An analytical approximation approach for pricing European options in a two-price economy

Abstract 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. In this paper, we present a numerical method to calculate the bid and ask prices for the European options. The numerical method is based on the combination of Fourier cosine approximations and numerical integration, which provides an efficient and fast way to compute the bid and ask prices and calibrate the model parameters in real market. Numerical experiments demonstrate the accuracy of our presented numerical method by comparing with Monte Carlo simulation. To better illustrate the practicability of our presented numerical method, we consider the European options written on SSE 50 ETF traded at the Shanghai Stock Exchange.