Learning outcomes

After this module you can:

1. Derive the forward price $F_0 = S_0 e^{(r-q)T}$ by constructing both the cash-and-carry and the reverse cash-and-carry arbitrage, and the discrete-dividend version $F_0=(S_0-I)e^{rT}$.
2. Value an existing forward contract and state the no-arbitrage band for a forward price when borrowing and lending rates differ and trading costs are present.
3. Compute the daily mark-to-market cash flows and margin calls of a futures position, and the return on margin for a given price move.
4. Prove that futures and forward prices coincide when interest rates are deterministic, and sign and size the futures–forward gap when rates are stochastic.
5. Decompose a hedger's effective price into the futures price and the basis at close-out, and explain basis risk.
6. Derive the minimum-variance hedge ratio $h^*=\rho\sigma_S/\sigma_F$, its hedge effectiveness $\rho^2$, and the beta-hedge contract count $N^*=\beta V_P/V_F$; estimate them from data and size a Nifty futures hedge in lots.
7. Read open interest correctly, including the accounting identity behind it and the reasons the popular price/OI labels carry little predictive information.
8. Write the cost-of-carry relation with storage cost and convenience yield, $F_0=S_0e^{(r+u-y)T}$, and explain why it is an inequality for consumption commodities.