Systematic Noise: Micro-movements in Equity Options Markets

Abstract Equity options are known to be notoriously difficult to price accurately, and even with the development of established mathematical models there are many assumptions that must be made about the underlying processes driving market movements. As such, the theoretical prices outputted by these models are often slightly different from the realized or actual market price. The choice of model traders use can create many different valuations on the same asset, which may lead to a form of systematic micro-movement or noise. The analysis in this paper demonstrates that approximately 1.7%-4.5% of market volume for options written on the SPY ETF within the last two years could potentially be due to systematic noise. JEL Classification: G12

Adam Wu Indiana University April 2017 Special thank you to Dr. Michael Alexeev for research process guidance and support

107 S Indiana Ave, Bloomington IN 47405 adamwu@indiana.edu / +1 (415) 969 0380 Introduction The first known usage of an option dates back several thousand years ago to the ancient Greek philosopher Thales of Miletus, as Aristotle describes in Politics. Predicting that the coming season would bear a very successful olive harvest, Thales, being merely a poor philosopher, acquired the right to use the olive presses that turned olives into oil for a small deposit. When the season came and Thales’ prediction about the weather turned out to be correct, he was able to make enormous profits for a very small investment. This contract that Thales made with the owners of the olive presses is no different from the many modern financial contracts we use today, collectively known as derivatives. The focus of this paper is on a special type of financial derivative known as an option. An option is a contract that gives the contract-holder the right (but not the obligation) to buy or sell an asset, within a specified period of time, at a specified price. To clarify some of the terminology, this specified price is called the option’s Strike Price, and the last day that the contract may be exercised is called the Maturity Date.
Further, there are two main classes of options. European options are ones that can only be exercised on a specific date (i.e. March 25, 2019), while American options may be exercised at any point up to the maturity date. In recent years, there has been the rise of more complex derivatives such as Asian options, compound options (options written on an option), and others with an embedded equity or debt security—which are even more difficult to value accurately and are outside the scope of this paper. In practice, nearly all public exchange-traded stock options in the world are of the American form1.
From the anecdote above, it’s clear that options can have very lucrative payoffs while limiting downside risk. However, an important question is on the actual valuation of these options due to their complexity (i.e. how much should Thales actually pay the olive press owners?). In the early 1970s, a major breakthrough in pricing equity options was achieved by mathematicians known as the Black-Scholes model. Since then, the Black-Scholes model has been extended on heavily, with many of its assumptions challenged and relaxed, leading to a number of other models such as analytical approximations, lattice tree methods, or statistical simulations. However, as with any theoretical model, each comes with their own set of assumptions and computational methods which makes the pricing of an option in practice slightly different depending on which model one uses. As these valuations may form a key factor in trading strategies and decisions, the choice of model and their respective mispricings may be creating a form of systematic micro-movement in the equity options market.

1Note that the terms European and American do not have anything to do with the continents. The labels were coined in a 1965 article by Nobel Laureate Paul Samuelson as he was supposedly discouraged from researching options due to their complexity by his European colleagues, and so proceeded to name the simple options ‘European’. Overview of Derivative Pricing Models Black-Scholes-Merton Options Model In 1973, mathematicians Fischer Black, Myron Scholes, and Robert Merton developed a stochastic differential equation that modelled the fair price of an option over time, winning the Nobel prize for economics in 1997. As one of the earliest formal mathematical models for the valuation of options, this breakthrough has had immense impact on how traders price these assets or hedge their portfolios even today. This section will briefly explain the main ideas behind the Black-Scholes Model, as well as cover its key assumptions and limitations1. Let 𝜇𝜇= 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑜𝑜𝑜𝑜 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝜎𝜎= 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑣𝑣𝑣𝑣𝑣𝑣𝑣

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