forward rate 作为middle rate 本身受volatility 影响吗？

问题如下：

选项：

Update binomial interest rate tree (Volatility=10%) to reflect the current volatility, which is now 15%. If the assumed volatility is changed, the forward rates shown in binomial interest rate tree will most likely:

A.

spread out.

B.

remain unchanged.

C.

converge to the spot rates.

解释：

Correct Answer: A

Volatility is one of the two key assumptions required to estimate rates for the binomial interest rate tree. Increasing the volatility from 10% to 15% would cause the possible forward rates to spread out on the tree as it increases the exponent in the relationship multiple between nodes (e^xσ, where x = 2 times the number of nodes above the lowest node in a given year in the interest rate tree). Conversely, using a lower estimate of volatility would cause the forward rates to narrow or converge to the implied forward rates from the prevailing yield curve.

B is incorrect because volatility is a key assumption in the binomial interest rate tree model. Any change in volatility will cause a change in the implied forward rates.

C is incorrect because increasing the volatility from 10% to 15% causes the possible forward rates to spread out on the tree, not converge to the implied forward rates from the current yield curve. Rates will converge to the implied forward rates when lower estimates of volatility are assumed.