Explicit Caplet Implied Volatilities for Quadratic Term-Structure Models

TL;DR

This paper derives an explicit asymptotic approximation for caplet implied volatilities within quadratic term-structure models, offering both theoretical accuracy guarantees and numerical validation.

Contribution

It introduces a novel explicit asymptotic approximation for caplet implied volatilities in quadratic term-structure models, with accuracy analysis and numerical experiments.

Findings

The approximation achieves high accuracy in numerical tests.

The method provides explicit formulas for implied volatilities.

The approach extends existing models with a new asymptotic technique.

Abstract

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we perform experiments in order to gauge the numerical accuracy of our approximation.