Arbitrage and risk-neutral pricing
Replication, state prices, self-financing strategies, risk-neutral measures, Girsanov and change of numeraire.
5 lessons open · 5 planned
Steps 4, 5, 6, 15 and 17 are part of the option pricing path, a 22-step course from discounting to Black–Scholes.
Pages you can open
Pricing by replication: one period
If a stock can only go up or down, what is an option on it worth today?
State prices and no-arbitrage
When do strictly positive state prices exist?
Backward induction on a binomial tree
If a stock moves up or down in each of several periods, what is an option on it worth today?
Discounted prices are martingales under Q
Which probability turns the price of an option into an average of its payoff?
Self-financing strategies
A strategy buys and sells shares as prices move. When does it need no money beyond what it cost at the start?
Planned
In learning order. These are not pages yet.
- What determines prices in an incomplete market?Graduate
- How a stochastic discount factor prices riskGraduate
- Utility indifference pricing: a price between the no-arbitrage boundsGraduate
- How Girsanov's theorem changes driftGraduate
- Why changing the numeraire changes the pricing measureGraduate
How it connects
Builds on Optimization Probability Linear algebra Stochastic calculus and SDEs Equities and portfolios Derivatives Stochastic processes Bonds and interest rates Proof, logic and sets connection
Leads to Derivatives Hedging and calibration Interest-rate models Monte Carlo and numerical pricing Equities and portfolios Bonds and interest rates PDE methods
Subjects marked “connection” are linked by a related idea, not by a prerequisite.