Charm

Charm (also called delta decay or delta bleed) measures how much an option's delta changes as one day passes, with all other factors held constant. It is a second-order Greek that captures the interaction between delta and time. If a call option has a delta of 0.40 and a charm of -0.02, its delta will drift to approximately 0.38 after one day, assuming the stock price and implied volatility remain unchanged.

Why It Matters

Charm explains why your portfolio's directional exposure shifts overnight even when the stock has not moved. If you sell an OTM put with a delta of -0.25, charm tells you that delta will move closer to zero each day as the option decays — your position becomes less directionally sensitive over time. Conversely, an ITM option's delta moves closer to 1.0 (or -1.0 for puts) as expiration approaches.

For traders managing delta-neutral portfolios, charm is the reason you need to rebalance your hedges daily. Market makers monitor charm constantly because it drives the overnight change in their delta exposure. For retail traders, understanding charm helps explain why short-dated positions behave differently than expected from one day to the next.

How It Works

Charm is the derivative of delta with respect to time, or equivalently, the derivative of theta with respect to the stock price. Its sign and magnitude depend on moneyness:

For OTM options:

• OTM call delta drifts lower over time (charm is negative for calls)
• OTM put delta drifts closer to zero over time (charm is positive for puts, making delta less negative)

For ITM options:

• ITM call delta drifts higher toward 1.0 over time
• ITM put delta drifts toward -1.0 over time

For ATM options:

• Charm is close to zero. ATM deltas stay near 0.50 until very close to expiration.

Charm accelerates near expiration. Just as gamma spikes for short-dated ATM options, charm effects intensify in the final days. An option that was 0.30 delta with 30 days left might see delta shift by 0.005 per day, but with 3 days left, the daily shift could be 0.03 or more.

Charm in practice:

• If you are short OTM options, charm works in your favor — delta exposure shrinks daily
• If you are hedging a portfolio with options, charm means your hedge ratio changes overnight
• Charm is most significant for short-dated options and near-expiration positions

Quick Example

You sell a 30-delta put on stock JKL with 14 days to expiration. Charm for this position is approximately +0.015 per day (the put delta moves toward zero). After 5 days, even if the stock has not moved, your put's delta has shifted from -0.30 to roughly -0.225. Your directional exposure has decreased by 25% purely from the passage of time.

With only 3 days left and the stock still at the same price, charm accelerates. The delta might drop from -0.15 to -0.05 in a single day, rapidly reducing your exposure as expiration approaches.