Dr. Timothy Klassen is the CEO and founder of Vola Dynamics LLC. It was founded in 2016 and won an FIA innovator award that year. Timothy will also be speaking at QuantMinds Americas on arbitrage-free parametric implied volatility surface fitting.
Recall that most options market participants think about valuation and risk in volatility rather than price space. This is for various good reasons, related to both human intuition and technical considerations (in particular, idiosyncratic vol moves usually happen on a much slower time scale than underlier moves). Implied volatility surfaces (and borrow curves for equity names) are the fundamental building blocks of any derivatives business, whether it involves just the vanilla options which were used to imply the volatility surfaces, or flow derivatives, or more involved exotics and structured products.
So, the first question is, what characterizes a “good” volatility surface? The first requirement that comes to mind is that it should “match the market”. In today's high-frequency world this is an a priori ill-defined concept. Clearly, a naive matching of mid prices/vols is not a good idea, in general, if nothing else then because spreads can be very wide and the mid a not very good indicator of fair value. So we will replace the naive idea with matching the market in a “bias-free” and “smooth” manner, matching a suitable "micro price” of each option as much as possible, within the spread. Although these terms have some common sense intuitive meaning, they could also be discussed for a while, but that is beyond the scope of this piece (come to my talk!). We will refer to such a matching of the market as “accurate”, for short.
Another requirement is that vols/prices should be arbitrage-free, certainly when taking transaction costs into account, ideally even when ignoring them. Desirable features are that at least the strike-dependence of each maturity’s implied vols can be parametrized via an explicit curve, with intuitive and largely “orthogonal” parameters that tend to be slowly varying over time. Finally, it should be possible to fit these parametric curves and surfaces very fast and robustly, in an automated fashion with little or no human intervention.
Any serious options market participant needs to do produce valuations and greeks in a fashion that has at least one or two of the three attributes: accurate, robust, and fast. Automated trading operations, like market makers in very liquid markets (such as futures options or US equity and index options), need all three attributes. Others, like risk managers, clearing houses and exchanges, had, at least historically, a bit more leeway because they had some digression as to when exactly to produce their final valuation and risk numbers, i.e. they had time to redo a failing step in their processes or apply human overrides. But with the increasing number of tradable products, increasing volumes, and regulatory pressure for properly validated and (near) real-time valuation and risk models and processes, all market participants are more and more in need of speed, accuracy, and robustness, preferably as part of a fully automated process.
Implied volatility surfaces are the fundamental building blocks of any derivatives business.
Producing volatility surfaces in this manner is well-known to be a hard problem. For liquid underliers like equity stocks, ETFs, or indices, or various futures, the problem already starts with the question of what kind of volatility curves to use. No curves currently in the public domain allow good fits for names like SPY, AAPL, AMZN, SPX, VIX or futures like the E-minis. For less liquid names, where spreads are wide and trades are few and far between for most options, the problem is more about how to optimally spread the little information there is across all strikes and maturities in a sensible manner, in particular in an arbitrage-free manner.
In our talk we will discuss how all of the above goals can be achieved. The results (together with proper cash dividend modeling) are available as part of the Vola Dynamics analytics library, the first commercial product that allows one to produce valuations and greeks suitable for any options business, whether involving traders, risk managers, or valuation agents, whether at a prop shop, a bank, a hedge fund, or a clearing house, exchange or regulator.
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