Derivatives

Derivatives in short lessons: how forwards, futures, swaps and options are priced and valued, with the payoffs drawn out and the exam traps flagged.

How this topic is tested, its exam weight and study tips: Derivatives exam guide.

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Derivatives formula sheet

All 110 formulas of the topic, each explained. Every module page ends with its own formulas; the key formulas are here. Downloads come with a subscription or a pass; the free trial does not include them.

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  1. 01

    Derivative Instrument and Derivative Market Features

    5 lessons · ~66 min 39 cards

    What a derivative is and the features every contract shares (underlying, counterparties, maturity, settlement, contract size), the split between firm commitments and contingent claims, why issuers and investors use derivatives, the main underlyings from equities to credit, and how over-the-counter and exchange-traded markets work, including central clearing through a CCP.

  2. 02

    Forward Commitment and Contingent Claim Features and Instruments

    7 lessons · ~83 min6 videos 40 cards

    The main derivative instruments and how they pay off: forwards, futures and swaps as firm commitments with linear payoffs, options and credit default swaps as contingent claims with one-sided payoffs, the value and profit of long and short calls and puts at expiration, and how a forward compares with a call or a short put on the same underlying.

  3. 03

    Derivative Benefits, Risks, and Issuer and Investor Uses

    6 lessons · ~75 min 37 cards

    Why market participants use derivatives (risk transfer, new exposures, price discovery, operational and market efficiency), what can go wrong (implicit leverage, complexity, basis, liquidity, counterparty credit and systemic risk), and how issuers and investors differ in the way they use them, including hedge accounting.

  4. 04

    Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

    6 lessons · ~71 min4 videos 37 cards

    Why no-arbitrage pins a forward price to the spot price, how a forward can be rebuilt from the underlying plus borrowing or lending, and how the cost of carry (the risk-free rate, storage costs, dividends, coupons, convenience yield or a second currency's interest rate) decides whether the forward price sits above or below spot.

  5. 05

    Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

    7 lessons · ~87 min4 videos 44 cards

    How a forward's price is set once at inception while its value starts at zero, drifts with the spot price, time and interest rates, and ends as the settlement amount; how carry costs, income and two interest rates (for FX) change that valuation; and how zero rates, discount factors and implied forward rates are derived for interest rates, which have a term structure, and used to price forward rate agreements.

  6. 06

    Pricing and Valuation of Futures Contracts

    5 lessons · ~61 min2 videos 36 cards

    How futures are priced at inception exactly like forwards, how daily settlement through a margin account changes their value over time, how short-term interest rate futures are quoted and compared with FRAs, and why forward and futures prices can differ: interest rate correlation and volatility, the convexity bias, and the narrowing effect of central clearing.

  7. 07

    Pricing and Valuation of Interest Rates and Other Swaps

    6 lessons · ~79 min2 videos 34 cards

    How an interest rate swap relates to a series of forward rate agreements, how its price (the par swap rate) is solved from zero rates and implied forward rates, why issuers and investors prefer swaps, and how a swap's value starts at zero and then moves with periodic settlements, the passage of time and changes in expected forward rates.

  8. 08

    Pricing and Valuation of Options

    6 lessons · ~71 min2 videos 36 cards

    How an option's price splits into exercise value and time value, what moneyness tells you, why no-arbitrage sets upper and lower bounds on European call and put prices, how replicating an option differs from replicating a forward, and how the underlying price, exercise price, time, interest rate, volatility and carry benefits or costs push option values up or down.

  9. 09

    Option Replication Using Put–Call Parity

    5 lessons · ~59 min2 videos 39 cards

    Why a fiduciary call and a protective put must cost the same, how that put–call parity relationship prices one European option from the other and exposes arbitrage, how rearranging it builds synthetic calls, puts, shares, bonds and covered calls, how swapping the share for a forward gives put–call forward parity, and how the same logic describes equity as a call and risky debt as a bond minus a put on firm value.

  10. 10

    Valuing a Derivative Using a One-Period Binomial Model

    6 lessons · ~73 min2 videos 34 cards

    How a one-period binomial model values a European option: let the underlying move up or down, combine the option with a hedge ratio of the underlying to build a riskless portfolio, discount at the risk-free rate, and see why the same answer comes from risk-neutral probabilities that ignore real-world probabilities and investor risk preferences.