Option Lambda (Elasticity)
Computes the lambda of a call option, also called omega or elasticity: the percentage change in the premium for each one-percent change in the underlying's price. It's the delta times S/C, and it measures the leverage built into the option. A lambda of 6, for instance, means the option moves, in percentage terms, about six times faster than the stock, which is why options amplify gains and losses. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
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Option Lambda (Elasticity)
Computes the lambda of a call option, also called omega or elasticity: the percentage change in the premium for each one-percent change in the underlying's price. It's the delta times S/C, and it measures the leverage built into the option. A lambda of 6, for instance, means the option moves, in percentage terms, about six times faster than the stock, which is why options amplify gains and losses. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
The leverage hidden inside an option
Everyone knows options are leveraged, but few know how to measure by how much. Lambda, also called omega or elasticity, puts a number on it: it tells you the percentage change in the premium for each one-percent change in the underlying's price. It isn't delta in absolute terms, it's delta translated into the language of percentage return.
The calculation is delta times S over C, the asset price divided by the option premium. A lambda of 6 means that if the stock rises 1%, the option tends to rise close to 6% — and falls in the same proportion when the stock retreats. That multiplication is what explains why options can pay off big or go to zero in a short window. The further out of the money and the cheaper the option, the bigger the lambda and the greater the leverage.
The calculation is for a call with no dividends and uses the Black-Scholes price as the denominator. Enter spot price, strike, interest rate, term in years and volatility. Lambda is an instantaneous measure: it holds for right now and shifts as the asset and the premium move, so treat it as a portrait of the current leverage, not a fixed figure.
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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.
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Computes the price of a call option with the Bachelier model, which assumes the price follows normal (arithmetic) motion instead of lognormal. Because it allows negative prices, it came back into fashion for pricing options on assets that can go negative, as happened with oil in 2020 and with some spreads. The volatility here is absolute, in price units, not a percentage. The premium is e^(−rT)·[(F−K)·N(d) + σ√T·φ(d)]. Enter the forward price, the strike, the interest rate, the normal 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.