Forwards, Futures & Swaps — Pricing & Valuation

Learning objectives

By the end you can:

1. State and apply the general no-arbitrage cost-of-carry model, and correctly select which compounding convention (continuous (equities, indices, commodities), simple/money-market (FX forwards, FRAs), or discrete periodic (swap legs)) applies to a given instrument, without mixing them.
2. Price an equity index forward/future from a spot level, a financing rate, and a dividend yield (the continuous-yield method), and a single-stock forward from discrete, dated cash dividends (the PV-of-dividends method); detect a mispriced quote and size the cash-and-carry or reverse-cash-and-carry arbitrage it implies.
3. Derive and apply Covered Interest Rate Parity (CIP) to price a deliverable USD/INR forward, distinguish it structurally from an offshore Non-Deliverable Forward (NDF), and compute an NDF's cash settlement against a fixing.
4. Price a commodity forward from a financing rate, a storage/insurance cost, and a convenience yield; distinguish contango from backwardation and back out an implied convenience yield from an observed backwardated quote.
5. Bootstrap a forward interest rate from two zero rates of different maturities (pricing a Forward Rate Agreement), and compute the FRA's discounted cash settlement against a realized reference rate.
6. Explain why a forward settles once at maturity while a future is marked to market daily, compute a multi-day futures variation-margin sequence including a maintenance-margin breach and margin call, and value an outstanding OTC forward before its maturity by the replacement-cost method.
7. Value a plain-vanilla interest rate swap as the difference of a fixed-rate bond and a floating-rate bond (equivalently, as a portfolio of FRAs); derive the par swap rate from a discount curve; value an existing off-market swap and reconcile the direct PV computation against the (contract rate − par rate) × annuity shortcut to the last decimal.
8. (Productivity objective: R10 duality.) Recognize that derivatives pricing is the corpus's single highest AI-over-trust risk region, and route every AI-assisted curve build or pricing task through your own recomputed discount factors and reconciliation checks, never through the model's stated number alone.
9. Apply every technique in both an Indian and a US market. Nifty/Bank Nifty index futures, the USD/INR forward and NDF, and an INR OIS-based interest-rate swap; the CME E-mini S&P 500 future, SOFR futures/FRAs, and a USD interest-rate swap, and connect each valuation forward to the hedge-accounting treatment (M1.09) and the portfolio-risk sizing (M9.01, M3.02) it eventually feeds.

Every objective above is a pricing objective, which leaves a layer out on purpose. The taxonomy those instruments sit inside, forward commitments against contingent claims, exchange-traded against over-the-counter, the clearing house and what it does to counterparty risk, and the honest list of what derivatives are for and what they cost, is owned by DV1.04 and is worth reading either before or after this node. Price first or classify first, the order does not matter; skipping the classification does.

The duality, stated once (R10). As in every module of this program's AI-facing threads, this node carries two objectives at once. The understanding objective (items 1–7 and 9) is what the mastery gate rewards: you earn the pass by deriving the price and reconciling the checks yourself, by hand or in code you wrote and understand. The productivity objective (item 8) is the payoff you keep: knowing that this specific region of the corpus is where a fluent, confidently-wrong AI answer is most dangerous, and building the habit of never letting one enter a valuation unverified. A tool can amplify a correct pricing engine; it can do nothing for a wrong one, and it will never tell you which you have.

Prerequisites & connections

Builds on. Almost nothing formally: DV1.01 is the first node of the Derivatives branch and, like every branch's opening node in this Ring, it unlocks with no prerequisite. Informally, it leans on tools you already own. M3.01 (time value of money) supplies the discounting mechanics, present value, discount factors, compounding, that every formula below is built from. M1.09 §4.9.2 already gave you the accounting side of derivatives at awareness level: fair-value hedges (both legs to P&L), cash-flow hedges (effective portion to OCI, recycled when the hedged item hits P&L), and the FVTPL bucket that catches derivatives by default. This module never re-derives that; it supplies the other half, how the instrument itself is priced and valued, so that when M1.09's OCI note says "cash-flow hedge reserve," you now know exactly what number is sitting inside it. M9.01 (Kelly, conviction × downside, the anti-ruin overlay) and M3.02 (CAPM, the efficient frontier, systematic risk) gave you the vocabulary for why a desk hedges or sizes an exposure at all; this module supplies the instruments those decisions are executed with, without re-teaching either the sizing math or the frontier.