Short-Rate-Dependent Volatility Models

Tim Leung and Matthew Lorig

Papers from arXiv.org

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.

Date: 2026-01
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