Default-free bond futures and options on default-free bond futures: Theoretical and empirical investigation
Hsin, Chin-Wen
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Permalink
https://hdl.handle.net/2142/21496
Description
Title
Default-free bond futures and options on default-free bond futures: Theoretical and empirical investigation
Author(s)
Hsin, Chin-Wen
Issue Date
1990
Doctoral Committee Chair(s)
Bera, Anil K.
Department of Study
Finance
Discipline
Finance
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Economics, Finance
Language
eng
Abstract
This study investigates the pricing behaviors of default-free bond futures and American options on default-free bond futures based on the framework of Brennan and Schwartz (1979). In their model, the state space of interest-rate-dependent claims is spanned by the instantaneous spot interest rate and the long-term consol rate. This design is chosen to incorporate the features of interest-rate-dependent claims and to avoid inconsistencies in other pricing models for general assets. This study assumes that the logarithm of these two factors follow a linear transformation of an Ornstein-Uhlenbeck process. The prices of these contingent claims are solutions to a set of partial different equations subject to proper boundary conditions. As there is no closed form solutions to these equations, a finite-difference method, line-hopscotch method, is employed.
To implement the pricing model, one has to empirically estimate (i) the parameters in the interest rate processes and (ii) the risk premium parameter associated with the short spot rate. An exact discrete time model is derived such that one can use discrete time empirical data to estimate parameters in the continuous interest rate processes. Maximum likelihood estimation results show that the parameter estimates are affected by the choice of proxy variable, sample period and the size of sampling interval. It is most obvious fort those parameters in the short rate process.
The model prices of default-free bonds, default-free bond futures and options on default-free bond futures are solved successively by the numerical method. The empirical results indicate insignificant pricing errors for Treasury bond futures. However, the model does not perform well for pricing options on T-bond futures. A sensitivity analysis is conducted. It suggests that the long rate process is important in determining the pricing behavior of these claims. Also, the long rate affects the security prices differently than the short rate does.
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