The Black-Scholes-Merton Model

This lecture covers the Black-Scholes-Merton model, a continuous-time economy with a constant riskless rate and a standard Brownian motion generating uncertainty. It explains the dynamics of the discounted price, self-financing strategies, continuous trading, and the replicating strategy for call options. The lecture also delves into the Black-Scholes-Merton partial differential equation (PDE), the hedging portfolio, dividend pricing, and the Feynman-Kac representation. It concludes with insights on the put option, the replicating strategy, and the linear pricing nature of the PDE.