8 Difficult Equity Derivatives Interview Questions

While the equities side of sales and trading has shrunk in headcount over the past decade - as many desks like cash equities have been almost entirely automated - equity derivatives is as strong as ever.

In fact, most equity derivatives desks across the street are in desperate need of new talent on the both the sales and trading side and are trying to expand out rapidly.

This all shouldn't be too surprising, given that firms like Goldman Sachs, J.P. Morgan, and Morgan Stanley and are racking up in some cases 200% gains in equity derivative desk revenue in 2020 and 2021.

So, taking a step back, when we talk about equity derivatives in the S&T context, what exactly are we talking about?

The first point is that we aren't talking about desks going out and buying up retail flow (e.g. some random person buying a singular call option on a supposedly hot stock). This is an area of market making done by hedge funds - via payment for order flow - where they pass on a bit of savings to the user, a bit of money to the platform, and keep a bit for themselves. 

The reason why some quant hedge funds (like Citadel Securities and Virtu Financial) are fine going and buying up lots of retail order flow in an indiscriminate manner without knowing who is behind the order, is that they assume everything is just random. A random person buying a call option here, or a put option there, doesn't actually have any insight into the market so these hedge funds aren't as worried about being caught on the wrong side of a bunch of trades.

This leads into the second point, equity derivative desks at sell-side banks (like GS, JPM, Citi, Barclays, etc.) are dealing with clients who are institutional, sophisticated, and probably have some level of "edge". Because of this sales people and traders think carefully when a client comes through wanting to do a trade.

Third, the trades that these large, sophisticated clients come to a sell-side equity derivatives desk wanting to execute are often large and sophisticated types of trades! These are trades that need to either be thought about for at least a few minutes or need a pricing model far beyond what's standard.

Note: A client could come through wanting 1,000 calls on Ford, for example, which an equity derivatives desk may give a price for in a few seconds (by just using one of their standard pricing models or even just placing it in Bloomberg). 

The fourth point is that, like in every area of modern sales and trading, the goal is ultimately to be a market maker and to clip a fee for doing each transaction. The larger and more thorny the transaction, the larger the fee will be. In an equity derivatives context what this means practically is that the bank wants to execute the trade at a given price that will allow them to quickly go out and hedge their exposure to the trade (e.g. not make or lose money no matter how the trade unfolds over time) and clip a spread between the revenue brought in from the trade and the cost of hedging out that trade. 

The fifth (and final) point I'll make about an equity derivatives desk is that everyone has a very distinct role.

• Sales people are constantly talking to clients and pitching them often quite esoteric potential equity derivative trades
• Traders are figuring out a price and then hedging out their position as best and as quickly as they can
• Structurers are coming up with some esoteric potential trades that sales people can pitch (and perhaps helping traders with pricing more complicated trades clients want to do)
• Quants are creating, monitoring, and tracking the risk tools that are keeping track of the desks exposure and developing new pricing and hedging tools for the desk

No matter which role within an equity derivatives desk you'll be on, it's going to be quite complicated! As a sales person, you may not be responsible for hedging out gamma risk, but you still need to understand the gamma embedded in a trade you're bringing a trader. 

Hopefully this gives you a general idea of the structure of a sell-side equity derivatives desk and what it really involves. Given the retail popularity of equity derivatives, I imagine most have quite well misconceptions as to the nature of work and how the desk makes money. Now lets's get into some questions.

Equity Derivatives Interview Questions

Below are some equity derivative questions you can expect in a sell-side sales and trading interview. In other words, if you're interested in the equity derivatives desk at Goldman, Citi, etc. 

Remember that if you're applying for a summer analyst position in sales and trading you will not be picking your desk prior to your interview. So these questions would only possibly come up if you express an interest in equity derivatives to your interviewer and they happen to work somewhere in the equities division.

Question 1: What does implied volatility really mean?

Question 2: As volatility rises what happens to the value of either calls or puts?

Question 3: How is delta non-linear? What's this even mean?

Question 4: When is gamma at its lowest?

Question 5: What would a vega of $0.40 mean?

Question 6: If we have a long call position, does it have a negative or positive delta, gamma, theta, vega, and rho?

Question 7: What does skew refer to?

Question 8: Why would you ever put on a long straddle?

What does implied volatility really mean?

Implied vol can be thought of as being backwards looking. It's like being asked how much oil there is in your car -- you need to actually put the dipstick in and find out.

Simply put, implied volatility is the volatility built into the actual dollar price of an option. Instead of using a volatility assumption, you figure out the volatility by looking at the trading at in the market to determine the volatility it must have to give that market price. 

If it makes more sense to you, perhaps think about implied volatility as really meaning the "observed" or "real-world" volatility we see in a given option.

As volatility rises what happens to the value of either calls or puts?

As volatility rises the value of either a call or a put increases. Think about it this way, if I have a strike price that's way out of the money (OTM) then what is most likely to get me to the strike price: higher or lower volatility? 

The answer is obviously higher volatility as with higher volatility we have bigger price jumps and if we're far from being in the money we need big price jumps to get there.

How is delta non-linear? What's this even mean?

Let's remember that delta is just the measure of the change in the option value given a change in the underlying (assuming that everything else is held constant).

So, for example, a long call would be delta positive given that as the price of the underlying moves up, you have an increase in the value of the long call). 

Now if we have very large moves in the underlying, our predicted delta won't actually perfectly align. This is due to gamma (which measures the change in delta, or is the second derivative of the price of the underlying moving) and the idea of convexity. 

So when we say that equity derivative traders on the sell-side try to hedge out their exposure as soon as they do a trade (to clip a spread and lock in profits) we're being a bit too oversimplifying.

Because in reality if a hedge fund comes in with a large trade, then as the underlying moves how much we should delta hedge is not quite right. We need to take into the effects of gamma and convexity for large movements or else we will be underweight or overweight on our hedge.

This is part of what makes equity derivatives books so messy, complex, and interesting. There are lots of tail risks embedded that are only able to be seen when the trader's book is really under stress. 

When is gamma at its lowest?

Gamma tends to be at its lowest when the option is very OTM or very ITM. Gamma is highest when you are ATM as you're oscillating around the option being in or out of the money.

As you get further ITM or OTM your delta hedging needs, in other words, don't change much for any given change in the underlying. 

Remember that what we're measuring here is the rate of change. So a way we can rephrase all of this is by saying the rate of change of gamma is highest when ATM, because your delta hedging needs will be changing most for any small movement in the underlying.

Whereas, when you're far OTM or ITM small changes barely affect your need to change the rate of your delta hedging. 

It's kind of like when you're driving on the highway, changing your speed up or down 5MPH isn't overly noticeable. However, if you're driving through a school zone you'll really notice if you're over or under the speed limit by 5MPH. 

What would a vega of $0.40 mean?

A vega of $0.4 would mean that for a 1% change in the volatility of the option, the option will increase or decrease in value by $0.40. Here we're referring to the assumed volatility of the option. 

If we have a long call position, does it have a negative or positive delta, gamma, theta, vega, and rho?

In the equity derivatives guide in the sales and trading course, I go over definitions and various little cases like this if you like these questions. 

So for a long call, we have a positive delta as we already mentioned. As the value of the underlying moves up, then the option value increases, thus the delta is positive. The same is true of gamma, which measures the rate of change of delta. 

Theta is negative as the less time we hold the long call position, the less change we'll have an event that leads to it being ITM. 

The vega is positive for the reasons we already discussed (the more volatile the underlying, the higher chance it'll get in the money). Likewise, rho is also positive as a change of interest rates boosts the option value of a long call. 

What does skew refer to?

Equity derivatives has a bit of a unique language that can make it a bit intimating to deal with. That's why I've tried to rephrase some of the answers here to hopefully make them a bit more understandable (hopefully I've been successful!).

All skew refers to really is that with options you obviously can have a diversity of strike prices and a diversity of expiration dates. Skew is when you look at the difference in implied volatility for options that are in the money, at the money, and out of the money while having the same expiration date (so obviously, by definition, they must have different strike prices!). 

Why would you ever put on a long straddle?

This would most likely be to reflect a belief on your part that levels of volatility will rise. You'll do a long call and a long put on the same underlying with the same strike price and time to expiry. The strike chosen will be often where the underlying is trading now.

Remember in previous questions we've talked about how how higher levels of volatility are positive for long calls and puts (as it gives them a greater change of being ITM). You may think that these positions (a long call and a long put) would somehow cancel themselves out and be opposites. However, if we have rising volatility that'll push both prices in an asymmetric fashion (the one that goes ITM will rise in greater value than the one OTM will lose in value due to rising vol). 

Conclusion

Equity derivatives is an area of sales and trading that isn't for everyone. Even if you're in sales, you're still going to need to have a strong technical background in order to get placed there.

However, equity derivatives offers a great learning experience, plenty of exit opportunities, and very strong compensation.

One of the benefits of being on the equity derivatives desk is that you are learning something that is more valued outside the realm of sell-side investment banks. This stands in contrast to areas like municipal bond trading that pigeon hole your exit opportunities quite a bit (given how niche that product is).  

If some of these questions seem quite advanced for you, remember that these won't necessarily come up in a traditional sales and trading interview unless you express an interest in joining the equity derivatives desk. 

With that being said, you should know these kinds of questions because when you join sales and trading as a summer analyst - and try to get placed on the equity derivatives desk - you will have a quasi-interview where you will get these kinds of questions.

If you're looking for even more questions, be sure to check out the sales and trading interview questions I compiled or get all the sales and trading guides (which include dozens more equity derivative specific questions). 

I created these guides because there are no practical resources out there on sales and trading (not only in terms of interview questions, but also helping you understand what various desks do and what one is perhaps right for you). 

Good luck!