Learning outcomes

After this module you can:

1. Prove the cash-and-carry upper bound $F \le S e^{(r+u)T}$, prove that no arbitrage lower bound exists for an agent without inventory, and state the bound that does exist for an inventory holder or a metal borrower.
2. Derive, from the competitive-storage equilibrium, why low inventories produce backwardation and high inventories produce contango close to full carry, and read a futures curve as an inventory signal.
3. Decompose a futures excess return exactly into spot return and roll yield, and compute how much a long-only index investor loses to a contango curve.
4. Derive the Hotelling rule and the Barsky–Summers "gold as a durable asset" relation, and say where each fails.
5. Price Indian gold from the international price by import parity (troy-ounce conversion, USDINR, BCD, AIDC, GST), reproduce an MCX price to within 0.1%, and decompose a rupee gold return into gold, FX and duty parts.
6. Test the gold/silver ratio for mean reversion properly: ADF with correct critical values, AR(1) half-life $h = -\ln 2/\ln\varphi$, its OU interpretation, its small-sample bias and its confidence interval.
7. Describe the crude market's structure (OPEC+, shale, Brent/WTI/Dubai, the Indian basket, EIA inventories, crack spreads) and trace an oil shock through INR, CPI and OMC stocks.
8. Read an MCX contract specification (lot, quote, tick, tender period, devolvement of options), and price an MCX option on futures with Black-76.