Technology Category
Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Mixed Discrete/Continuous SearchMachine Learning: Learning with Manifolds
Short-Rate-Dependent Volatility Models
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
short-rate-dependent volatility
European option pricing
interest rate models
volatility modeling
Innovation
Methods, ideas, or system contributions that make the work stand out.
short-rate-dependent volatility
explicit pricing formula
characteristic function
European option pricing
implied volatility
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