Shortcomings of the Black Scholes-Merton Options Pricing Model

                                                                                                                   T = Time to Expiration

The Black Scholes-Merton options pricing model conflates a cumulative standard normal distribution with a probability distribution, applicable to all securities, or underlying assets which is demonstrably untrue as manifested by its cumulative function of d1, the initial discount rate. Furthermore, the model assumes deterministic rates, dividends, and volatility in addition to no gap risk. It’s assumption of no gap risk is predicated on the erroneous notion that a security can be hedged continuously until delta-neutral irrespective of the conditions. Contrary to this latent supposition of the Black Scholes model, assets lack price consistency as they often gap, or jump between or during trading intervals; thus, precluding the hedging of various forms of various derivative positions, such as short options or credit swaps with the underlying asset. Additionally, the model assumes  the constancy of interest rates ,dividends, and volatility for the asset preceding expiry. Consequently, significant errors in the calculation of Rho and Vega may ensue resulting in an inaccurate options price as the collective volatility of interest rate/dividend changes and IV is inextricably related to the P/L of the position in question since the gamma of an ATM option is greatest at maturity; hence, the known path-dependency of vanilla options.