w to Calculate Options Prices and Their Greeks
How to Calculate Options Prices and Their Greeks: Exploring the Black Scholes Model from Delta to Vega
PIERINO URSONE
This edition first published 2015
© 2015 Pierino Ursone
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Preface
In September 1992 I joined a renowned and highly successful market-making company at the Amsterdam Options Exchange. The company early recognised the need for hiring option traders having had an academic education and being very strong in mental calculation. Option trading those days more and more professionalised and shifted away from “survival of the loudest and toughest guy” towards a more intellectual approach. Trading was a matter of speed, being the first in a deal. Strength in mental arithmetic gave one an edge. For instance, when trading option combinations, adding prices and subtracting prices – one at the bid price, the other for instance at the asking price – being the quickest brought high rewards.
After a thorough test of my mental maths skills, I was one of only two, of the many people tested, to be employed. There I stood, in my first few days in the open outcry pit, just briefly after September 16th 1992 (Black Wednesday). On that day the UK withdrew from the European EMS system (the forerunner of the Euro), the British pound collapsed, the FX market in general became heavily volatile – all around the time the management of the company had decided to let me start trading Dollar options.
With my mentor behind me, I stood in the Dollar pit (training on the job) trying to compete with a bunch of experienced guys. My mentor jabbed my back each time when a trade, being brought to the pit by the floorbrokers, seemed interesting. In the meantime he was teaching me put–call parity, reversals and conversions, horizontal and time spreads, and whereabouts the value of at the money options should be (just a ballpark figure). There was one large distinction between us and the other traders; we were the only ones not using a computer printout with options prices. My mentor was certain that one should be able to trade off the top of the head; I was his guinea pig.
In those days, every trader on the floor was using a print of the Black Scholes model, indicating fair value for a large set of options at a specific level in the underlying asset. These printouts were produced at several levels of the underlying, so that a trader did not need to leave the pit to produce a new printout when new levels were met. Some days, however, markets could be so volatile that prices would “run off” the sheet. As a result the trader would have to leave the pit to print a new price sheet. It was exactly these moments when trading in the pit was the busiest: not having to leave the pit was an advantage as there were fewer traders to compete with. So, not having to rely on the printouts would create an edge while liquidity in trading would be booming at those times.
All the time we kept thinking of how to outsmart the others, how to value options at specific volatility levels and how, for instance, volatility spreads would behave in changing market circumstances. Soon we were able, when looking at option prices in other trading pits, to come up with fairly good estimates on the prevailing volatilities. We figured out how the delta of in the money options relate to the at the money options, how the at the moneys have to be priced and how to value butterflies on the back of the delta of spreads and more. Next to that we had our weekly company calculation and strategy sessions. There was a steady accumulation of knowledge on options pricing and valuing some of the Greeks.
After having run my own company from 1996 to 2001 at the Amsterdam exchange, I entered the energy options market, a whole different league. There was no exchange to trade on, no clearing of trades (hence counterparty risk), the volumes were much larger and it was professional against professional. As a market maker on the exchange one was in general used to earning a living on the back of the margins stemming from the differences in bid and asking prices (obviously we were running some strategies at the same time as well). Now however, with everyone knowing exactly where prices should be, all margins had evaporated. As a result, the only way to earn money was to have a proper assessment of the market and have the right position to optimise the potential profits. So I moved from an environment where superior pricing was a guarantee for success to an area where only the right strategy and the right execution of this strategy would reap rewards. It truly was a challenge how to think of the best strategy as there is a plethora of possible option combinations.
It has been the combination of these two worlds which has matured me in understanding how option trading really works. Without knowing how to price an option and its Greeks it would be onerous to find the right strategy. Without having the right market assessment it is impossible to generate profits from options trading.
In this book I have written down what I have learned in almost 20 years of options trading. It will greatly contribute to a full understanding of how to price options and their Greeks, how they are distributed and how strategies work out under changing circumstances. As mentioned before, when setting up a strategy one can choose from many possible option combinations. This book will help the reader to ponder options and strategies in such a way that one can fully understand how changes in underlying levels, in market volatility and in time impact the profitability of a strategy.
I wish to express my gratitude to my friends Bram van der Lee and Matt Daen for reviewing this book, for their support, enthusiasm and suggestions on how to further improve its quality.
Chapter 1
Introduction
The most widely used option model is the Black and Scholes model. Although there are some