Sales and Trading Interview Guide: Option Greeks Primer – Preface
A word of fair warning. This is a trivial book by quantitative standards.
It is trivial because as a handbook it doesn’t present proof, pose revolutionary solutions or spend time deriving interesting partial differential equations (PDE). If you were looking for any of these three items, please feel free to put the book down now. We won’t hold it against you.
This is a book about teaching intuition – intuition for a topic that despite its importance to trading desks, doesn’t get fair coverage in business school text books or the student side of the academic world. This morning when I asked a colleague about the coverage of Vega, Vanna and Volga in his examination materials for a well-respected risk management exam, I was informed that the materials added up to just under three paragraphs. Only one of which was relevant, the other two were for background. Only Vega was mentioned, Vanna and Volga were not covered.
It’s just as bad as it used to be for convexity two decades ago.
The interesting part is that there is really no shortage of material on the subject. When it comes to option Greeks, the topic catches the fancy of PhD students all over the world. We have an abundance of high quality research papers, practitioner handbooks and publications but not enough class time for entry-level students or professionals. Which is compounded further by the terminology chasm. God forbid if you are a fresh arrival in the field, a recent hire at a trading desk, or even worse, at the internal risk management group, learning and getting comfortable with the language is a task. The real challenge is scaling the wall of notation and context before you can decipher the literature available in the field.
On Building Intuition
Trading requires a combination of discipline, process and intuition. Of the three intuition is the most difficult to teach, since discipline and process are an incentives and control game. While individual intuition can be built over years of experience there are tools that make it easier to pick and transfer intuition faster.
Institutional intuition gets passed on between generations of traders through shadowing, standards, trader’s lore and floor legends. This passage becomes easier if you have a knack for the subject, if you already know some of the rules or if you are familiar with the trading language.
The sales and trading language has many dimensions dealing with execution, trading strategy, customer behaviour and product variations. This book only focuses on one very limited aspect of that language – the aspect dealing with option Greeks and hedging.
The challenge with this part of the language lies partly with terminology (a range of Greek symbols), partly with presentation (partial differential equations), with calculations (a combination of Greek symbols and partial differential equations) and with interpretation (can you please say that again in a language that we can all understand).
Most business school derivative courses run out of time and patience before the derivative product universe has been covered, let alone spend time on how to read, predict or forecast the behaviour of exotic Greek symbols. We certainly manage to touch them (briefly) and talk about them superficially but we have never had time to do justice to the topic.
Advance derivative courses only cover pricing (and if you are lucky spend limited time on sensitivities and Greeks) because of conflicts with other topics in the outline. Sometimes as business school students all you will get are case notes and text references that are long on definitions and calculations but short on guidance and practical applications.
This is unfortunate because the option price sensitivity topic is difficult to grasp for any audience given its non-linear nature. It takes time to think comfortably in the non-linear world. We understand simple, straightforward, single dimensional relationships very well. When asked to envision a new dimension or even worse collate reactions from multiple dimensions into a single trading decision, our mental frameworks tend to breakdown. And frankly speaking the PDEs don’t help at all. A decade and change ago it was an interview question on the behaviour of the third moment of a derivative security that stumped me on Fleet street. Not much has changed since then.
To develop an appreciation for this topic you need at least a few weeks of hands on modelling experience followed by a few months of active application of the same concepts on a trading desk in shadow mode. The reason why you have purchased this book is because you don’t have a few weeks or a few months. You possibly have a few hours or a night before that interview or risk presentation is due.
We can’t teach intuition or a new language in a few hours. But we can certainly get you started. The book uses a tutorial template. Primary lessons are compressed into short bite sized pieces. There are some equations but we limit ourselves to curt references; we don’t spend time on them or their derivations. We do spend time on ground rules and behaviour.
As an interviewer, I am more likely to ask you about how Gamma is going to behave under a given scenario and the relevant trade when that scenario occurs. I may ask you how that is different from Vega’s reaction rather than ask for its partial differential equation (though I may ask for the latter too, depending on my mood and how much I dislike you). If you really push me, I may also ask that third moment question. I am more interested in how you think, your ability to grasp a concept, your awareness of the context and capacity to appreciate how positions may flip directions; your intuition, rather than your memory.
The only way to do this is to make you walk through thought experiments dressed as EXCEL spreadsheets. Read the chapter, dissect the model, build it on your own time, follow up with exercises and what is next questions. Repeat. Numbers, models and graphs that we have tweaked ourselves have a higher chance of being retained, than those on printed papers or electronic screens.
What do we cover?
The book is organized in five parts.
Part I – The refresher
The first part consists of two chapters (chapter zero and one) as background and refresher of basic materials that can easily be skipped by more experienced readers. They cover basic themes, a few relationships and numerical examples to reinforce calculation and usage conventions of Greeks.
Part II – Delta hedging simulations
The second part begins with a simple Delta hedging simulation for a vanilla call option. The simulation is used to examine the components of hedging P&L. We extend the model to vanilla put options. We use the P&L model to build a better understanding of the behaviour of Delta and two minor Greeks.
Part III – Volatility Surfaces
The third part is dedicated to volatility. My personal demons as a student in the field were volatility surfaces and hedging higher order Greeks. Volatility, Vega and Gamma surfaces, therefore, make an extended appearance. So does the topic of hedging higher order Greeks using EXCEL Solver.
Part IV – Hedging higher order Greeks
We begin with hedging a single position with deep out of money options and then graduate to a portfolio of short positions and more sophisticated Solver models. Solver is used to illustrate multiple scenarios, objective functions and hedging perspectives for Gamma and Vega neutral hedging models.
Part V – Applications
The fifth part ties up a few loose ends by reviewing two application questions, spending some additional time on Theta and Rho and closing up with annexures.
Our assumption is that you have some familiarity with options and other derivatives, the Black Scholes pricing model and Monte Carlo Simulations in EXCEL. If that is not true, please get up to speed on the basics before reading further.
And now let’s go waltz with our Greek friends.
Jawwad Ahmed Farid
25 June 2014