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The volatility of the instantaneous spot interest rate implied by arbitrage pricing – a dynamic Bayesian approach. (English) Zbl 1157.91353

Summary: This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk-neutral measure and propose a filtering estimation algorithm for a time-discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating in order to estimate the volatility function. Our time discretisation can be justified by the fact that data are observed discretely in time. The method is applied to US Treasury rates of various maturities to compute a (posterior) distribution for the parameters of the volatility specification.

MSC:

91B28 Finance etc. (MSC2000)
93E11 Filtering in stochastic control theory
62P20 Applications of statistics to economics
91B24 Microeconomic theory (price theory and economic markets)
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