Pricing the derivatives

• Arbitrage 套利
• Replication
• Risk neutrality

Present value of discounted cash flow (DCF) 未来现金流折现求和

The value of the financial asset = Expected future price + interim payments (e.g. dividends or coupon interest, discounted at a rate appropriate for the risk assumed) E(St) + interim cash inflow (dividends) - interim cash outflow

• Arbitrage空手套白狼：law of one price Buy Low Sell High, exploit the arbitrage opportunity quickly, then make the prices converge

1. no risk
2. no investment无初始投资

Law of one price: assets that produce identical future cash flows

• Replication An asset and hedging position of derivatives on the asset

Asset + Derivative = Risk-free asset Asset - Risk-free asset = -Derivative Long asset, short bond, long forward