Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments December 18, 2015 erstellt
Beschreibung:
An important assumption of the Black and Scholes option pricing model in 1973 is that underlying stock market liquidity has full liquidity. However, if the liquidity is not sufficient, the behavior of the investors, replicating an option by self financing portfolio, will cause the underlying stock price changes and therefore result in the systematic bias between BS option price and real option price. According to the no arbitrage equilibrium principle, this paper added liquidity premium created by option replication to the geometric Brownian motion of underlying assets, then deduced the liquidity-adjusted generalized option pricing differential equation, and we proved that the equation has a unique analytical solution. Since an explicit analytical solution cannot derived from the liquidity-adjusted generalized option pricing differential equation, the finite difference method is used to solve the numerical solution of the model, and we proved that the numerical solution is stable. Through empirical research on Shanghai 50ETF options market, we find that the numerical solution is more close to the real option price than the BS model