Behind every options trade is a pricing model, a mathematical framework that turns the stock price, Strike Price, time and volatility into a theoretical value.
Black-Scholes model (1973)
The foundation of modern pricing theory. It gives a closed-form solution for European options from 5 inputs: current price, Strike Price, time to expiration, IV, and the risk-free interest rate.
Limits of Black-Scholes assume constant volatility (IV actually changes), continuous movement with no jumps, and European options only. A starting point, not the final answer.Binomial model
It pictures the stock moving in discrete steps, up or down. Its strength: it handles American options (which can be exercised early).
Monte Carlo simulation
It generates thousands of possible price paths. For each path it computes the option's value. Fair value = the discounted average of all outcomes. It excels at complex multi-asset strategies.
Heston model (1993)
It fixes the core problem in Black-Scholes: constant volatility. In Heston, volatility itself is a random variable. It produces a more realistic Volatility Smile.
GARCH models
It analyzes historical data to forecast future volatility. Volatility Clustering: high volatility tends to be followed by high volatility.
| Model | Best for | Main limitation |
|---|---|---|
| Black-Scholes | Fast pricing, European | Constant volatility |
| Binomial | American options | Slow with dense grids |
| Monte Carlo | Complex strategies | Uses heavy computing resources |
| Heston | Modeling volatility Skew (Volatility Smile) | Complex to calibrate |
| GARCH | Forecasting historical volatility | Falters in new regimes |
* This is a hypothetical illustration and does not reflect actual results. Results vary with market conditions and execution timing.
How Finviro uses these models Finviro uses the Black-Scholes model to compute the gamma of every open contract from its implied volatility and time to expiry, then adds them up into Gamma Exposure, the Gamma Flip (Gamma Flip) and the Call Wall and Put Wall. No AI and no machine learning: the method is published and can be checked.