A Jump Diffusion Model with Fast Mean Reverting Stochastic Volatility for Pricing Vulnerable Options

Simple item page
dc.contributor.advisorAnanda Omutokoh Kubeen_US
dc.contributor.advisorCyprian Ondieki Omarien_US
dc.contributor.authorKalekye, Nthiwa Joy
dc.date.accessioned2024-02-06T12:31:54Z
dc.date.available2024-02-06T12:31:54Z
dc.date.issued2023-10
dc.descriptionA 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.en_US
dc.description.abstractThe 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.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttps://ir-library.ku.ac.ke/handle/123456789/27578
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectJump Diffusion Modelen_US
dc.subjectMean Reverting Stochastic Volatilityen_US
dc.subjectPricing Vulnerable Optionsen_US
dc.titleA Jump Diffusion Model with Fast Mean Reverting Stochastic Volatility for Pricing Vulnerable Optionsen_US
dc.typeThesisen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
A Jump Diffusion Model with Fast Mean Reverting....pdf
Size:
297.38 KB
Format:
Adobe Portable Document Format
Description:
Full text Thesis
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
MST-Department of Mathematics