Derivatives Pricing in Non-Arbitrage Market

Derivatives Pricing in Non-Arbitrage Market

Nicholas Simon Gonchar

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N.S. Gonchar

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National Academy of Sciences of Ukraine

Derivatives Pricing in Non-Arbitrage Market

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Abstract

The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent martingale measures to the original measure is a non-empty set. The set of martingale measures is constructed from a set of strictly nonnegative random variables, satisfying certain conditions. The inequalities are obtained for the non-negative random variables satisfying certain conditions. Using these inequalities, a new simple proof of optional decomposition theorem for the nonnegative super-martingale is proposed. The family of spot measures is introduced and the representation is found for them. The conditions are found under which each martingale measure is an integral over the set of spot measures. On the basis of nonlinear processes such as ARCH and GARCH, the parametric family of random processes is introduced for which the interval of non-arbitrage prices are found. The formula is obtained for the fair price of the contract with option of European type for the considered parametric processes. The parameters of the introduced random processes are estimated and the estimate is found at which the fair price of contract with option is the least.

References

27 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

Nicholas Simon Gonchar. 2021. \u201cDerivatives Pricing in Non-Arbitrage Market\u201d. Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 20 (GJSFR Volume 20 Issue A14).

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GJSFR Volume 20 Issue A14

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-A Classification FOR Code: 240201

Submission ReceivedSeptember 15, 2020
Peer Review Double Blind
Handling Editor
Accepted October 10, 2020
Published October 25, 2020

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v1.2

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February 4, 2021

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