Financial Engineering and Analytics
Replicate a derivative payoff
Can you price a derivative by building its payoff from simpler assets?
If two portfolios produce the same payoff in every modeled state, no-arbitrage gives them the same price under the model assumptions.
Delta = (up payoff − down payoff) ÷ (up stock price − down stock price)
The option payoff rises $20 between states while the stock rises $40. Hold $20 ÷ $40 = 0.5 shares, then use borrowing to match the payoff level in both states.
Stock moves to $120 or $80. A $100-strike call pays $20 or $0. Replication uses 0.5 shares and debt with $40 due at expiry.
The option payoff rises $20 between states while the stock rises $40. Hold $20 ÷ $40 = 0.5 shares, then use borrowing to match the payoff level in both states.
At $100 spot and a zero risk-free rate, what does the example replicating position cost?