Short-Rate-Dependent Volatility Models

2026-01-31

AI Summary

This study addresses the pricing of European options when the volatility of the underlying asset is influenced by the short-term interest rate. The authors propose a novel stochastic volatility model that explicitly couples asset volatility with the short-rate dynamics. By deriving the joint characteristic function, they obtain, for the first time within this coupled framework, a closed-form analytical pricing formula for European options. The implied volatility is then efficiently computed via numerical inversion techniques. This approach extends the applicability of conventional stochastic volatility models and demonstrates high pricing accuracy across several tractable submodels admitting analytical characteristic functions. Notably, the method successfully reproduces implied volatility surfaces consistent with market observations.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• short-rate-dependent volatility
• European option pricing
• interest rate models
• volatility modeling

Innovation

• short-rate-dependent volatility
• explicit pricing formula
• characteristic function
• European option pricing
• implied volatility