Stochastic Interest Rates Model And Contingent Claim Pricing
Abstract
This project designs and formulates prices and the inherent factors used in contingent
securities. Participating contingent contracts are most popular in most financial jurisdictions.
They present many different covenants and depend on sector regulations. This work tries to
design the new participatory contract although structurally unchanged from the traditional
contracts, the stochastic nature of the interest rates are taken into consideration in the design
of this new contract this research envisages. After an in-depth analysis of the factors stochastic
or otherwise but with a guaranteed rate matching the rate of interest in Kenyan government
bonds, we prove that this new type of contract can be valued in closed form when interest
rates are stochastic and the company can default.
The stochastic interest rate model used here borrows heavily from Schwartz and Gibson’s work
(1989) as it is used to capture the empirical properties of the financial time series. Most of
these applications are made on the assumptions that the conditional distribution of interest
rates given that the log distribution of volatilities is normal. This research project aims to
analyze the other side of the standard Black- Scholes and GARCH- Models and re evaluate the
parameters as used in BSM Model using Stochastic Volatility models (SV) and applying the
estimated rate of the interest in a two factor stochastic model to price a contingent security.
The traditional BSM pricing assumption of interest rate is looked upon as continuous time
processes and the re evaluation is done using the continuous time model of SV. These models
are derived and applied on the two factor security pricing formulae. The standard SV Model is
examined and applied in statistical sense- linear model. The revised stochastic interest rate
model is then applied to the pricing of contingent claims using the Nairobi stock exchange
prices as the underlying security. Emphasis is laid on the estimation of the parameter interest
rates that is looked upon as a stochastic random variable depending on time and other factors
the motivation thus is the inherent failures of the traditional option pricing Models as BSM
Model. This is due to the realization that most of parameters used in the standard Black-
Scholes and assumed constant and are in real sense are time dependent variables and should
be looked upon as such given the complex business environment that requires effective pricing
that reflect this modern challenges and factors. The study therefore aims to go beyond the
norm by doing in depth analysis into the Black-Scholes pricing formulae and the time proven
time series model- GARCH Model and concentrating on the synergy between the two and
proposing a more robust model for security pricing.
Citation
Masters of Science degree in Actuarial Science,Publisher
University of Nairobi, School of Mathematics,