Quantitative Finance

Quantitative Finance

Quantitative finance Black-Scholes model formula for option price (revolutionary in 1973) Binomial model probability tree for option price (simpler than Black-Scholes) Monte Carlo simulation random simulations for risk assessment Brownian motion random movement (model of price changes) Geometric Brownian motion random movement in logarithmic scale (stock price model) Stochastic calculus calculus with randomness (mathematics of finance) Ito's lemma fundamental formula of stochastic calculus (used everywhere) Greeks (Delta, Gamma, Vega, Theta, Rho) option sensitivities (Delta = to price, Gamma = to change in Delta, etc.) Risk-neutral valuation valuation as if risk does not matter (technical trick) Martingale pricing fair price under martingale (no arbitrage) No-arbitrage principle no free money (prices must be consistent) Replicating portfolio portfolio that mimics an option (in Black-Scholes formula) Dynamic hedging continuous rebalancing of protection (managing Delta) Local volatility volatility depending on price level (more complex than constant volatility) Stochastic volatility volatility that changes by itself (volatility of volatility) GARCH models volatility models (its clustering: volatile days grouped) Mean reversion price returns to average (statistics) Copulas link between two variables (not just correlation) Factor models factor models (price depends on factors: P/E, momentum, etc.) Machine learning in finance machine learning (price prediction, fraud detection)