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Explanation:
The term structures of volatility for a model with mean reversion and a model without mean reversion are indeed dramatically different. In a model without mean reversion, rates are determined solely by the current economic conditions. Any shocks to the short-term rate will affect all rates equally, leading to parallel shifts and a flat-term volatility structure. On the other hand, in a model with mean reversion, short-term rates are significantly influenced by current economic conditions, while longer-term rates are significantly influenced by long-term economic conditions. This results in a term structure of volatility that is not flat but has a certain shape, reflecting the mean-reverting nature of the rates. Therefore, the term structures of volatility for these two models would be dramatically different.
Choice B is incorrect. The term structures of volatility for the model with mean reversion and the one without mean reversion would not be the same. Mean-reverting models assume that there is a long-term average value towards which rates tend to revert, which affects the shape of their term structure of volatility. On the other hand, non-mean-reverting models do not have this feature, leading to different term structures.
Choice C is incorrect. It's not accurate to say that both models would be much more volatile and their patterns cannot be determined through a small set of data. While it's true that volatility can vary in financial modeling, it doesn't necessarily imply that both models will always exhibit high levels of volatility or that their patterns are indeterminable from a small dataset.
Choice D is incorrect. The assertion that the model with mean reversion would give less accurate term structures than the one without mean reversion isn't universally true. The accuracy of these models depends on various factors such as assumptions made, data used and how well they align with real-world market behaviors rather than solely on whether they incorporate mean reversion or not.
Things to Remember
Q.1666 Financial institutions use mean-reverted as well as non-mean-reverted parameters to match the par rates of securities with those of the market. After graphing the term structures of mean-reverted as well as non-mean-reverted models, what would you expect?
A
The model with mean reversion and the one without mean reversion would result in dramatically different term structures of volatility.
B
The model with mean reversion and the one without mean reversion would result in same term structures of volatility.
C
Both models would be much more volatile and their patterns cannot be determined through a small set of data.
D
The model with mean reversion would give less accurate term structures than the one without mean reversion.
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