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ACTUARIAL SCIENCE 445/845: Asset Liability Management
Midterm Two  Fall 2010
Aids: Calculator,
Answer all questions in the space provided. Show your work.
Name: ____________________
Marks: _____________________/30
ID#:
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Course (445 or 845):___________
Concept Questions
1. [4 marks] Briefly explain the difference between arbitragefree and equilibrium interest
rate models. Give two examples of each type of model (just the names, not the equations
are needed).
Answer:
Equilibrium models rely on economic theory to build a model of the stochastic behaviour
of interest rates. In these models, the term structure is an output (so they may not be able
to match the observed term structure of interest rates). Examples include the Vasicek and
CoxIngersollRoss models.
Arbitragefree models are able to match the current term structure of interest rates (the
term structure is an input). They are calibrated to prevent arbitrage opportunities.
Examples include the HoLee, BlackDermanToy, and HullWhite models.
2. [4 marks] Briefly explain the procedure for calibrating an interest rate lattice to a given
term structure of interest rates and rate volatilities using the BlackDermanToy model
(equations are not necessary).
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 Fall '09
 ChristianeLemieux

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