A Financial Derivatives of Asset and Liability: An Improved Black Scholes Model

This work provides an improved Black-Scholes model by incorporating inflation rate, dividend yield and risk free rate. The resulting pricing equation for derivatives and, in particular, the formula for European call options is then shown to depend explicitly on the drift of the underlying asset, which is following a geometric Brownian motion. It is visualized that with the present model, the predicted results by the model could be closer to real data. The adjusted pricing model could partly also explain the mystery of volatility smile. The present model also provides answers to many finance professionals and academics who have been intrigued by the effect of inflation rate, dividend yield and risk free of their asset. The model provides generally different fair values for financial derivatives compared to the Black-Scholes model. In particular, the present model predicts that the original Black-Scholes model tends to undervalue for example European call options.