Numerical Controls & Customization

Last reviewed: May 17, 2026 by Options Analysis Suite Research.

Numerical Controls & Customization

The Options Analysis Suite provides extensive control over numerical methods, allowing users to fine-tune accuracy, performance, and model behavior. These professional-grade controls enable customization for everything from quick estimates to publication-quality results.

PDE Grid Configuration

Set the base spatial and time resolution for the finite difference solver. The validated refinement preset uses 256 spatial steps, 256 time steps, and Richardson Extrapolation enabled. Internal refinement may use larger grids than the base request.

• Spatial and Time Steps: Increasing resolution can reduce discretization error and increases runtime. Coarse grids are useful for estimates but do not carry the published accuracy certification.
• Richardson Extrapolation: Enabled by default. Combines nested grid resolutions to improve accuracy. Turn it off for faster, lower-accuracy estimates; the published Greek budgets require the validated refinement preset.
• Automatic Settings: Grid layout, spatial order, startup damping, and smoothing are chosen internally for the backend and contract. They are not separate user controls.
• Computation Method: Choose CPU or GPU. GPU availability and runtime depend on the device; an unavailable or failed GPU solve is retried on CPU.

Monte Carlo Configuration

• Path Counts:
  • Quick Estimate: 1,000-10,000 paths (<0.1 seconds)
  • Standard Accuracy: 50,000-100,000 paths (0.2-0.5 seconds)
  • High Precision: 500,000-1,000,000 paths (1-2 seconds)
  • Publication Quality: Up to 10,000,000 paths (5-10 seconds with WebGPU/Web Workers)
  • Impact: Error scales as O(1/√N), so 4x paths = 2x accuracy
• Random Number Generator:
  • Pseudo-Random: Mersenne Twister (fast, standard)
  • Quasi-Random: Sobol sequences (better convergence, recommended for high-dimensional problems)
  • Scrambled Sobol: Randomized low-discrepancy (best convergence for most applications)
• Variance Reduction Toggles:
  • Antithetic Variates: ON by default (2x efficiency for symmetric payoffs)
  • Control Variates: ON for European options (uses Black-Scholes as control)
  • Importance Sampling: OFF by default (enable for deep OTM options)
  • Moment Matching: ON by default (ensures theoretical mean/variance)
• Time Discretization:
  • Steps per Path: 1 (terminal value) to 252 (daily monitoring)
  • Default: 50 steps for barrier/lookback options, 1 step for vanilla Europeans
  • Impact: More steps needed for path-dependent payoffs
• GPU Acceleration:
  • Auto-Detect: Use GPU if available and path count > 10,000
  • Force GPU: Always use WebGPU (errors if unavailable)
  • Force CPU: Use Web Workers only (for debugging or comparison)
  • Hybrid: CPU for setup/Greeks, GPU for path generation

Convergence Tolerances

• Implied Volatility Solver:
  • Absolute Tolerance: 1e-6 (0.0001% vol precision)
  • Relative Tolerance: 1e-8 (price-relative convergence)
  • Max Iterations: 100 (Newton-Raphson) or 50 (bisection)
  • Initial Bounds: [0.001, 5.0] (0.1% to 500% vol)
• Model Calibration:
  • Objective Function Tolerance: 1e-6
  • Parameter Step Tolerance: 1e-8
  • Max Function Evaluations: 1000 (Nelder-Mead), 500 (Levenberg-Marquardt)
  • Multi-Start Runs: 1-10 (to avoid local minima)
• Greeks Finite Difference Step Sizes:
  • Spot (S): h = S × 0.01 (1% bump)
  • Volatility (σ): h = 0.01 (1% absolute vol bump)
  • Time (t): h = 1/365 (1 day)
  • Rate/Dividend (r, q): h = 0.0001 (1bp)
  • Adaptive: Smaller steps near discontinuities or boundaries

Model-Specific Controls

• Binomial Trees:
  • Tree Type: CRR, Jarrow-Rudd, Leisen-Reimer
  • Steps: 10-2000 (user-adjustable)
  • Dividend Handling: Proportional, fixed, escrowed, or manual ex-dates
• Heston Model:
  • Integration Method: Gauss-Legendre quadrature, adaptive Simpson
  • Integration Points: 32-256 (more points = better accuracy for long-dated options)
  • Feller Enforcement: Warn only, or clamp parameters to satisfy 2κθ > ξ²
• SABR Model:
  • Approximation: Hagan (fast), PDE (accurate)
  • β Constraint: Free (0-1), fixed at 0.5 (CEV), or fixed at 1.0 (lognormal)
  • Arbitrage Checks: Enable/disable negative density detection
• FFT Methods:
  • Grid Size: 2^N points (N=8 to N=14, i.e., 256 to 16384 strikes)
  • Damping Factor: α = 0.5-2.0 (controls smoothness vs. accuracy trade-off)
  • Strike Spacing: Automatic or manual (log-spaced strikes)

Performance Tuning

• Caching:
  • Calibration Results: 100-item LRU cache (reuse fitted parameters)
  • Greeks Cache: Store recent calculations for parameter sensitivity analysis
  • Surface Grids: Cache volatility/gamma surfaces for rapid retrieval
  • Clear Cache: Manual flush for fresh recalculations
• Parallelization:
  • Worker Pool Size: Auto (CPU core count), or manual (1-16 workers)
  • Batch Size: Number of strikes/expirations processed per worker
  • GPU Batch Size: Paths per WebGPU dispatch (auto-tuned for hardware)
• Precision vs. Speed Presets:
  • Fast: Minimal steps, coarse grids, 10k MC paths (1-2 seconds)
  • Balanced: Standard settings, 100k MC paths (5-10 seconds)
  • Accurate: Fine grids, 1M MC paths, tight tolerances (30-120 seconds)
  • Custom: User-defined all parameters

This page is part of the Options Analysis Suite documentation hub. Browse the glossary for term definitions.