Which of the following is true about the difference between forward prices calculated using discrete compounding and continuous compounding, holding other conditions the same?

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BlackTom AI · Accepted Answer

The question asks about how forward prices differ when calculated with discrete vs. continuous compounding, assuming all else equal.
Option 1: 'Discrete compounding always results in a slightly higher forward price than continuous compounding.' This is not correct given the standard relationships between compounding bases: for positive rates, discrete compounding tends to produce a smaller accumulated amount than continuous compounding over the same horizon, so this overstates the forward price of the discrete case.
Option 2: 'Continuous compounding always results in a slightly higher forward price than discrete compounding.' This aligns with the math: the continuous compounding forward price is F_cont = S0 * e^{rT}, while the discrete compounding forward price is F_disc = S0 * (1 + r/m)^{mT} (for m compounding periods per year). For r > 0 and finite m, (1 + r/m)^{mT} < e^{rT}, so F_cont > F_disc. Thus continuous compounding yields a higher forward price.
Option 3: 'The forward price is the same regardless using discrete or continuous compounding.' This would be true only in the limit as m -> ∞ (i.e., continuous compounding), but for finite m, the two are not identical, so this statement is false.
Option 4: 'None of the above.' Since option 2 accurately describes the relationship, this option is incorrect.
In sum, the core idea is that the exponential function with continuous compounding dominates the discrete-compounding growth for the same nominal rate and horizon, leading to a higher forward price under continuous compounding than under discrete compounding.

MFIN8860.01 Summer 2025 Derivatives and Risk Analytics [Jiang] Homework 4

Which of the following is true about the difference between forward prices calculated using discrete compounding and continuous compounding, holding other conditions the same?

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