Cluster C: Options Pricing Models
From intuitive no-arbitrage arguments through Black-Scholes to numerical methods. How options get their prices and why models matter.
Why Options Have Prices: Intuitive Pricing
Supply/demand, no-arbitrage principle, put-call parity as a constraint, replication arguments
Put-Call Parity and Arbitrage Bounds
Derivation, synthetic positions, conversion/reversal arbitrage, dividend effects on parity
The Binomial Model
One-step and multi-step trees, risk-neutral pricing, convergence to continuous models, American option pricing via backward induction
Black-Scholes-Merton Framework
Assumptions (constant vol, log-normal returns, continuous trading, no dividends), the BSM formula, what it gets right and what it gets wrong
BSM Assumptions vs Reality
Fat tails (real markets violate normality), jumps, stochastic volatility, discrete hedging, transaction costs, dividends
Monte Carlo Simulation
Random path generation, convergence rates, variance reduction techniques (antithetic, control variates), pricing path-dependent payoffs
Finite Difference Methods
PDE formulation, explicit/implicit/Crank-Nicolson schemes, boundary conditions, American exercise via free boundary