Short-Rate-Dependent Volatility Models

TL;DR

This paper introduces a class of short-rate-dependent volatility models for pricing European options, providing explicit formulas via characteristic functions and demonstrating numerical methods for implied volatility calculation.

Contribution

It develops explicit pricing formulas for European options in models where volatility depends on the short rate, with analytical characteristic functions for certain models.

Findings

Explicit pricing formulas derived for specific models

Analytical characteristic functions enable direct option valuation

Numerical methods for implied volatility are demonstrated

Abstract

We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic function. We provide examples of models in which the characteristic function can be computed analytically and, thus, the value of European options is explicit. Numerical implementation to produce the implied volatility is also presented.