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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=kโˆ—(eโˆ’r)โˆ—dt+gโˆ—dwdr = k * (e - r) * dt + g* dwdr=kโˆ—(eโˆ’r)โˆ—dt+gโˆ—dw

In this context:

  • drdrdr represents the change in the short-term interest rate,
  • eee is the expected long-term average of the short-term interest rate,
  • kkk denotes the speed of mean reversion,
  • rrr is the current short-term interest rate,
  • ฯƒ\sigmaฯƒ is the annual volatility of the short-term interest rate, quantified in basis points,
  • dtdtdt signifies the time period in years, and
  • dwdwdw is a random variable that follows a normal distribution with zero mean and a standard deviation equal to the square root of dtdtdt.

The following data has been gathered for the analysis:

  • Current short-term interest rate (rrr): 3.35%
  • Long-term expected short-term interest rate (eee): 4.55%
  • Mean reversion rate (kkk): 0.06
  • Annual volatility in basis points (ฯƒ\sigmaฯƒ): 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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