Option Charm (Delta Decay)
Computes the charm of an option, also known as delta decay, which shows how much the delta shifts with each passing day, all else equal. It is a second-order Greek (∂delta/∂time) that traders watch to see how a hedge needs to be rebalanced near expiry, where it spikes. For a call with no dividends it is −φ(d1)·(2rT − d2·σ√T)/(2T·σ√T). The result comes per year and per day. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
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Option Charm (Delta Decay)
Computes the charm of an option, also known as delta decay, which shows how much the delta shifts with each passing day, all else equal. It is a second-order Greek (∂delta/∂time) that traders watch to see how a hedge needs to be rebalanced near expiry, where it spikes. For a call with no dividends it is −φ(d1)·(2rT − d2·σ√T)/(2T·σ√T). The result comes per year and per day. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
The Greek that warns your hedge is about to drift
Anyone running a delta-neutral book knows the delta won't sit still. One of the things that moves it is the plain passage of time, and charm is the Greek that measures exactly that: how much the delta changes each day with no move in the underlying. It's a second-order sensitivity, the kind that only shows up on the radar of people who rebalance often.
Charm tends to get ignored when expiry is far off, because it's small. The trouble is the home stretch: close to the exercise date it spikes, and a book that looked balanced on Friday can open lopsided on Monday purely because of the weekend. Watching charm helps you anticipate that adjustment instead of chasing the loss after the fact.
The result comes per year and per day, computed for a call with no dividends. Just enter spot price, strike, interest rate, term in years and volatility. Like every Greek, it's a snapshot of the moment: useful for sizing the hedge adjustment now, not for predicting where the delta lands a month out.
Related Tools
Option Veta (Vega Decay)
Computes the veta of an option, the Greek that measures how much the vega changes with each passing day. Since vega captures the premium's sensitivity to volatility, veta shows whether that sensitivity is shrinking over time, and it does: near expiry vega tends to zero, so a call's veta is usually negative. It's a second-order Greek that helps anticipate how the volatility exposure will behave. The result comes per year and per day, for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Call Dual Delta
Computes the dual delta of a call option: the premium's sensitivity to the strike price, that is, dC/dK. While ordinary delta measures the reaction to the underlying's price, dual delta measures how much the option would change if the strike were slightly different. For a call it equals −e^(−rT)·N(d2) and has a practical reading: in absolute terms it approximates the risk-neutral probability of the option finishing in the money. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Option Color (Gamma Decay)
Computes the color of an option, the third-order Greek that shows how much the gamma changes with each passing day, all else equal. Since gamma measures how fast the delta moves, color tells you whether that speed is accelerating or slowing as expiry approaches, handy for anyone managing gamma positions near the exercise date, where an at-the-money option's gamma spikes. The result comes per year and per day, computed for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Option Theta (Black-Scholes)
Computes the theta of a European call option under Black-Scholes, the Greek that measures how much premium the option bleeds with each unit of time that passes. The formula pairs the decay of extrinsic value, −S·φ(d1)·σ/(2√T), with the strike-discount effect, −r·K·e^(−rT)·N(d2). For a call with no dividends theta is always negative: time works against the buyer. The result comes as annual theta and per day (÷365). Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Contingent-Premium Call Option
Computes the fair premium of a contingent-premium call option, also called pay-later. The buyer pays nothing upfront: the premium is only due at expiry, and even then only if the option finishes in the money. For the deal to be fair, that deferred premium must be larger than a plain call's, compensating for the risk the seller receives nothing. The formula divides the Black-Scholes value by the exercise probability. Enter price, strike, rate, dividend, volatility and term.
Option Dual Gamma
Computes the dual gamma of a call option: the second derivative of the price with respect to the strike, ∂²C/∂K². While gamma measures the price's curvature relative to the asset, dual gamma measures the curvature relative to the strike, and it's tied to the risk-neutral probability density of the future price — in fact, dual gamma is exactly that density discounted. It's used to extract implied price distributions from option prices. Enter the spot price, the strike, the rate, the volatility and the term.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.