ACTUARIAL SCIENCE 445/845: Asset Liability Management
Midterm One  Fall 2009
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Answer all questions in the space provided. Show your work.
Name: ____________________
Marks: _____________________/35
ID#:
_____________________
Course (445 or 845):___________
Concept Questions
1. [5 marks] Briefly explain what the option adjusted spread of an interest rate derivative
security is, and describe how it is used to calculate effective duration.
2. a) [1 mark] Give the stochastic differential equation for the Vasicek interest rate
model.
b) [2 marks] Briefly explain what is meant when it said that the Vasicek model of interest
rates is not an arbitrage free term structure model.
c) [2 marks] Briefly explain what is meant when it is said that the model exhibits mean
reversion of the short rate.
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Problems:
3. a) [8 marks] The returns on stocks
A
and
B
have a bivariate normal distribution. Stock
A
has expected return
μ
A
and standard deviation
σ
A
> 0, while stock
B
has expected
return
μ
B
and standard deviation
σ
B
> 0. You invest
w
A
> 0 dollars in stock
A
and
w
B
> 0
dollars in stock
B
. Let VaR
A
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 Fall '09
 ChristianeLemieux
 Normal Distribution, Vasicek

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