Pricing, hedging, and risk management for financial derivatives.
The fundamental relationship between calls, puts, and the underlying
Discrete-time option pricing via replication and risk-neutral probabilities
The foundational option pricing formula
Spreads, covered calls, collars, and arbitrage with options
Delta, gamma, theta, vega — sensitivity measures
Inverting BSM to extract market expectations
Simulation-based derivative pricing
Barrier, Asian, digital, and lookback options — payoffs, pricing, and Greek behaviour
Smile, skew, term structure, SVI parameterization, and sticky strike vs sticky delta
P&L decomposition via Greeks, realized vs implied vol trading, and optimal hedging frequency
Early exercise boundary, binomial pricing, dividends, and Longstaff-Schwartz