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Volatility and the pricing of interest rate derivative claims
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Volatility and the pricing of interest rate derivative claims
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Volatility and the pricing of interest rate derivative claims
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Dissertation
Volatility and the pricing of interest rate derivative claims
1993
Overview
That financial time series exhibit time dependent volatility is by now a well established fact. Many studies over the years have documented and investigated this feature, predominantly for stock and foreign exchange markets. This study focuses on particular interest rate markets. To start, the volatility characteristics of the three month Treasury Bill market are examined. This occurs in the context of estimating various models for the yield on this Bill. A model selection procedure is proposed, based on stochastic simulation, which allows various suggested specifications to be discriminated between, selecting the most appropriate model in a statistical sense. Continuous time stochastic volatility models of the three month interest rate are then estimated and compared to constant volatility versions. Here, it is found that these latter inadequately model the dynamic properties of interest rates and that stochastic volatility models perform better in this regard. The implications for pricing interest rate derivative securities of stochastic volatility is then examined. Current popular pricing models usually prescribe the volatility of the state variable to be constant, which is restrictive in light of the evidence on interest rate volatility. Using samples of Treasury Bill and Bond futures options, constant volatility and stochastic volatility pricing models are compared. For Treasury Bill futures options, there does not seem to be an advantage to using a complicated stochastic volatility model. A constant volatility model performs equally as well. For Treasury Bond futures options, a constant volatility model also performs as well as the stochastic volatility version, provided the volatility parameter is allowed to vary through time. Finally, several situations are considered in which the importance of accounting for volatility is demonstrated. The first is in the pricing of very long term options, where future volatility movements critically affect option prices. The second concerns portfolio management. Portfolios containing options are exposed to volatility movements, which should be hedged if risk reduction is the goal of the portfolio manager.
