Finance & economics 10 topics
Finance & economics
Quant finance
10 topics 10 math concepts connects to 6 fields
Quantitative finance uses mathematical models to price derivatives, manage risk, and construct portfolios. Built on stochastic calculus, partial differential equations, and probability theory, it connects deeply to physics, statistics, and optimisation.
Topics in this field
Black–Scholes Model
The foundational option pricing model. Derives a fair price from stochastic calculus and no-arbitrage.
stochastic calculus optimization gaussian distribution
Bond Pricing & Duration
Valuing fixed-income securities and measuring their interest rate sensitivity. Duration and convexity are the core risk metrics.
differential equations probability theory optimization
Copulas
Functions that model the dependence structure between random variables independently of their marginal distributions.
probability theory gaussian distribution linear algebra
Geometric Brownian Motion
The stochastic process driving the Black-Scholes model. Ensures prices stay positive and returns are log-normally distributed.
stochastic calculus gaussian distribution differential equations
Interest Rate Models
Stochastic models for the yield curve. Used to price bonds, swaps, caps, and swaptions.
stochastic calculus differential equations gaussian distribution
Monte Carlo Methods in Finance
Simulating asset paths to price exotic derivatives and compute risk measures. The workhorse of quantitative trading desks.
monte carlo methods stochastic calculus probability theory
Portfolio Optimization
Finding the allocation of capital across assets that maximises return for a given risk level. Markowitz's mean-variance framework is the foundation.
linear algebra convex optimization probability theory
Risk-Neutral Pricing
The no-arbitrage framework for pricing derivatives. Any derivative price equals the discounted expectation under the risk-neutral measure.
stochastic calculus measure theory probability theory
Stochastic Volatility
Models where volatility itself is random. The Heston model gives closed-form option prices and captures the implied volatility smile.
stochastic calculus differential equations fourier transform
Value at Risk
The loss level not exceeded with a given probability over a given horizon. The industry-standard risk measure for regulatory capital.
probability theory gaussian distribution monte carlo methods