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This lecture introduces the Black-Scholes-Merton model, a continuous-time market model where uncertainty is generated by a Brownian motion. It covers the dynamics of stock prices, discounted prices, continuous trading strategies, self-financing conditions, call option pricing, the Black-Scholes-Merton equation, and replicating strategies. The lecture also discusses the put-call parity, option pricing dynamics, boundary conditions, and the Feynman-Kac formula for option pricing.