Charm Exposure measures how dealer delta hedges change purely due to the passage of time. While theta measures how option prices decay, charm measures how delta itself decays—forcing dealers to continuously adjust their hedges even when price and volatility remain constant.

What is Charm?

Charm (also called delta decay or DdeltaDtime) is a second-order Greek:

$\text{Charm} = \frac{\partial \Delta}{\partial T} = -\frac{\partial \Theta}{\partial S}$

As time passes, option deltas drift toward their terminal values:

• OTM options: delta → 0
• ITM options: delta → ±1.00

This drift forces dealers to re-hedge.

Why Charm Matters

Consider a dealer who sold OTM calls and delta-hedged by buying stock:

Day	Call Delta	Shares Held (Hedge)
Monday	-0.30	+30 shares
Tuesday	-0.25	Need only +25 shares
Wednesday	-0.20	Need only +20 shares

Result: The dealer must sell shares each day just to maintain the hedge, even assuming no price or implied volatility changes.

Charm Flows: The Mechanics

OTM Calls (Dealer Short)

• Delta becomes less negative as time passes
• Dealer must sell underlying to re-hedge
• Creates selling pressure into expiration

OTM Puts (Dealer Short)

• Delta becomes less positive as time passes
• Dealer must buy underlying to re-hedge
• Creates buying pressure into expiration

The Net Effect

The aggregate charm exposure across all strikes determines the directional bias:

Net Charm	Market Implication
Positive	Buying pressure from delta decay
Negative	Selling pressure from delta decay
Near zero	Balanced flows

When Charm Dominates

Charm flows are most significant:

Time-Based Patterns

• Overnight: ~16 hours of charm decay priced in at open
• Weekends: 48+ hours of decay hits Monday open
• Into OPEX: Charm accelerates as gamma spikes

Market Conditions

• Low volatility: Gamma/vanna effects subdued, charm more visible
• Pinned markets: Price relatively stable, time decay is a more dominant force
• Pre-event: Calm before CPI/FOMC, charm flows dominate

Charm vs. Theta

Aspect	Theta	Charm
Measures	Option price decay	Delta decay
Affects	Option holder's P&L	Dealer's hedge ratio
Market impact	None directly	Creates directional flows
Peak	ATM options	OTM options

Practical Application

Overnight Charm

Calculate expected charm flow overnight:

$\Delta\text{Hedge} = \sum_K \text{Charm}_K \times OI_K \times \frac{16}{24}$

This predicts directional pressure at market open.

OPEX Week

As expiration approaches:

1. Charm accelerates (more delta decay per hour)
2. OTM deltas collapse toward zero
3. Significant hedge adjustments required
4. Often creates drift toward max-pain

VannaCharm's Approach

We calculate charm exposure continuously throughout the trading day, accounting for:

• Actual time to expiration (not simplified T-1 assumptions)
• Per-strike IV from our smoothed volatility surface
• Both call and put contributions from dealer perspective

Related Concepts

• Gamma Exposure (GEX) - Price-driven hedging
• Vanna Exposure (VEX) - Volatility-driven hedging
• 0DTE Options - Extreme charm effects