Financial Mathematics
Explore time and risk models; arbitrage and discrete pricing; continuous models and limits. Concepts and connections are available independently of video coverage.
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Geometric Brownian motion
A multiplicative stochastic differential model keeps positive initial asset prices positive.
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Black–Scholes model
Option pricing follows a diffusion market with restrictive volatility, trading and friction assumptions.
Brownian motion
Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
Model risk
Incorrect assumptions, calibration or use can invalidate model-based conclusions.
No-arbitrage
A market model excludes zero-cost trades with nonnegative and sometimes positive payoff.
Binomial pricing models
Up-and-down price moves support backward valuation under no-arbitrage assumptions.
Knowledge connections
- Black–Scholes model · Related · Map context
- Model risk · Related · Map context
- No-arbitrage · Related · Map context
- Brownian motion · Related · Map context
- Brownian motion · Prerequisite · Map context