DerivaSteps
Learn financial derivatives step by step
Short lessons on options, futures and swaps. Read the idea, try a question, then practise with new numbers until you get it right. Free, with no account.
Try a question
How each lesson works
A skill counts as mastered after three correct answers in a row, once each kind of question in it has been answered correctly. It then comes back for a short review on this page after 1 day, and after each correct review the wait grows to 3, 7, 14 and then 30 days, to help you keep it.
The levels
Level 1: Payoffs and profit
The payoff of an option or a forward, the profit after an option’s premium, open interest, and how two positions compare.
Level 2: Forwards and futures
How a forward price is set so that no one can make a riskless profit, what a forward is worth later, currencies and short sales, and how futures gains and losses are paid each day.
- The forward price of a share
- The forward price with dividends
- The value of a forward contract
- Currency forwards and interest rate parity
- The cost of carry: storage costs and yields
- Convenience yield, contango and backwardation
- Arbitrage with a mispriced forward
- Short selling
- Daily settlement of futures
- When a margin call comes
- Mixed practice: all ten skills
Level 3: Interest rates and swaps
Compounding, discounting future payments, zero rates from bond prices, what an interest-rate or currency swap is worth, and why swaps can help both sides.
- Compounding
- Converting a rate between compounding frequencies
- Pricing a bond with zero rates
- Zero rates from bond prices
- Forward rates from zero rates
- The value of an FRA
- Swap payments
- The value of a swap
- Valuing swaps between payment dates
- Comparative advantage and the gain from a swap
- Mixed practice: all ten skills
Level 4: Binomial trees
Pricing options on a tree of up and down moves in the share price: the hedge, working backwards from expiry, American options, and delta and gamma.
Level 5: Option prices and strategies
What an option’s price is made of, the rules that tie prices together, and strategies built from several options: put-call parity, the bounds on a price, spreads and straddles.
Level 6: Hedging with futures
How a futures hedge fixes the effective price up to the basis, the number of contracts that reduces a price risk the most, and hedging a share portfolio with a stock index.
Level 7: Black-Scholes-Merton and the Greeks
The formula for a European option’s price, with dividends, stock indices and currencies, the volatility it needs, and how the price changes with each of its inputs: delta hedging and the other Greeks.
Option calculator
Price a European or American call or put, see what each Greek means with your numbers, and follow every step of the calculation.