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AIMS Mathematics

2021, Volume 6, Issue 7: 7199-7214. doi: 10.3934/math.2021422
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Research article

Valuation of bid and ask prices for European options under mixed fractional Brownian motion

  • 1.
    School of Business, Nanjing Normal University, Nanjing 210023, China
  • 2.
    School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received: 09 January 2021 Accepted: 26 April 2021 Published: 28 April 2021

  • MSC : 91G20, 91-10, 62P05

  • In this paper, we study the valuation of the bid and ask prices for European options under the mixed fractional Brownian motion with Hurst index $ H > 3/4 $, which is able to capture the long range dependence of the underlying asset returns in real markets. As we know, the classical option pricing theories are usually built on the law of one price, while ignoring the impact of market liquidity on bid-ask spreads. The theory of conic finance replaces the law of one price by the law of two prices, allowing for market participants sell to the market at the bid price and buy from the market at the higher ask price. Within the framework of conic finance, we then derive the explicit formulas for the bid and ask prices of European call and put options by using WANG-transform as a distortion function. Moreover, numerical experiment is performed to illustrate the effects of the Hurst index and market liquidity level on bid and ask prices.

    Citation: Zhe Li, Xiao-Tian Wang. Valuation of bid and ask prices for European options under mixed fractional Brownian motion[J]. AIMS Mathematics, 2021, 6(7): 7199-7214. doi: 10.3934/math.2021422

    Related Papers:

  • In this paper, we study the valuation of the bid and ask prices for European options under the mixed fractional Brownian motion with Hurst index $ H > 3/4 $, which is able to capture the long range dependence of the underlying asset returns in real markets. As we know, the classical option pricing theories are usually built on the law of one price, while ignoring the impact of market liquidity on bid-ask spreads. The theory of conic finance replaces the law of one price by the law of two prices, allowing for market participants sell to the market at the bid price and buy from the market at the higher ask price. Within the framework of conic finance, we then derive the explicit formulas for the bid and ask prices of European call and put options by using WANG-transform as a distortion function. Moreover, numerical experiment is performed to illustrate the effects of the Hurst index and market liquidity level on bid and ask prices.


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