Module temporal 

Temporal interpolation for fixed time grid construction

This module provides functionality to interpolate volatility metrics across multiple maturities to construct standardized time grids. It extends the single-maturity linear IV interpolation to handle multi-maturity option chains.

Overview

The temporal interpolation module enables traders and quants to:

• Build consistent volatility surfaces across standardized expiry ladders
• Interpolate between observed maturities using different methodologies
• Extrapolate to shorter/longer tenors when appropriate
• Maintain mathematical consistency with strike-space interpolation

Interpolation Methods

Three temporal interpolation methods are supported:

LinearTte

Direct linear interpolation on time-to-expiration vs metric value pairs. Simple and intuitive, suitable for most applications.

LinearVariance

Interpolates total variance (ω = σ²T) and converts back to implied volatility. Mathematically consistent with no-arbitrage conditions and variance swaps. Recommended for professional trading systems.

SquareRootTime

Scales volatility by √(T_target/T_base). Common approximation for short-term extrapolation when volatility is mean-reverting.

Usage Pattern

1. Collect multi-maturity option chain data
2. Configure TemporalConfig with desired fixed days and interpolation method
3. Call build_fixed_time_metrics() to generate standardized time grid
4. Use resulting metrics for pricing, Greeks, and risk management

Example

use surface_lib::{MarketDataRow, LinearIvConfig, TemporalConfig, build_fixed_time_metrics};

let temporal_config = TemporalConfig {
    fixed_days: vec![1, 7, 14, 30],
    ..Default::default()
};
let strike_config = LinearIvConfig::default();

let metrics = build_fixed_time_metrics(
    &market_data, forward, &temporal_config, &strike_config
)?;

Functions

build_fixed_time_metrics

Build fixed time metrics by interpolating across multiple maturities