Constructing an expiration settlement map from listed open interest

What open interest records

Open interest counts only contracts that remain open. It rises when a new long and a new short are created together and falls when both sides close. Each listed unit pairs one long with one short.

That remaining book is the raw material for an expiration-day map. The construction below turns the listed series into a settlement-cost curve and then compares that curve with the live index.

How settlement price is formed

On the illustrated cash-settled index, settlement price was formed by averaging 31 one-minute samples between 15:30 and 16:00. That late-session span is the expiration period, the short window when settlement of cash-settled index options is determined from sampled underlying prints.

The expiration window showed elevated activity. The samples in that window, not a single last print, are what the listed book is settled against.

Why quarterly months carry more open interest

January, April, July, and especially October typically carried higher open interest. Longer-term and multiyear series expired in those quarterly expiration months, and nearby price swings were larger.

A denser book means more strikes contribute cash to the settlement-cost curve. The map is built from that larger set of open contracts.

Delta-neutral hedges into expiration

Professional books were required to stay hedged the same day. They used opposite underlying trades for long and short calls and puts so that each option remained approximately delta-neutral. A delta-neutral hedge is an offsetting stock or futures position sized so that a small move in the underlying leaves the combined option-plus-hedge book approximately unchanged.

Call delta was described as ranging from 0 to 1 and put delta from 0 to -1. The hedge share count had to be revised as those ratios changed through the life of the option.

Hedging a short call and a short put together need not leave the combined book flat. One worked example bought 50 shares against the call, sold 75 against the put, and still showed a net loss of 100 after a 2-point rise. Editorial. Residual exposure of that kind is one reason the listed book still has a cash interest in where settlement price prints.

Building the settlement-cost curve

At expiration, in-the-money cash-settled index options transfer value from shorts to longs. A 350 put with open interest 662 against a 340 settlement implied 662000 of cash due on that strike alone. That cash is settlement-cost. It is computed from strike, settlement print, open interest, and contract multiplier.

Summing that cash across every in-the-money strike for many candidate prints produced a settlement-cost curve. The minimum, about 340 in the illustrated month, was treated as the market-wide optimum expiration price. The optimum expiration price is the candidate settlement level at which the sum of cash due across in-the-money strikes is minimized for the listed open-interest book.

Reading the open-interest index

As expiration approached, the underlying was described as tending toward that low-settlement-cost print. That level is where most listed options typically expired out of the money.

A five-day open-interest index compared with the live market, and the same series recast as a 0-to-100 oscillator, was used to judge whether settlement was likely above or below the current print. The open-interest index is the constructed series that locates the low-settlement-cost expiration level implied by current open interest.

Editorial. The comparison is a reading of the constructed map against the live index. It does not turn the map into a standalone directional call.