10_28_2010 Alternative_Term_Structure_Models

10_28_2010 Alternative_Term_Structure_Models - FIXED INCOME...

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1 NAME OF INITIATIVE OR GROUP FIXED INCOME SECURITIES Fall 2010 – FNCE 235/725 Prof. Stephan Dieckmann OCTOBER 28, 2010 ALTERNATIVE TERM STRUCTURE MODELS
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2 General Criteria • Short-term interest rates appear to exhibit some degree of mean reversion • Short-term interest rates are more volatile than long-term interest rates • Should be consistent with no-arbitrage principles • What exactly is modeled? • How is the volatility of interest rates modeled? • How many factors are driving the model? • How good is the fit to current market prices?
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3 Vasicek Model • One factor model for short-term interest rates • Has several intuitively appealing features: Short rate approaches a long-run mean with a certain speed Volatility of short-term rates is higher than volatility of longer maturity rates • However, this model can produce negative interest rates , with a positive probability • Changes in short-term rates have constant volatility • We have seen a discrete time binomial tree version of the model in class, there also exists a continuous time version …
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4 Vasicek Model … d r = κ ( μ - r ) dt + σ dz • Such an equation describes how the short-term interest rate, r , evolves through time • Has a deterministic component given by κ ( μ - r ) dt • And a random component given by σ dz - just think of dz as a random variable drawn from a normal distribution, mean zero • Interest rates can become negative, because the volatility
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This note was uploaded on 03/27/2012 for the course FNCE 235 taught by Professor Roussanov during the Spring '09 term at UPenn.

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10_28_2010 Alternative_Term_Structure_Models - FIXED INCOME...

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