# MidtermTwoAnswers - ACTUARIAL SCIENCE 445/845 Asset...

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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#: _____________________ Course (445 or 845):___________ Concept Questions 1. [4 marks] Briefly explain the difference between arbitrage-free 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 Cox-Ingersoll-Ross models. Arbitrage-free 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 Ho-Lee, Black-Derman-Toy, and Hull-White 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 Black-Derman-Toy model (equations are not necessary).

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