HJM Local Volatility Model

TL;DR

This paper presents a local volatility modeling approach within the HJM framework that enables fast, accurate, and arbitrage-free calibration to European options, specifically applied to interest rate derivatives.

Contribution

It introduces a novel local volatility model using the Small Volatility Approximation in HJM, improving calibration speed and accuracy for interest rate options.

Findings

Faster and more accurate than parameterized models

Deterministic and rapid sensitivity calculations

Effective calibration for interest rate swaptions and caplets

Abstract

Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is significantly faster and more accurate than any parameterized model. The implementation is demonstrated specifically for interest rate swaptions and caplets. A key component of this method is the Small Volatility Approximation within the HJM interest rate model, which is used to calculate sensitivity of forward bond volatility. These calculations are deterministic and fast, with excellent calibration accuracy. A detailed description of the calibration procedure is provided.