Vanna and Charm: The Greeks That Move Markets Around OPEX

Summary. Two second-order greeks change dealer hedges even when spot does not move: vanna, through implied volatility, and charm, through the passage of time. Both grow in importance as a large expiration approaches. This article derives charm, shows how it shrinks the deltas of out-of-the-money options in the days before expiry, estimates the resulting dealer flow for a hypothetical chain, and explains how vanna and charm interact around monthly option expiration (OPEX) and scheduled macro events.

1. The calendar

Standard monthly equity and index options expire on the third Friday of the month. Monthly SPX options are settled on that Friday's opening prices, while SPX Weeklys (SPXW) expiring the same day settle at the close [1]. In March, June, September and December the monthly expiration coincides with the expiration of index futures and futures options, which concentrates more open interest on a single date. Because so much open interest disappears at once, the hedges attached to it are unwound in the days before and on the expiration itself.

2. Charm: delta decay with time

Charm is the rate at which delta changes as time passes, holding spot and volatility fixed [2]. With zero rates and dividends, for both calls and puts,

For out-of-the-money options, time decay pushes delta toward zero; for in-the-money options it pushes delta toward one in absolute value. Figure 1 shows two puts on a 6,000 index with spot held constant. The 5,850 put (2.5% out of the money) has a delta of about −0.28 with 21 trading days left, −0.13 with five days and essentially zero on the final day. With five days left its delta is rising by about 0.023 per day.

3. What charm does to dealer hedges

Under the convention that dealers are short customer-bought puts and long customer-sold calls [3]:

• Short out-of-the-money puts. A short put has positive delta, which dealers hedge by selling futures. As the put's delta decays toward zero, the hedge is too large, and dealers buy back futures.
• Long out-of-the-money calls. A long call has positive delta, hedged by selling futures. As the call's delta decays, the hedge is again too large, and dealers buy back futures.

Both wings point the same way: with spot and volatility unchanged, the passage of time leads to dealer buying. Figure 2 estimates the one-day charm exposure (CHEX) for the hypothetical chain used in this series. Net dealer delta falls by about $3.1 billion over one trading day, which implies buying of that size if spot and volatility stay put. The figure is large in this example because a quarter of the chain's open interest expires the next day; it scales with the share of open interest near expiry.

4. Vanna into and after expiration

Vanna, covered in detail in vanna walls versus gamma walls, has the same sign structure under this convention: a fall in implied volatility reduces dealer delta, leading to buying. In the days before a large expiration, two forces commonly align:

• Time decay shrinks out-of-the-money deltas (charm), leading to dealer buying.
• Implied volatility often drifts lower when no shock arrives, which also leads to dealer buying (vanna).

When both are present, the result is a supportive flow into expiration that does not depend on new information. After the expiration, the open interest that generated these flows is gone, and the next expiry's positioning takes over. Practitioners often describe the following week as a period in which other flows, such as macro news, have more influence on price.

The conditions matter. If customers are net long calls rather than short, the call-wing contribution reverses. If implied volatility rises into expiration, vanna works against charm. The direction is an output of the positioning estimate, not a fixed calendar pattern.

5. Scheduled macro events

Implied volatility usually rises before scheduled announcements and falls after them, as the event's variance leaves the option prices (see why IV spikes before Fed days). Under the convention above, the post-event fall in implied volatility produces dealer buying through vanna. Separately, Lucca and Moench documented large average equity returns in the 24 hours before scheduled FOMC announcements [4], although later work finds that this pre-announcement drift largely disappeared after 2015 [5]. Event-related flows are therefore best treated as conditional on positioning and on the size of the volatility move, not as a reliable calendar trade.

6. Reading the exposures

1. In expiration week, compare the size of CHEX with GEX. Large charm relative to gamma means time alone is a material source of flow.
2. Estimate the change in implied volatility you expect into the expiration and convert it to dealer flow with VEX.
3. Check whether the largest VEX and CHEX strikes coincide with the gamma walls. Coinciding levels concentrate several hedging flows on one price.
4. After expiration, rebuild the map from the next open interest report.

DataFirst shows GEX, DEX, VEX and CHEX on the same strike axis and highlights strikes where several exposures line up.

For educational and informational purposes only. Not financial advice. Options trading involves substantial risk of loss. Figures use a hypothetical option chain and the Black-Scholes model.

References

1. Cboe Global Markets. S&P 500 Index options (SPX, SPXW) product specifications. www.cboe.com/tradable_products/sp_500/spx_options/specifications/
2. Haug, E. G. (2007). The Complete Guide to Option Pricing Formulas (2nd ed.). McGraw-Hill.
3. SqueezeMetrics. (2016, revised 2017). Gamma Exposure (GEX). White paper. squeezemetrics.com/monitor/download/pdf/white_paper.pdf
4. Lucca, D. O., & Moench, E. (2015). The pre-FOMC announcement drift. Journal of Finance, 70(1), 329–371. doi.org/10.1111/jofi.12196
5. Kurov, A., Wolfe, M. H., & Gilbert, T. (2021). The disappearing pre-FOMC announcement drift. Finance Research Letters, 40. ideas.repec.org/a/eee/finlet/v40y2021ics1544612320315956.html