Options on Bonds: Implied Volatilities from Affine Short-Rate Dynamics

TL;DR

This paper develops an explicit asymptotic approximation for bond option implied volatilities within affine short-rate models, validated through numerical experiments to assess accuracy.

Contribution

It introduces a novel explicit approximation method for bond option implied volatilities in affine short-rate models, enhancing computational efficiency.

Findings

Approximation closely matches numerical results in specific models

Method provides a quick way to estimate implied volatilities

Numerical experiments demonstrate high accuracy of the approximation

Abstract

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical experiments in order to gauge the accuracy of our approximation.