The situation
A stock priced at ₹100 can finish at ₹125 or ₹80. A ₹100 strike call pays ₹25 or zero. Use a zero interest rate and no frictions.
Your task
How many shares and how much borrowing replicate the call?
Reveal step-by-step solution
Set up the problem
Delta = (₹25 − ₹0) ÷ (₹125 − ₹80) = 5/9 shares.
Work through the numbers
Borrow ₹80 × 5/9 = ₹44.44 so the down-state value is zero. The up-state portfolio pays (₹125 − ₹80) × 5/9 = ₹25.
Interpret the result
Cost = ₹100 × 5/9 − ₹44.44 ≈ ₹11.11. It matches both modeled payoffs.
What to remember
Solve share quantity from payoff differences and then solve the cash position in one state. Verify the other state.