Why Rho Has Different Signs in Black–Scholes and Black-76

Summary

The document asks why the interest-rate sensitivity, or rho, of calls and puts appears to have different signs under Black–Scholes and Black-76. It reports Black-76 formulas in which call and put rho are both negative, then contrasts them with the familiar Black–Scholes result: positive call rho and negative put rho.

The text does not provide an answer or explain the modeling distinction behind the discrepancy. It is therefore useful mainly as a focused question about comparing model conventions and rate sensitivities. Readers should treat the stated formulas as the question’s premise; without a response, the document supplies no derivation, assumptions, or evidence to resolve it.

Key ideas

• The author notices different reported rho signs for calls and puts in Black–Scholes and Black-76.
• The document presents the discrepancy as an unresolved question.
• It gives no derivation or assumptions that would explain the difference.

Tags

# Why the sign of RHO in BSM and Black76 Model is opposite?


# Why the sign of RHO in BSM and Black76 Model is opposite?












I find the formula of RHO using Black76 model (Source, alternatively see Wikipedia and scroll to "Under the Black model"): $$ RHO_{call} = -t*c $$ $$RHO_{put} = -t*p$$ which means the sign of rho < 0.

But when use BSM (Source)， the $RHO_{call}>0,RHO_{put}<0$, so I am very confused. I'll very appreciate for anyone's help!

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