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Paper / 2026SMQ / 242890407814864
PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable Jäckel Operator
Anastasis Kratsios / Blanka Horvath / Hans Buehler / Raeid Saqur / Yannick Limmer
machine learning / numerical methodsResource overview

PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable Jäckel Operator

Paper2026

by Anastasis Kratsios, Blanka Horvath, Hans Buehler, Raeid Saqur, Yannick Limmer

Tags
machine learningnumerical methodsoption pricingvolatility surface

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Suggested foundations for options and derivatives pricing and volatility models and surfaces. Specialist prerequisites vary by paper.

Before you read

  1. The Binomial Model

    Build replication and risk-neutral probabilities in a tractable model.

  2. Market Model and Risk-Neutral Valuation

    Distinguish pricing probabilities from physical forecasts.

  3. Stochastic Processes, Brownian Motion and Itô's Lemma

    Follow diffusion-based models and their assumptions.

  4. ARCH and GARCH

    Separate conditional volatility from observed returns.

Go further

  1. The Black-Scholes PDE, Formula and Implied Volatility

    Connect the pricing equation, closed-form value and implied volatility.

  2. Stochastic Volatility and the Heston Model

    Study a correlated stochastic-variance model.

  3. Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions

    Interpret prices across strikes and expiries.

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Explore Derivatives Pricing and Computational Finance Explore Advanced Derivatives and Exotic Options

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