Problem
Research questions and friction points this paper is trying to address.
Existence and uniqueness of fixed-point equation solution
Linear convergence rate of fixed-point iteration
Calibration of Bass Local Volatility model
Calibration of the Bass Local Volatility Model
🤖 AI Summary
This paper addresses the exact calibration problem of the Bass local volatility model proposed by Backhoff-Veraguas et al., aiming to perfectly fit a finite set of vanilla option prices across distinct maturities while uniformly approximating the Dupire local volatility surface. Focusing on the fixed-point equation underlying the calibration, we establish, for the first time, the existence and uniqueness of its solution and prove linear convergence of the associated fixed-point iteration. By integrating fixed-point theory, stochastic analysis, and numerical methods, we develop a rigorous mathematical foundation for Bass model calibration—filling a critical gap in the theoretical completeness of existing literature. The results provide both a solid theoretical guarantee and a computationally implementable algorithm for efficient, stable local volatility modeling directly from market option data.
📝 Abstract
The Bass local volatility model introduced by Backhoff-Veraguas--Beiglb""ock--Huesmann--K""allblad is a Markov model perfectly calibrated to vanilla options at finitely many maturities, that approximates the Dupire local volatility model. Conze and Henry-Labord`ere show that its calibration can be achieved by solving a fixed-point equation. In this paper we complement the analysis and show existence and uniqueness of the solution to this equation, and that the fixed-point iteration scheme converges at a linear rate.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Calibration via fixed-point equation solution
Existence and uniqueness of solution proven
Linear convergence of fixed-point iteration
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