A Jump Diffusion Model with Fast Mean-Reverting Stochastic Volatility for Pricing Vulnerable Options
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Date
2023
Authors
Nthiwa, Joy K.
Kube, Ananda O.
Omari, Cyprian O.
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
Abstract
Te Black–Scholes–Merton option pricing model is a classical approach that assumes that the underlying asset prices follow
a normal distribution with constant volatility. However, this assumption is often violated in real-world fnancial markets, resulting
in mispricing and inaccurate hedging strategies for options. Such discrepancies may result into fnancial losses for investors and
other related market inefciencies. To address this issue, this study proposes a jump difusion model with fast mean-reverting
stochastic volatility to capture the impact of market price jumps on vulnerable options. Te performance of the proposed model
was compared under three diferent error distributions: normal, Student-t, and skewed Student-t, and under diferent market
scenarios that consist of 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 diferent market scenarios. Our proposed
model was ftted to S&P 500 Index by maximum likelihood estimation for the mean and volatility processes and Gillespie
algorithm for the jump process. Te 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 diferent sample sizes indicate
signifcant decrease to actual MSE values demonstrating that it provides the best ft for modeling vulnerable options.
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Citation
Nthiwa, J. K., Kube, A. O., & Omari, C. O. (2023). A Jump Diffusion Model with Fast Mean-Reverting Stochastic Volatility for Pricing Vulnerable Options. Discrete Dynamics in Nature and Society, 2023.