Narrow Results

Fischer Black and Myron Scholes (1973) assumed asset prices follow lognormal distributions and derived the famous Black–Scholes option pricing formula. The lognormal assumption implies the asset price will never be negative and has zero as its lower bound. By relaxing the negative and zero bound, we derive a Black–Scholes-like option pricing formula for asset prices following a shifted lognormal distribution with a lower bound. The formula can be applied to price options with negative prices and negative strikes.