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.
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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.
The Greek that measures the delta's acceleration
If gamma is already a second-order Greek, color goes one floor higher: it's the third derivative, and it measures how gamma itself changes over time. That sounds abstract, but it has a very concrete meaning for a trader. Gamma tells you how fast the delta moves; color tells you whether that speed is rising or falling day after day.
This matters most in the home stretch. On a near-the-money option, gamma explodes as expiry arrives, and color is what captures that explosion before it happens. For anyone holding a gamma position, it's the difference between rebalancing in a panic and rebalancing ahead of time. Far from expiry, color is small and almost nobody watches it.
The calculation here is for a call with no dividends, and the result comes per year and per day. Just enter spot price, strike, interest rate, term in years and volatility. Like every high-order Greek, it's a sensitive, instantaneous measure: useful for seeing the gamma's trend now, not for pinning down where it will end up.
Related Tools
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.
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.
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.
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.
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.
Black-76 Call Price (Options on Futures)
Works out the premium of a European call option on futures with the Black-76 model, the variant of Black-Scholes used when the underlying is a futures or forward contract. The price is e^(−rT)·[F·N(d1) − K·N(d2)], with d1 and d2 built from the futures price, the strike, the volatility and the term. Because the future already embeds the cost of carry, the discount hits both terms and the interest rate never shows up inside d1. It is the standard for options on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual volatility.
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.