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Risk Neutral Measure Determination from Price Ranges: Single Period Market Models.

Henryk Gzyl1, German Molina2, Enrique Ter Horst3

  • 1Centro de Finanzas, IESA, Caracas 1011, Venezuela.

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Summary
This summary is machine-generated.

This study introduces a novel maximum entropy method to determine risk-neutral measures from bid-ask price ranges for financial assets. This approach offers a computationally efficient solution for pricing derivatives when exact asset prices are unknown.

Keywords:
bid-ask pricesmaximum entropy with errors in the datarisk neutral measures

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Area of Science:

  • Quantitative Finance
  • Financial Mathematics
  • Computational Finance

Background:

  • Risk-neutral measures are crucial for asset valuation in complete market models, assuming exact current asset prices.
  • Bid-ask ranges, rather than exact prices, are often available for underlying assets or their derivatives.
  • Determining risk-neutral measures from incomplete price information is essential for accurate derivative pricing.

Purpose of the Study:

  • To develop a method for estimating risk-neutral measures when only bid-ask ranges are known.
  • To provide a computationally efficient and fast approach for this estimation.
  • To enable accurate pricing of other derivatives based on this information.

Main Methods:

  • An extended maximum entropy method is proposed.
  • The method utilizes bid-ask ranges of underlying assets to infer risk-neutral measures.
  • The approach is designed for computational simplicity and speed.

Main Results:

  • The proposed method successfully determines risk-neutral measures from bid-ask ranges.
  • The approach is computationally simple and fast.
  • This provides a practical solution for derivative pricing with incomplete market data.

Conclusions:

  • The extended maximum entropy method offers a novel and efficient solution for determining risk-neutral measures from bid-ask ranges.
  • This method facilitates more accurate derivative pricing in scenarios with incomplete price information.
  • The approach has practical implications for financial modeling and risk management.