The Black-Scholes Model

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In this video, we give an introduction to the famous Black-Scholes model and derive its Partial Differential Equation (PDE) by replication. We will see that any European contingent claim satisfies this equation, with closed-form analytical solutions in some cases, and we have in this framework a hedging strategy offsetting the risk in the portfolio.

0:00 Introduction
0:32 Model Assumptions
1:15 Risky Asset - Geometric Brownian Motion
1:53 Risk Free Asset
2:09 European Contingent Claim
2:26 Self-Financing Portfolio
3:02 Derivation of the Black-Scholes Equation
4:35 Boundary Conditions and Black-Scholes Formula for European Calls and Puts

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