[ABE-L] Seminário de Probabilidade - IM-UFRJ - 16 de março - Vinicius Albani (IM-UFRJ)

[Maria Eulalia Vares]

Dear colleagues,



Our first seminar of 2026 will be held on Monday, March 16, from *3:30 p.m.
to 4:30 p.m*. (Rio de Janeiro local time).  The meeting will take place at
room *C116- Bloco C - CT** – Instituto de Matemática – UFRJ. *There will be
no transmission online.

Speaker:  Vinicius Viana Luiz Albani (IM-UFRJ)

Title: *Joint Calibration of S&P 500 and Volatility Index Smiles by a
Stochastic Volatility Framework*


Abstract:

In recent years, the quantitative finance community has faced the challenge
of developing models capable of jointly calibrating the observed call and
put option prices on the S&P 500 and the VIX volatility index. Many
existing approaches rely on non-Markovian dynamics, which often implies
substantial theoretical complexity in the pricing framework and may lead to
computationally demanding numerical implementations. In contrast, we
propose a Markovian framework based on a stochastic volatility model with
functional parameters. Within this setting, we derive a partial
differential equation governing the VIX dynamics. Moreover, the associated
forward Kolmogorov equation and its adjoint partial differential equation
are employed to compute option prices on both the S&P 500 and the VIX.

This structure significantly simplifies the pricing and calibration
procedures while preserving modeling flexibility. Nonetheless, important
theoretical questions remain open, particularly concerning well-posedness
and analytical properties of the proposed system. These issues will be
discussed in the talk. The problem is based on tools from stochastic
analysis, partial differential equations, and functional analysis.
Numerical experiments based on real market data will be presented to
demonstrate the practical viability of the methodology.



More complete information about the seminars can be found at

https://ppge.im.ufrj.br/seminarios-de-probabilidade/

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares
-- 
Maria Eulalia Vares
Professora Titular - Instituto de Matemática - UFRJ
Coordenadora do Programa de Pós-Graduação em Estatística
https://ppge.im.ufrj.br/
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