Volatility Estimation Using Mean Reverting European Logistic Type Option Jump Diffusion Process and Transaction Cost

Mean reversion is a financial term used in options pricing to describe the trend of stocks. Mathematical concepts in mean reversion have been used many a times in predicting interest rate trends and stock pricing. Many researches that have been done show that the price of a given commodity revert to their equilibrium level and therefore it cannot increase exponentially. On the other hand, jump diffusion processes are used in modern finance to capture discontinuous behavior in asset pricing. The pricing of assets in jump diffusion is consistent with the volatility smile often observed in financial markets. Work has been done on mean reversion process with Geometric Brownian Motion and jump diffusion process and also on estimation of volatility using mean reverting European Logistic Type Option but still these models could not accurately predict stock prices in case of a calamity. The concept of mean reversion and jump diffusion process on volatility together with transaction cost which could be useful in that case had not been covered in financial literature. Therefore, this led to this study on deriving a model and estimation of volatility using mean reverting European logistic type option pricing with jump diffusion process and transaction cost. The knowledge of Geometric Brownian Motion, Logistic Brownian Motion and Vasicek model was used to derive the volatility equation. Data that was collected from Nairobi security exchange was analyzed using the STATA software to check the reliability of the formed model. Volatility and transaction costs are key drivers of asset price behavior, especially in emerging markets where structural inefficiencies and informational asymmetries are more pronounced. The adoption of a mean-reverting logistic-type model with jump diffusion and transaction costs provided a data-driven perspective that more accurately captured the complexities of real-world financial markets. The findings can be used by investors to predict the future stock’s price which would assist them in formulating investment strategies so that they make reasonable profits. It would also be used to estimate the impact of a calamity and encourage investors to diversify in businesses or insure the stock to minimize the loses they may incur.