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.
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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 delta that watches the strike, not the asset
The usual delta answers one question: how much does the option move when the underlying moves? Dual delta flips the focus and asks something else: how much would the premium change if the strike were slightly different? It's the derivative of the price with respect to the strike, a less famous sensitivity but a deeply practical one.
The neat part is the interpretation. For a call, dual delta equals −e^(−rT)·N(d2), and the absolute value of that number is, in essence, the risk-neutral probability of the option finishing in the money. So on top of measuring sensitivity to the strike, it throws in a direct read of the exercise odds baked into the model. Anyone comparing options across strikes uses this all the time.
The calculation is for a European call with no dividends. Enter spot price, strike, interest rate, term in years and volatility, and the tool returns the dual delta. Remember that probability is the one from Black-Scholes' risk-neutral world, not a forecast of the real one, but it's the number the market actually prices.
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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.