Option Epsilon (Dividend Sensitivity)
Computes the epsilon of a call option, also called psi: the premium's sensitivity to the asset's continuous dividend yield, that is, dV/dq. The larger the expected dividend, the lower the call's value, because part of the asset's return leaks to whoever holds the stock rather than the option. That's why a call's epsilon is negative and equals −S·T·e^(−qT)·N(d1). It's the Greek that ties pricing to the dividend yield. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
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Option Epsilon (Dividend Sensitivity)
Computes the epsilon of a call option, also called psi: the premium's sensitivity to the asset's continuous dividend yield, that is, dV/dq. The larger the expected dividend, the lower the call's value, because part of the asset's return leaks to whoever holds the stock rather than the option. That's why a call's epsilon is negative and equals −S·T·e^(−qT)·N(d1). It's the Greek that ties pricing to the dividend yield. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
The Greek nobody remembers: the dividend
The famous Greeks react to price, time and volatility. Epsilon, also called psi, looks after a variable usually left out of the conversation: the dividend. It measures how much an option's premium changes when the asset's expected dividend yield shifts. It sounds secondary, but on stocks that pay healthy dividends it makes a real difference to the price.
The logic is straightforward. A dividend is money that goes to whoever holds the stock, not to whoever holds the call. The more a company promises to distribute, the less the right to buy the stock in the future is worth, because you miss out on those payments. That's why a call's epsilon is negative: more dividend, less premium. The formula is −S·T·e^(−qT)·N(d1).
The calculation here is for a European call. Enter spot price, strike, interest rate, term in years and volatility. The result comes in price units per full change in yield; divide by 100 to read it per percentage point of dividend. It's an instantaneous sensitivity, like all Greeks, so it holds for the current scenario.
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Option Vera (DvegaDrho)
Computes the vera of an option, also called rhova: a second-order cross Greek that measures how much the vega changes when the interest rate moves, that is, the derivative of vega with respect to r. It's an obscure sensitivity, used by desks that need to understand how volatility exposure interacts with rate changes. The closed form is −vega·√T·d1/σ, and it's easy to get wrong: the correct version uses d1, not the product d1·d2. 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.
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.
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.
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.
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.