Key Takeaways

  • Charm is delta's change per calendar day. It is the reason an option position's share-equivalent delta moves overnight even when the underlying price does not.
  • The sign convention is shown with every result: positive means delta rises as time passes, negative means it falls.
  • Analytic charm and the finite-difference delta after a real interval are both shown, with the gap between them, so the approximation is visible.
  • The model is Black-Scholes-Merton with a continuous dividend yield and European exercise. American options and discrete dividends are outside it.
  • Nothing is fetched. Every figure comes from the numbers you enter, and the output is a model calculation, not a forecast or a recommendation.

Charm Explorer

Fill in the option and the position, then calculate. The hypothetical example loads a 30-day at-the-money call with made-up inputs.

Option

A user-supplied input held constant. Enter 25 for 25%.

Measured as calendar days divided by 365. Up to 3,650.

Position and interval

Must be shorter than the time to expiration. The table advances in steps of this length.

The date the inputs are assumed to describe. It labels the result and sets the expiration date; it is never fetched.

Sign convention. Charm is delta's change per calendar day as time passes. Positive: delta rises. Negative: delta falls. A short position reverses the sign of every share-equivalent figure.

Methodology Disclosure

Every result carries these assumptions. They are fixed by the tool, not chosen by the data.

  • Model. Black-Scholes-Merton with a continuous dividend yield, evaluated through the delta and d1/d2 of Swoopr Investment's own options pricing library (the one behind the Options Greeks Visualizer). Charm is the one added formula, and it is checked against a finite difference of that library's delta.
  • Exercise style. European. American options can be exercised early, so their delta and charm differ.
  • Rate and dividend treatment. The risk-free rate and the dividend yield are constant, continuously compounded annual rates that you supply. Discrete dividends and borrow costs are not modelled.
  • Time basis. Calendar days divided by 365, for both the time to expiration and the interval.
  • Implied volatility. A user-supplied input, held constant. It is not fitted to a quote and does not change as time passes.
  • Sign convention. Charm is d(delta)/dt with t the calendar time elapsing, which equals minus d(delta)/dT for T the time remaining. Positive means delta rises as a day passes.
  • Timestamp. The valuation date field. If left empty the result reports no valuation date. The tool never reads a clock or a market feed to fill it.

How to Read the Output

Delta now is the option's sensitivity to the underlying price at the entered time to expiration. Analytic charm is the instantaneous rate of change of that delta per calendar day. Delta after the interval recomputes delta with the interval removed from the time remaining, holding everything else fixed: that is a finite-difference delta, the actual change rather than a rate.

Share-equivalent hedge drift converts the change into shares for the whole position: contracts times multiplier times the delta change, with a minus sign for a short position. It is the amount by which the position's delta exposure moves from time alone. Spot and volatility moves are separate effects, measured by gamma and vega, and are not included.

Charm usually matters most for options close to expiry and near the strike, where delta changes fastest. The Swoopr guides Charm Exposure and Net Charm explain how the same quantity is aggregated across a whole options market. This tool works on one position and one set of assumptions.

What This Tool Does Not Do

  • It does not fetch prices, implied volatilities, rates or dividends. Whatever you enter is the whole input.
  • It does not price American exercise, discrete dividends, skew or a changing implied volatility surface.
  • It does not forecast delta or the underlying price. It shows how a model's delta changes with the passage of time alone.
  • It gives no advice on whether to hedge, when, or how much. Results are educational calculations from the inputs supplied, not personalized financial advice.

Frequently Asked Questions

What is charm in options?

Charm is the rate at which an option's delta changes as calendar time passes, also called delta decay or delta bleed. It is the second derivative of the option price, once with respect to the underlying price and once with respect to time. A charm of -0.004 per day means the option's delta falls by about 0.004 over one day if the underlying price, implied volatility and interest rates do not move.

What does the sign of charm mean?

This page measures charm as the change in delta per calendar day elapsing. A positive value means delta rises as a day passes. A negative value means delta falls. Out-of-the-money options usually show delta drifting toward zero, and deep in-the-money options show it drifting toward its limit of one in magnitude. Some texts define charm as the derivative with respect to time remaining, which flips the sign, so the convention is always stated beside the result.

How is hedge drift calculated here?

Hedge drift is the change in the position's share-equivalent delta over the chosen interval. The tool multiplies contracts, the contract multiplier and the option delta to get shares, applies a plus sign for a long position and a minus sign for a short position, then compares the share figure now with the figure after the interval. Spot, volatility, rates and dividend yield are held constant, so it isolates the effect of time alone.

Why does the analytic charm differ slightly from the finite-difference change?

Analytic charm is an instantaneous rate, while the finite-difference figure is the actual change in delta over a whole interval. Delta is curved in time, so a one-day change and a one-day rate of change are close but not equal, and the gap grows with longer intervals and as expiry approaches. The page shows both values and their difference so the approximation error is visible.

Does this work for American options or discrete dividends?

No. The model is Black-Scholes-Merton with a continuous dividend yield and European exercise. American options can be exercised early, so their delta and charm differ, especially for puts, deep in-the-money options and high dividend yields. Discrete dividend dates and borrow costs are not modelled. Treat the output as a model calculation under stated assumptions, not as a quote.

References

The formulas are the standard closed-form results of the Black-Scholes-Merton framework. No statistic on this page comes from an external dataset, and the worked example is hypothetical.

  • Black, F. and Scholes, M. (1973), "The Pricing of Options and Corporate Liabilities", Journal of Political Economy 81(3): the original option pricing model.
  • Merton, R. C. (1973), "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science 4(1): the extension to a continuous dividend yield.

Jurisdiction: not applicable (mathematical model). Last reviewed by the Swoopr Editorial Team in October 2026. This page is educational and is not personalized investment advice.

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