On the European logistic-type option pricing with jump diffusion
Date
2019-08
Authors
Oduor, Brian
Mulambula, Adanje
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
Black- Scholes formed the foundation of option pricing. However, some of its assumptions like
constant volatility and interest among others are practically impossible to implement hence other
option pricing models have been explored to help come up with a much reliable way of predicting
the price trends of options. Black-scholes assumed that the daily logarithmic returns of individual
stocks are normally distributed. This is not true in practical sense especially in short term intervals
because stock prices are able to reproduce the leptokurtic feature and to some extent the volatility
smile". To address the above problem the Jump-Diffusion Model and the Kou Double-
Exponential Jump-Diffusion Model were presented. But still they have not fully addressed the
issue of reliable prediction because the observed implied volatility surface is skewed and tends
to flatten out for longer maturities; the two models abilities to produce accurate results are
reduced. The study ventures into a research that will involve European logistic-type option
pricing with jump diffusion which has not been addressed anywhere in the financial literature.
The knowledge of logistic Brownian motion will be used to develop a logistic Brownian motion
with jump diffusion model for price process. Existence of jump diffusion will be tested using
Augmented Dickey-Fuller (ADF) test. Finally, estimation of volatility will be done using the
formed model. The methodology will involve analysis of jump diffusion models for pricing
process in particular Vasicek model. Logistic Brownian motion that incorporates jump diffusion
process will be considered and then volatility will be estimated using maximum likelihood
estimates. Data collected from Nairobi Security market will be analyzed to check the reliability
of the formed model. It is hoped that this model will be used by long-term investors to know the
impact of jump diffusion behavior of stocks on assets before allocating decisions and profitability
of trading strategies. Furthermore, it will help investors to know whether or not stock returns
exhibit jump diffusion.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords
Jump-Diffusion, Brownian motion, Augmented Dickey-Fuller (ADF) test