
Explanation:
The model used in this scenario generates a term structure of volatility that slopes downwards. This is because the volatilities of par rates decline with term in this model. When the graph of volatilities against different terms is plotted, the mean reversion and volatility parameters are chosen to fit the implied two-point volatilities. These could be, for example, 2- and 10-year volatilities or longer terms, such as 10- and 30-year volatilities. As a result, the model matches the market at these longer terms but overstates the volatility for shorter terms. This is because mean reversion lowers the volatility of longer-term par rates, but the model does not account for this effect as accurately for shorter terms. Therefore, the conclusion that the model matches the market at longer terms but overstates the volatility for shorter terms is accurate.
Choice A is incorrect. The model does not understate the volatility for shorter terms. In fact, the model generates a term structure of volatility that slopes downwards, indicating that mean reversion reduces the volatility of long-term par rates, not short-term ones.
Choice B is incorrect. The statement contradicts with the information given in the question. The model does not overstate the volatility for longer terms; instead it shows a reduction in long-term par rates' volatility due to mean reversion.
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Q.1667 An FRM exam candidate draws a graph showing the volatilities of par rates with different term structures including short-term as well as long-term term structures. Mean reversion and volatility parameters are graphed against each other. The model generates a term structure of volatility that is sloping downwards, as mean reversion lowers the volatility of long term par rates.
From such a graph, we can conclude that:
A
the model matches the market at longer terms but understates the volatility for shorter terms.
B
the model matches the market at shorter terms but overstates the volatility for longer terms.
C
the model matches the market at longer terms but overstates the prices for shorter terms.
D
the model matches the market at longer terms but overstates the volatility for shorter terms.
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