Charm is one of the lesser-known second-order Greeks, but understanding it can give you an edge in managing options positions, especially as expiration approaches. While most traders focus on delta, gamma, theta, and vega, charm explains something important: how your delta exposure changes simply due to the passage of time. In this guide, we will demystify charm and show you how it affects your trades.
What is Charm?
Charm measures the rate of change of delta with respect to time. In mathematical terms, charm is the derivative of delta with respect to time, or equivalently, the derivative of theta with respect to the underlying price.
Simple definition: Charm tells you how much your delta will change overnight, assuming the stock price stays the same. It measures delta decay.
Charm is sometimes called delta bleed or delta decay because it shows how delta erodes as time passes. This is distinct from gamma, which shows how delta changes when the stock price moves.
How Charm Works
As time passes, options behave more like their intrinsic value. This means:
- Out-of-the-money options have delta that approaches zero
- In-the-money options have delta that approaches 1 (for calls) or -1 (for puts)
- At-the-money options can have delta that moves either direction depending on conditions
Charm quantifies this movement. A positive charm means delta is increasing over time. A negative charm means delta is decreasing over time.
Charm by Option Type
Out-of-the-Money Calls
OTM calls typically have negative charm. Their delta decreases over time because as expiration approaches, there is less and less chance they will end up in the money. An OTM call with 0.30 delta today might have 0.25 delta tomorrow, even if the stock does not move.
In-the-Money Calls
ITM calls typically have positive charm. Their delta increases toward 1.0 as expiration approaches because they are increasingly likely to stay in the money. An ITM call with 0.70 delta might have 0.75 delta tomorrow.
At-the-Money Options
ATM options are interesting. Their charm can be either positive or negative depending on whether they are slightly ITM or OTM. Near expiration, ATM options have the most unstable delta and can swing dramatically.
Example: Charm Impact Overnight
You own a call option with the following characteristics:
- Current delta: 0.35
- Charm: -0.02
- Stock price: $100 (unchanged overnight)
Tomorrow morning, even with no stock movement:
- New delta: 0.35 + (-0.02) = 0.33
- Your position lost 2 delta per contract overnight
- For 10 contracts, that is 20 delta of exposure change
Why Charm Matters for Hedging
If you delta hedge your portfolio, charm can cause your hedge to drift even when the market is closed or the stock does not move. This is particularly important:
1. Over Weekends
Two days of charm accumulate over a weekend. If you are perfectly delta neutral on Friday, you might wake up Monday with significant delta exposure.
2. Near Expiration
Charm accelerates dramatically in the final days before expiration. Delta can change rapidly just from time passing, requiring more frequent hedge adjustments.
3. For Large Portfolios
Small charm per option multiplied by thousands of contracts creates meaningful overnight delta drift that needs management.
Example: Weekend Delta Drift
Friday close: Your portfolio is delta neutral
- Position: Short 100 OTM calls with delta 0.25 and charm -0.015
- Position delta: -2500 (short 100 x 100 shares x 0.25)
- Stock hedge: Long 2500 shares (+2500 delta)
- Net delta: 0
Monday open (stock unchanged, 2 days passed):
- New call delta: 0.25 + (2 x -0.015) = 0.22
- New position delta: -100 x 100 x 0.22 = -2200
- Stock hedge: Still +2500 delta
- Net delta: +300 (you are now long delta)
You need to sell 300 shares to rebalance.
Charm and Gamma Relationship
Charm and gamma are related through time. Gamma tells you how delta changes with price. Charm tells you how delta changes with time. Together, they give you a complete picture of delta dynamics.
Near expiration, both gamma and charm increase dramatically for ATM options. This makes short-dated ATM positions particularly challenging to manage.
Practical Applications of Charm
1. Anticipating Hedge Adjustments
By knowing your portfolio's charm, you can predict tomorrow's delta and prepare your hedge adjustments in advance.
2. Weekend Positioning
Before weekends or holidays, consider how charm will affect your delta over the break. You might adjust your hedge on Friday to account for weekend decay.
3. Expiration Week Trading
During expiration week, charm becomes dominant. Short OTM options lose delta quickly, while short ITM options gain delta. Plan your trading around this accelerated decay.
4. Options Roll Timing
When rolling options to later expirations, consider charm. Rolling OTM options early preserves more delta. Waiting allows charm to erode delta further.
Calculating Your Charm Exposure
Total portfolio charm is the sum of individual position charms, accounting for contract size and number of contracts:
Portfolio Charm = Sum of (Position Charm x Contracts x 100)
This tells you how many delta your portfolio will gain or lose per day from time passage alone.
Charm vs Other Second-Order Greeks
Charm is one of several second-order Greeks:
- Gamma: How delta changes with price
- Charm: How delta changes with time
- Vanna: How delta changes with volatility
- Vomma/Volga: How vega changes with volatility
Professional traders monitor all of these to fully understand their risk exposure.
Track Advanced Greeks
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Summary
Charm measures how delta changes as time passes, independent of stock price movement. Understanding charm helps you anticipate how your delta exposure will drift overnight and over weekends. This is particularly important near expiration when charm accelerates. By monitoring charm, you can make better hedging decisions and avoid surprises from delta decay. While not as commonly discussed as the first-order Greeks, charm is essential knowledge for serious options traders.
Continue exploring advanced Greeks with our guides on vanna and volga.