The Influence of Stochastic Volatility and Transaction Cost on LGBM
Abstract
This paper presents a differential form of the stock market price dynamics, this differential form is an extension of the original logistic geometric Brownian motion (LGBM) by introducing stochastic volatility and transaction cost into the model. Using Ito's lemma, we obtain the stock market price dynamics under geometric Brownian motion (GBM) and logistic geometric Brownian motion (LGBM) in the presence of transaction cost and stochastic volatility. Furthermore, we present some numerical simulations to investigate the impact of some important sensitive parameters on the stock market price and observed that the presence of stochastic volatility and transaction cost in the LGBM help to accurately predict asset price behaviour in the market.
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