Module interp 

Functions

bs_delta

Black-Scholes delta calculation with dividend yield Uses the standard normal CDF from statrs for precision x = ln(K/F), so d1 uses -x for standard Black-Scholes formula

build_linear_iv

Main function to build complete linear IV output Orchestrates all the above functions to produce the final result

build_linear_iv_from_market_data

Convenience function to build linear IV output using underlying price from market data Uses the underlying_price from the first market data point as the forward price

compute_all_metrics

Compute risk reversal and butterfly metrics for all symmetric delta pairs

compute_atm_iv

Compute ATM implied volatility via linear interpolation at x=0

compute_fixed_delta_iv

Solve for the log-moneyness that gives the target delta Uses Brent’s method for robust convergence

compute_fixed_delta_iv_with_config

Solve for the log-moneyness that gives the target delta with configurable extrapolation Uses Brent’s method for robust convergence

compute_metrics

Compute risk reversal and butterfly metrics from delta IVs (backward compatibility)

linear_interp

Linear interpolation in variance space Returns None if query_x is outside the range and extrapolation is disabled or fails

linear_interp_with_config

Linear interpolation with configurable extrapolation Returns None if query_x is outside the range and extrapolation is disabled or fails

prepare_points

Compute sorted (log-moneyness, total_variance) points from market data Filters out invalid IVs (market_iv <= 0), handles duplicates by averaging, and sorts by log-moneyness