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Financial Risk Manager Part 2

Financial Risk Manager Part 2

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A fixed-income desk quantitative analyst at an investment bank aims to predict future short-term interest rates using the Vasicek model. This model is defined by the following equation: [dr = k * (e - r) * dt + g* dw]

In this context:

  • (dr) represents the change in the short-term interest rate,
  • (e) is the expected long-term average of the short-term interest rate,
  • (k) denotes the speed of mean reversion,
  • (r) is the current short-term interest rate,
  • (\sigma) is the annual volatility of the short-term interest rate, quantified in basis points,
  • (dt) signifies the time period in years, and
  • (dw) is a random variable that follows a normal distribution with zero mean and a standard deviation equal to the square root of (dt).

The following data has been gathered for the analysis:

  • Current short-term interest rate ((r)): 3.35%
  • Long-term expected short-term interest rate ((e)): 4.55%
  • Mean reversion rate ((k)): 0.06
  • Annual volatility in basis points ((\sigma)): 120 bps

Using these inputs, the analyst constructs an interest rate tree and projects the anticipated short-term interest rate for the 8th year. Additionally, the analyst calculates the time required for the short-term interest rate to revert halfway to its long-term average. Based on this analysis, what would be an accurate statement for the analyst to make?*

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