Search research articles

Search research articles

Related Experiment Videos

Option pricing formulas based on a non-Gaussian stock price model.

¹Iris Financial Engineering and Systems, 456 Montgomery Street, Suite 800, San Francisco, California 94104, USA.

Physical Review Letters

|August 23, 2002

Summary

This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026

Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026

Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026

Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026

Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026

Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026

See all related articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

This study explains non-Gaussian stock option fluctuations using nonextensive thermodynamics. A new model simplifies option pricing by using a single volatility value, improving upon the standard Black-Scholes equation.

Area of Science:

Quantitative Finance
Statistical Mechanics
Financial Modeling

Background:

Standard option pricing models like Black-Scholes assume Gaussian distributions for stock returns.
Empirical data shows stock returns often exhibit non-Gaussian, fat-tailed behavior, leading to phenomena like the volatility smile.
The volatility smile necessitates multiple volatility inputs in the Black-Scholes model, complicating pricing.

Purpose of the Study:

To explain non-Gaussian fluctuations in financial options using nonextensive thermodynamics.
To develop a generalized Black-Scholes equation that accounts for these fluctuations.
To demonstrate a simplified approach to option pricing using a single volatility parameter.

Main Methods:

Application of nonextensive thermodynamics, specifically the parameter q, to model stock return distributions.

Related Experiment Videos

Derivation of a generalized Black-Scholes partial differential equation.

Obtaining closed-form solutions for option pricing under the generalized model.

Main Results:

A generalized Black-Scholes equation is derived, incorporating the nonextensive parameter q.
Using q=1.5, which accurately models empirical return distributions, a single volatility value effectively describes option prices.
This approach successfully models option prices without requiring multiple volatility inputs, addressing the volatility smile.

Conclusions:

Nonextensive thermodynamics provides a robust framework for understanding non-Gaussian option price dynamics.
The generalized Black-Scholes model offers a more accurate and simplified method for option pricing compared to the standard model.
A single, empirically derived volatility parameter can effectively capture option pricing behavior, resolving the volatility smile issue.