Rob Schwartz

Trading asset-based prediction markets vs short-term options In my career I’ve seen the rise of short-dated options from both the market making and exchange sides. Thoughts on trading binary-style financial prediction markets versus vanilla options, focusing on greeks. Prediction markets that settle to 1 or 0 based on underlying strike price are simply binary options, a construct that long pre-dates event contracts. In liquid underlyings a binary option can be replicated to a good approximation with a tight call spread. The reverse replication exists too: a vanilla option is a strip of binaries across the strike latter. The comparison ultimately breaks down due to discrete strikes, a truncated strike ladder, and two-sided transaction costs, but it provides a useful framework for deriving binary option properties. Here are a few of those properties, specifically options greeks, that are useful for modeling and trading binary option-style prediction markets: • The greeks for a binary option are shifted one derivative to the left of vanilla options. Binary option delta looks like vanilla option gamma. It peaks ATM, decays both directions, and spikes toward a delta function at expiry. • Binary option gamma changes sign at the strike. A long binary option holder is long gamma below the strike and short gamma above the strike. There is no position that can express “buying gamma into an event.” • Binary option vega also changes sign: OTM holders are long vol, ITM holders short vol, and ATM vega is near 0. All prediction market traders are inherently running a vol book. • Theta is non-monotone and can flip sign. Unlike a vanilla option, an ITM binary option gains from time passing. • Fully-collateralized binary options have an embedded interest rate. At current front-end rates, a 6-month contract's "probability" is biased low by ~2.5 points versus the true risk-neutral probability. The asymmetry between binary options and vanilla options reflect their ideal use cases. Binary options are a better instrument for a pure event view, while vanilla options remain the better instrument for exposure to the whole distribution of underlying prices.