1.3 The Volatility Smile

Initially, market makers priced options using the Black-Scholes model, implementing their own IV as a single value for all contract strikes. However, after the crash of 1987, market makers began pricing up options that were far away from spot to account for very infrequent but large moves. The natural effect of increasing the price of options far away from spot was that volatility must increase as well. The result is an IV curve that resembles a smirk or a smile.

Fundamentally, this means that the assumptions about the lognormal random walks that underlie the Black Scholes model failed to capture reality, and the pricing models that augment the Black Scholes equation are largely proprietary knowledge for each market maker. Although we do not know the models market makers use to price options, we know what the likely inputs are to those models: supply and demand for a given contract, the hedging risk carried by the market maker, the market maker’s knowledge of open orders and existing participant conditions, and historical correlations between current macro and trading conditions and expected future moves. Supply and demand for options contracts is key, and is a more recent phenomenon, mechanically made relevant by the sheer number of options contracts on the market. In markets today, the trading volume for options contracts is large enough to potentially account for most of the volume traded for all stocks, facilitated by market maker hedging of those traded options through buying and selling the underlying stocks.

This means that the shape of the volatility smile reveals information about the supply and demand for various strikes on an options chain, and that demand for options can translate directly to future moves on the underlying through market maker hedging. In future sections we will discuss how Gammastrike uses the shape of the IV smile to gauge where market participants expect future underlying price to move towards. For example, typically IV will be elevated for out of the money puts on the SPX (at low prices) to factor in the risk of a market crash, but call IV will be relatively flat (this is a smirk). However, when call demand becomes elevated, supply and demand will raise the price of those out of the money calls, thus raising the IV at those strikes. Then IV becomes a rough surrogate for market demand.

Figure 1.2 below shows the price of puts and calls as a function of the shape of the IV smile. Notice how when you increase the out of the money IV, the price of options out of the money increases. This increase is associated with a higher likelihood that these events may happen in the future than smaller moves near the money. That is, if there is a move that is large enough, even larger moves become more probable. But remember IV is also sensitive to supply and demand, and so elevated IV can indicate when demand is unusually high or low for an option contract. One can play this evolving supply and demand to profit from shifts in far out of the money options prices, even if the owner of the contract does not think it will ever go in the money.