2.4.1 Delta hedging

Option assignment risk is the largest danger for most options portfolios. This is the traditional long/short exposure. As mentioned in the greeks section, assignment risk, or how many shares one must buy/sell at expiration, is estimated based on the delta of the options contracts in the portfolio. Assignment risk can always be hedged through purchasing and selling the underlying instrument for the option. For example, a short AAPL call with a delta of 0.8 has an assignment risk of -80 shares at expiration, meaning the expectation is delivery of 80 shares. Buying 80 shares of AAPL at spot hedges this risk. If instead one has a long AAPL call with a 0.8 delta, the expectation is receiving 80 shares at expiration, which is hedged by shorting 80 shares of AAPL at spot. A summary of bought/sold calls/puts from the perspective of the market maker is in the table below.

Note that market participants hold the opposite bought/sold position of market makers. So if market participants are net long calls and/or net short puts, the market maker is short calls and long puts, and so must buy the underlying stock to hedge delta exposure. Thus, buying calls and selling puts creates market maker buying pressure on the underlying, and causes the price to rise. Conversely, selling calls and buying puts creates market maker selling pressure on the underlying, and causes prices to fall.

What if the underlying of an option isn’t directly tradeable? The most common example are indices such as SPX and VIX, which do not have issued shares to trade. In this case hedging must be done using other derivatives. The simplest hedge for an option is another option, but is problematic for a single market maker because they are the purchaser of last resort, so by definition have no one to trade an option hedge with. This is why indices often have multiple market makers, so some of the imbalance for a single market maker can be traded with other market makers. But this does not fully solve the problem, as in aggregate the market makers will have an unbalanced delta position that must be hedged.

In this case, market makers can hedge index option exposure with index futures. Doing so then exposes the market maker to interest rate risk, which can be hedged using bond options, interest rate swaps, and other rate sensitive instruments. One can quickly see how counterparty risk hedging quickly becomes a cancerous mass of tentacles, mechanically linking all assets and market participants into a tangled mess. From a philosophical perspective, the financial markets are a direct representation of the human condition: where we create endless distractions and worldviews to keep us from thinking about certain death. The spaghetti mass of cross-asset counterparty hedging creates the illusion for all participants that all risks are mitigated, sustained by a shared delusion that only catastrophe can unwind. For the trader, all that matters is that index options comprise most of the activity in the options market, hedging them can move the underlying components, and those hedges are sensitive to broad trends in other markets and even monetary policy.