Pricing of interest rate derivatives / Khor Chia Ying
A numerical method is proposed to find the time-t bond price of a zero-coupon bond with maturity time T under the Cox, Ingersoll and Ross (CIR) model described by a Lévy process. When the underlying distribution in the Lévy process is normal, the numerical results thus found for the bond prices a...
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| Format: | Thesis |
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2013
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| Subjects: | |
| Online Access: | http://pendeta.um.edu.my/client/default/search/detailnonmodal/ent:$002f$002fSD_ILS$002f988$002fSD_ILS:988499/ada?qu=Pricing+of+interest+rate+derivatives http://studentsrepo.um.edu.my/4159/1/Thesis_KHOR_CHIA_YING.pdf |
| Summary: | A numerical method is proposed to find the time-t bond price of a zero-coupon bond
with maturity time T under the Cox, Ingersoll and Ross (CIR) model described by a
Lévy process. When the underlying distribution in the Lévy process is normal, the
numerical results thus found for the bond prices are fairly close to the corresponding
theoretical values. The similar numerical method is next applied to evaluate the bond
price of a zero-coupon bond with maturity time T under the Chan, Karolyi, Longstaff
and Sanders (CKLS) model described by a Lévy process. The numerical results
obtained show that bond price decreases slightly when the parameter g in the CKLS
model increases, and the variation of the bond price is slight as the non-normality of the
underlying distribution in the Lévy process varies. A method is also proposed for
pricing the European call option with maturity T and strike price K written on a
zero-coupon bond with maturity S > T. The numerical results thus found show that
option price decreases as the parameter g in the CKLS model increases, and the
variation of the option price is slight when the non-normality of underlying distribution
in the Lévy process becomes more severe. So far, the parameters in the interest rate
models are assumed to be constants. The restriction on constant parameters is lifted by
describing the parameters as ones which follow a multivariate non-normal distribution.
Compared to the CKLS model with fixed parameters, the CKLS model with stochastic
parameters is found to yield more reasonable prediction interval for the future interest
rate. |
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