Workflow:Avhz RustQuant Model Calibration
| Knowledge Sources | |
|---|---|
| Domains | Quantitative_Finance, Calibration, Automatic_Differentiation, Optimization |
| Last Updated | 2026-02-07 19:00 GMT |
Overview
End-to-end process for calibrating pricing model parameters to observed market data using automatic differentiation and gradient descent optimization.
Description
This workflow demonstrates how to fit a pricing model (e.g., Black-Scholes) to real market option prices by optimizing model parameters to minimize the discrepancy between theoretical and observed prices. RustQuant's reverse-mode automatic differentiation (autodiff) engine computes exact gradients of the loss function, which are then used by gradient descent to iteratively adjust parameters. The calibration approach is general: any differentiable pricing formula can be calibrated against market data by defining an appropriate loss function.
Usage
Execute this workflow when you have observed market prices (e.g., option chains from an exchange) and need to determine the implied model parameters that best fit those prices. Common use cases include calibrating implied volatility across a surface of strikes and maturities, fitting stochastic volatility model parameters, or estimating any pricing model parameter from market data.
Execution Steps
Step 1: Prepare Market Data
Assemble the observed market data: option prices, their corresponding strikes, days to expiry, and any other contract-specific attributes. Also define the known market parameters (spot price, risk-free rate, dividend yield) that will remain fixed during calibration.
Key considerations:
- Data should cover the relevant strike and maturity range
- Fixed parameters (spot, rate, dividend) must be set to their current market values
- Multiple expiry dates can be calibrated independently or jointly
Step 2: Define the Loss Function
Construct a loss function that measures the difference between model-predicted prices and observed market prices. The standard choice is mean squared error (MSE) over all option contracts. The loss function must accept Variable types from the autodiff graph so that gradients can be computed automatically.
What happens:
- For each strike-price pair, the model pricing formula is evaluated using Variable inputs
- The squared difference between model and market price is computed
- All squared errors are summed and divided by the number of observations
- The result is a differentiable scalar loss value
Step 3: Initialize the Optimizer
Configure the gradient descent optimizer with a learning rate, maximum iteration count, and optional convergence tolerance. The optimizer will repeatedly evaluate the loss function and its gradient, then update the parameter estimates.
Optimizer parameters:
- Learning rate - Step size for parameter updates (e.g., 0.001)
- Max iterations - Upper bound on optimization steps (e.g., 1000)
- Tolerance - Optional convergence threshold for early stopping
Step 4: Run Optimization
Execute the optimization loop. At each iteration, the autodiff engine builds a computation graph for the loss function, computes the gradient via reverse-mode accumulation, and the optimizer updates the parameters in the direction of steepest descent.
What happens:
- The loss function is evaluated with current parameter guesses
- Reverse-mode autodiff computes exact gradients (no finite-difference approximation)
- Parameters are updated: param_new = param_old - learning_rate * gradient
- The process repeats until convergence or max iterations
Step 5: Extract Calibrated Parameters
Retrieve the optimized parameter values from the optimizer output. Validate the results by computing the final loss value and inspecting the fit quality across individual strikes and maturities.
Key considerations:
- Check that the final MSE is acceptably small
- Verify that calibrated parameters are within economically reasonable bounds
- Consider running calibration from multiple initial guesses to avoid local minima