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

Question

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.

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

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