying to batten down the hatches for year 2000, among other things.
DS: Liquidity has certainly dried up dramatically.
ER: I would hope that after Y2K issues are resolved early next year, we'll begin to see creativity flowing again. A lot of us work from the belief that all this exotic stuff over time becomes an additional set of colors to use in painting structures for clients. We've been using a somewhat simpler palette lately. In the long run, we want to be careful, because we don't want to paint something that clashes. We're best served by producing products that are useful and attractive to a variety of customers.
I think that's why financial engineering of products for corporate customers and even private clients is much healthier than it was five years ago. We have a bettereducated client base, and we've made the tools transparent in ways that were not so obvious years ago.
DS: What kind of structures will we see three or four years from now? More products based on newer asset classes such as volatility and correlation?
ER: Volatility products are in their infancy, and we're beginning to get a better handle on them. A good correlation product that isolates correlation the way a volatility swap isolates volatility has yet to make its way into the market. I think it would be a valuable addition. This kind of product would be easier to construct in foreign exchange than in equities, because there's no natural hedge for it in the equities world.
Ultimately, the old problems are still the good problems. What's the right way to hedge a vanilla option—other than simply selling it to somebody else? It isn't simply like buying a bond. If you're short an option and you're deltahedging it, there's no trivial answer. There's no lack of challenges to keep us busy.
