[Financial Engineering] Two Versions of Delta Hedging

As we did last time, delta hedging is a powerful tool in replicating a derivative portfolio. In this session, we are rethinking what we have done so far and implementing two versions of the delta hedging. The final answers should be the same because we are going to the same thing but with different perspectives.

In the beginning, my position is 0, and as soon as day 1 starts, I can get my delta. So I need to buy

(Δ₀–0) S₀ + (Δ₁ — Δ₀) S₁ + (Δ₂ — Δ₁) S₂ + … + (δ — Δ₋₂) S₋₁+ (Δ — Δ₋₁) S