The Study Of Option Pricing With The Correction Of Underlying Assets Liquidation

Black and Scholes proposed the classic option pricing model in1973. It is the most widely used European style option pricing model by researchers and investors. An important assumption of this model is perfect liquidity of the underlying stock market, that is to say, trading of any number of shares cause no pricing changes. However, research shows that position size and trading behavior of investors will affect the transaction price, even with good market liquidity, large-scale orders in a short period of time will cause reverse price changing. Models based on perfect underlying market liquidity derive systematic biased prices. In this paper, we find that liquidity affects option intrinsic value by changing option replication costs. According to the principle of no arbitrage equilibrium, this paper added liquidity premium produced by option replication to the underlying stock Geometric Brownian Motion equation and deduce the liquidity modified B-S differential equation. With the help of previous studies this paper proved the existence of a unique analytic solution to the modified equation. Analyzing the solution, this paper found that illiquidity changes the option value by affecting stock return volatilities and the modified price still meets the parity formula. This paper used the finite difference method to get a numerical solution of the modified model, because it is impossible to get the analytic one, and the method and its improved algorithm is stable. Empirical studies of Hong Kong index option markets shown that the modified pricing model is more accurate than B-S model; the modified model is more suitable for investors with long positions than for investors with short positions; from the contract perspective, the modified model is more suitable for out-of-the-money call option than in-the-money put option.