A Jump Diffusion Model with Fast Mean Reverting Stochastic Volatility for Pricing Vulnerable Options
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Date
2023-10
Authors
Kalekye, Nthiwa Joy
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
The Black-Scholes-Merton option pricing model is a classical approach that assumes the
underlying asset prices follow a normal distribution with constant volatility. However, this
assumption is often violated in real-world financial markets, resulting in mispricing and
inaccurate hedging strategies for options. Such discrepancies may result into financial
losses for investors and other related market inefficiencies. To address this issue, this
study proposes a jump diffusion model with fast mean-reverting stochastic volatility to
capture the impact of market price jumps on vulnerable options. The performance of the
proposed model was compared under three different error distributions: Normal, Student-t,
and Skewed Student-t and under different market scenarios that consist Bullish, Bearish,
and Neutral markets. In a simulation study, the results show that our model under Skewed
Student-t distribution performs better in pricing vulnerable options than the rest under
different market scenarios. Our proposed model was fitted to S&P 500 Index by maximum
likelihood estimation for the mean and volatility processes and Gillespie algorithm for
the jump process. The best model was selected based on AIC and BIC. Samples of the
simulated values were compared with the S&P 500 values and MSE computed at various
sample sizes. Values of MSE at different sample sizes indicate significant decrease to actual
MSE values demonstrating it provides the best fit for modeling vulnerable options.
Description
A Research Project Submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science (Statistics) in the School of Pure and Applied Sciences of Kenyatta University, October 2023.
Keywords
Jump Diffusion Model, Mean Reverting Stochastic Volatility, Pricing Vulnerable Options