The purpose in the thesis mainly discuss option pricing model with liquidity, which can be shown in the stock price and the stock's volatility. From the liquidity which affect the underlying's volatility, we firstly define the underlying's liquidity by change of underlying's volatility and derive the PDE through add liquidity into stochastic volatility process. From the liquidity which affect the underlying's price, the model has been proposed before. Thus, we combine two model to get a generalized PDE. The three aspects can explain this PDE, including loop between liquidity part and stock price, power between liquidity part and the liquidity fact, and the term which is affected by liquidity. Finally, we use the explicit finite difference to do numerical result.

1. Amihud Y. and H.Mendelson (1989), The effects of beta, bid-ask spread, residual risk, and size on stock returns, Journal of Finance, 44(2), page 469-486.
2. Black F. and M. Scholes (1973), The pricing of options and corporate liabilities, Journal of Political Economy, 81, page 637-654.
3. Cetin U. and R. Jarrow and P. Protter (2004), Liquidity risk and arbitrage pricing theory, Finance Stochastics, 8(3), page 311-341.
4. Cetin U. and R. Jarrow and P. Protter (2006), Pricing options in an extended black scholes economy with illiquidity: Theory and empirical evidence, Review of Financial Studies, 19(2), page 493-529.
5. Etiling C. and T. Miller (2000), The relationship between index option moneyness and relative liquidity, Journal of Futures Markets, 20(November), page 971-987.
6. Heston S.L. (1993), A closed-form solution for options with stochstic volatility with applications to bond and currency options, Review of Financial Studies, 6(2), page 327-343.
7. Hout In't K.J. and S. Foulon (2010), Adi finite difference schemes for option pricing in the heston model with correlation, International Journal of Numerical Analysis and Modeling, 7(2), page 303-320.
8. Hsai H.T. (2003), Liquidity and the pricing of options : evidence from taiwan index options, Tamkang University, Mater thesis.
9. Krakovsky A. (1999), Pricing liquidity into derivatives, Risk,December, pages 365-367.
10. Liu Ti (2006), How to evaluate liquidity : evidence and review, Shanghai Stock Exchange.
11. O'hara M. (1995), Market Microstructure Theory, Wiley.
12. Schwert G. W. (1989), Why does stock market volatility change over time?, Journal of Finance, 44(5), pages 1115-1153.
13. Shen Yih Wen (2004), Liquidity risk in option pricing-evidence from taiwan stock index options, Master thesis, Chang Gung University.
14. Syrkin M. (2011), Pricing derives with liquidity limitations, working paper.
15. Vassilis G (2008), Stochastic volatility and the volatility smile, Department of Mathematics, Uppsala University.
16. Wang Han Fen (2004), Dynamic volume-volatility relation, School of business and economics, University of Hong Kong, working paper.
17. Wilmott P. (1998), Derivatives : The Theory and Practice of Financial Engineering, Wiley.