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Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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A new logistic-type model for pricing European options.

Jaime A Londoño1, Javier Sandoval2

  • 1Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Manizales, Colombia.

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Summary

We developed a new financial market model using stochastic differential equations. This model accurately captures price evolution and outperforms the Heston Model during high volatility periods.

Keywords:
European optionLogistic modelVolatility smile

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Area of Science:

  • Quantitative Finance
  • Financial Modeling
  • Stochastic Analysis

Background:

  • Financial markets exhibit complex price dynamics.
  • Existing models may not fully capture volatility.
  • Accurate financial modeling is crucial for risk management.

Purpose of the Study:

  • To introduce a novel family of models for financial market price evolution.
  • To analyze the properties of these models, including arbitrage-free and completeness.
  • To empirically validate the proposed models against real-world data.

Main Methods:

  • Utilizing a two-dimensional system of stochastic differential equations (SDEs).
  • Driving the system with a single Wiener process.
  • Calibrating the model using S&P500 option prices (December 2007-2008).
  • Comparing performance against the Heston Model.

Main Results:

  • The proposed model family is proven to be well-defined, arbitrage-free, and complete.
  • Empirical calibration demonstrates model viability.
  • The new model shows superior performance during high volatility compared to the Heston Model.

Conclusions:

  • The proposed SDE-based model offers a robust framework for financial market analysis.
  • It provides a competitive alternative to existing models, especially under volatile conditions.
  • Further research can explore extensions and applications of this model family.