Option Pricing Model With Illiquidity And Empirical Study

Whether the no arbitrage theory is effective is related to liquidity of the market, because the presence of illiquidity increases arbitrage cost, and reduces arbitrage opportunities. In 1973, Black and Scholes built the option pricing model for vanilla European options. One of their assumptions was that the markets of underlying assets possessed sufficient liquidity, and so did the markets of options. Sufficient liquidity refers to a situation in which a trader can buy or sell any amount of assets at market price, having no effect on the price in a very short period of time. However, either in the markets of underlying assets, or the markets of options, transactions have an impact on the market price. So liquidity is not sufficient in both markets. In such a case, there is deviation between the true value and the BS option price.Based on the Black Scholes model, this paper added liquidity indicators of the underlying assets and options, building a risk free portfolio according to the no arbitrage theory, deriving the partial differential equation satisfied by the vanilla European options with illiquidity, and proved that this partial differential equation had a unique solution. In the aspect of empirical study, the price and delta calculated by the model of this paper were tested. In order to detect the accuracy of price calculated by the model, finite difference method was used. Based on the data from Hang Seng Index option markets and S&P 500 index option markets, MAE and RMSE were used to compare the pricing error of the two models. In order to detect the accuracy of delta calculated by the model, this paper compared the yield of option replication strategy with each delta calculated by each model. The more accurate the delta is, the lower overall cost of replication is, and the higher yield of the strategy is.Theoretically, option pricing model presented in this paper, considers the illiquidity of both underlying assets and option, further promoting the study of option pricing model. Practically, the model brings a more accurate price and higher yields for investors.