Ever since Black and Scholes introduced their famous option pricing formula, traders have been sensible about hedging their exposure to the various risk measures (price of the underlying, time till expiration, volatility, interest rates, dividends). Arguably, the most important exposure an option has is to the price movements of the underlying instrument. This sensitivity is labelled delta. Delta-hedging is a term familiar to every option trader. The importance of options with relatively short maturities - as defined by the trading volume and levels of open interest - has increased. Therefore, the risk in option trading nowadays is not just defined by the option delta. The importance of the option gamma, which measures the sensitivity of the option delta to changes of the underlying price, can create large delta exposures even on smaller moves in the price of the underlying and thus creates volatility spikes. This article shows how to use option gamma to identify 'pain levels' of the market.
Recap of option delta and gamma
The concept of option delta (Δ) is quite simple. Ex post, one would compare the change of the price of an option (V) with the price change of the underlying instrument (S). So how many dollars does the price of the option change if the price of the underlying changed by some dollar amount: