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

Abstract

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.

Keywords

• conic finance
• option pricing
• mixed fractional brownian motion
• bid-ask spreads
• wang-transform