The Law of One Price and Replication: No-Arbitrage Pricing from First Principles

The no-arbitrage forward price $F_0 = S_0 e^{rT}$ is not an assumption — it is a theorem, forced on the market by the activity of profit-hungry traders who exploit any deviation. If the forward price were higher than $S_0 e^{rT}$, every institutional desk with access to borrowing would execute the same trade: borrow cash, buy the asset, short the forward, earn a riskless profit. Competition would immediately drive the forward price back. If the forward price were lower, the same desks would short the asset and take the long forward side. The asset price and forward price are in a precise mechanical relationship that no persistent departure can survive.

• distinguish investment assets from consumption assets and explain why only the former can be priced by no-arbitrage replication;
• describe the mechanics of a short sale (borrow shares, sell, pay dividends, return shares) and explain the role of the margin account;
• derive $F_0 = S_0 e^{rT}$ via the two-sided arbitrage argument for an asset paying no income;
• extend the argument to known cash income ($F_0 = (S_0 - I)e^{rT}$) and known continuous yield ($F_0 = S_0 e^{(r-q)T}$);
• compute the mark-to-market value of an existing forward contract using $f = (F_0 - K)e^{-rT}$;
• identify why the Kidder Peabody error was a misunderstanding of cost-of-carry, not an arbitrage.

1. Investment assets vs consumption assets
2. Short selling mechanics
3. The forward price for an asset with no income
4. Known cash income
5. Known continuous yield
6. Valuing an existing forward contract
7. The cost-of-carry framework in perspective