Shanghai Jiao Tong University · Summer School 2026
BU263 Derivatives
BU263 covers forwards, futures, swaps and options, using John C. Hull as the main text. The course starts with how these contracts trade, then uses arbitrage pricing to value them. It also studies hedging, speculation, swaps, securitisation and the 2007–08 crisis.
Course overview
A derivative is a contract whose value depends on an underlying asset, such as a stock, bond, interest rate, currency or commodity. Exchange-traded futures and options, over-the-counter swaps, structured products and credit derivatives form a large part of modern finance. The course introduces the instruments, the markets in which they trade, and the arbitrage arguments used to price them. It also covers their use in hedging, speculation and risk transfer.
The course is organised in three blocks: forwards, futures and hedging; interest rates, swaps and the credit crisis; and options, including mechanics, properties and trading strategies. Each instrument is introduced through its market setting: exchanges, clearing houses, margining, day-count conventions and quotation conventions. Pricing then follows from arbitrage arguments applied to real markets such as SOFR, Treasury futures, CME and ICE contracts, and the 2008 crisis.
Learning outcomes
- describe the main derivatives, forwards, futures, swaps and options, and the markets they trade in, and distinguish the three users: hedgers, speculators and arbitrageurs;
- explain the mechanics of futures markets, including the clearing house, margining and marking-to-market, and design hedging strategies, including the minimum-variance hedge ratio and hedging an equity portfolio with index futures;
- measure interest rates and the term structure (zero rates, forward rates, SOFR), and price interest-rate futures and interest-rate swaps off the zero curve;
- use arbitrage and cost-of-carry arguments to determine forward and futures prices on investment assets, currencies and commodities;
- explain securitisation, structured credit, the 2007–08 financial crisis and the post-crisis valuation adjustments (XVAs);
- describe the mechanics of options markets, derive the bounds and put–call parity for stock options, and construct option trading strategies, including spreads, straddles and combinations.
Teaching & assessment
Teaching. A 2-hour-40-minute class each day, Monday to Friday, for three weeks; in addition, the teaching assistants run roughly 3 hours 20 minutes of discussion sessions per week. Teaching combines lectures, worked exercises and problem sets, and a group project, with extensive use of payoff diagrams and numerical examples. The exercises put the theory of hedging, arbitrage, and speculation to work on real instruments.
Assessment. The final grade combines attendance (12%), three quizzes (18%), a midterm (20%), a group assignment and presentation (20%), and a final examination (30%). Quizzes are short and held at the start of class; Quiz 1 (Topics 1–3) on Thursday 2 July, Quiz 2 (Topics 4–6) on Monday 6 July, and Quiz 3 (Topics 7–9) on Monday 13 July. The midterm (Topics 1–6) is on Friday 10 July; the group presentations on Thursday 16 July; and the final (Topics 7–11) on Friday 17 July.
Weekly schedule
| Day | Session | Readings |
|---|---|---|
| Week 1: Forwards, futures & hedging | ||
| Mon 29 Jun | Topic 1: Introduction to Derivatives | Hull 1 |
| Tue 30 Jun | Topics 2–3: Mechanics of Futures Markets & Hedging Strategies | Hull 2–3 |
| Wed 1 Jul | Topic 4: Interest Rates | Hull 4 |
| Thu 2 Jul | Quiz 1 (Topics 1–3) · Topic 5: Forward & Futures Prices | Hull 5 |
| Fri 3 Jul | Topic 6: Interest Rate Futures | Hull 6 |
| Week 2: Swaps, credit & into options | ||
| Mon 6 Jul | Quiz 2 (Topics 4–6) · Topic 7: Swaps | Hull 7 |
| Tue 7 Jul | Topic 8: Securitisation & the Credit Crisis of 2007–08 (with XVAs) | Hull 8–9 |
| Wed 8 Jul | Topic 9: Mechanics of Options Markets | Hull 10 |
| Thu 9 Jul | Review & midterm preparation (Topics 1–6) | Hull 1–8 |
| Fri 10 Jul | Midterm Examination (Topics 1–6) | |
| Week 3: Options, properties & strategies | ||
| Mon 13 Jul | Quiz 3 (Topics 7–9) · Topic 10: Properties of Stock Options | Hull 11 |
| Tue 14 Jul | Topic 11: Trading Strategies Involving Options | Hull 12 |
| Wed 15 Jul | Review & exam preparation (Topics 7–11) | Hull 7–12 |
| Thu 16 Jul | Group Project Presentations | |
| Fri 17 Jul | Final Examination (Topics 7–11) | |
Topic overview
Introduction to Derivatives
What a derivative is; exchange-traded versus over-the-counter markets; the four building blocks: forwards, futures, swaps and options; and the three users: hedgers, speculators and arbitrageurs.
Key idea: a derivative's value depends on an underlying asset. Equal payoffs must have equal prices.
Mechanics of Futures Markets & Hedging Strategies
The exchange, the clearing house (CCP) and margining; marking-to-market and convergence to spot; long and short hedges; basis risk and the optimal (minimum-variance) hedge ratio; hedging an equity portfolio with index futures.
Key idea: daily marking-to-market and the clearing house remove counterparty risk; hedging swaps price risk for basis risk, with hedge ratio h* = ρ σS/σF.
Interest Rates
Types of rates, including Treasury, repo and the transition from LIBOR to SOFR; compounding and measuring rates; zero rates, bond pricing and the term structure; forward rates; duration and convexity.
Key idea: the zero curve and the forward rates implied by it underlie the pricing of every fixed-income derivative.
Determination of Forward & Futures Prices
The cost-of-carry; pricing forwards on investment assets, with known income and known yield; the forward price of currencies and of commodities (with storage and convenience yield); futures versus forward prices.
Key idea: F0 = S0e(r−q)T. The forward price follows from cost-of-carry and arbitrage pricing, with no view on the future.
Interest Rate Futures
Day-count and quotation conventions; Treasury bond futures and the cheapest-to-deliver option; SOFR (and legacy Eurodollar) futures; duration-based hedging of an interest-rate exposure.
Key idea: duration-based hedging with rate futures lets a portfolio's interest-rate exposure be moved to any target, including zero.
Swaps
The mechanics of plain-vanilla interest-rate swaps; the comparative-advantage argument; valuing a swap as a pair of bonds or as a portfolio of forward-rate agreements; currency swaps; credit risk in swaps.
Key idea: a plain-vanilla swap is a portfolio of forward-rate agreements, valued by discounting off the zero curve.
Securitisation & the Credit Crisis of 2007–08
Securitisation, asset-backed securities and CDOs; the US housing bubble and the 2007–08 crisis; what went wrong and the lessons; and the post-crisis valuation adjustments, including CVA, DVA and FVA.
Key idea: securitisation without "skin in the game" and mispriced tail risk turned a housing downturn into a global financial crisis.
Mechanics of Options Markets
Calls and puts and the four basic positions; option payoffs and the underlying assets; specification of exchange-traded options; dividends, position limits and margining; the role of the options clearing corporation.
Key idea: an option is a right, not an obligation. The four positions, long call, short call, long put and short put, are the building blocks of every strategy.
Properties of Stock Options
The six factors affecting an option's price; upper and lower bounds; put–call parity; whether to exercise an American option early; and the effect of dividends.
Key idea: put–call parity c + Ke−rT = p + S0 links calls, puts and the underlying without model assumptions.
Trading Strategies Involving Options
Principal-protected notes; spreads, including bull, bear, butterfly and calendar; combinations, including straddles, strangles, strips and straps; and reading the resulting payoff diagrams.
Key idea: combining options can produce a wide range of payoff profiles used in structured products.
Textbook, reading & sources
The course follows Hull throughout, supported by the companion DerivaGem software and by the real markets and conventions the instruments trade in.
- Required text. Hull, John C. Options, Futures, and Other Derivatives. 10th ed. New York: Pearson, 2017.
- Reference text. Hull, John C. Fundamentals of Futures and Options Markets. 9th ed. Pearson, 2016. A gentler companion to the same material.
- Software. DerivaGem, the option-pricing and Greeks software accompanying Hull, used in exercises.
- Interest-rate benchmarks & the LIBOR–SOFR transition: the Federal Reserve Bank of New York's SOFR reference rate; US Treasury par-yield curves. Used for the zero curve, rate futures, and swaps.
- Exchanges & contract specifications: CME Group and ICE (futures and options specs, margining, settlement); the OCC (options clearing).
- Over-the-counter market: the ISDA Master Agreement and documentation; central counterparties (CCPs) and the post-crisis clearing mandate.
- The 2007–08 crisis & structured credit: Hull, Risk Management and Financial Institutions; the Financial Crisis Inquiry Commission report (2011); Gorton & Metrick, "Securitized Banking and the Run on Repo" (2012).
- Market data: exchange and vendor data (e.g. Bloomberg) for quotes, the term structure, and option chains used in worked examples.
