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QuantFinance foundations

Derivatives

Options, forwards, futures, swaps and their no-arbitrage relations.

4 lessons open · 20 planned

Steps 2, 3, 7, 8, 18, 19 and 20 are part of the option pricing path, a 22-step course from discounting to Black–Scholes.

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Option payoffs and put-call parity If two portfolios pay the same amount at expiration no matter where the stock ends, must they cost the same today? Option pricing path, step 2 · ~40 min Forward prices by cash-and-carry What price should you agree on today to buy an asset a year from now? Option pricing path, step 3 · ~35 min No-arbitrage bounds on option prices Which option prices violate no-arbitrage bounds? Option pricing path, step 8 · ~45 min When early exercise pays When is early exercise worth more than waiting? Option pricing path, step 7 · ~35 min

Planned

In learning order. These are not pages yet.

  1. Why futures and forward prices can differAdvanced undergrad
  2. How currency forwards connect two interest ratesAdvanced undergrad
  3. Why commodity forwards depend on convenience yieldAdvanced undergrad
  4. How a lookback option remembers the path extremeAdvanced undergrad
  5. How a CDS exchanges premiums for default protectionAdvanced undergrad
  6. How a forward rate agreement settlesAdvanced undergrad
  7. How a variance swap pays for realized volatilityGraduate
  8. Why a par interest rate swap starts at zero valueAdvanced undergrad
  9. How caplets build an interest rate capAdvanced undergrad
  10. How averaging changes an Asian optionAdvanced undergrad
  11. The Black–Scholes formula and binomial convergenceAdvanced undergrad
  12. The GreeksAdvanced undergrad
  13. Barrier optionsAdvanced undergrad
  14. Why a digital option has concentrated price sensitivityAdvanced undergrad
  15. Why correlation matters for a basket optionGraduate
  16. Black's model: pricing options on forwards, caps, and swaptionsAdvanced undergrad
  17. Quanto options: why a correlation term enters the driftGraduate
  18. What a swaption gives you the right to enterAdvanced undergrad
  19. What the volatility smile says about the risk-neutral distributionAdvanced undergrad
  20. Building a payoff from a strip of calls and putsAdvanced undergrad

How it connects

Builds on Corporate finance Probability Arbitrage and risk-neutral pricing Stochastic processes Bonds and interest rates Stochastic calculus and SDEs PDE methods Calculus Credit risk Equities and portfolios Optimization Hedging and calibration Numerical methods

Leads to Hedging and calibration Bonds and interest rates Monte Carlo and numerical pricing Credit risk Corporate finance Arbitrage and risk-neutral pricing PDE methods Interest-rate models Volatility and jump models

Subjects marked “connection” are linked by a related idea, not by a prerequisite.

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