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. Introduction
1.1 Motivation
1.2 Purpose
2. Literature Review
2.1 Liquidity
2.2 Volatility and Trading Volume
2.3 Stochastic Volatility Model
2.4 Option Pricing with Liquidity Risk of Underlying Assets
3. Methodology
3.1 Liquidity of Underlying Asset
3.2 Option Pricing with Liquidity of Underlying Assets
3.3 Liquidity on Stock Price and Stochastic Volatility
3.4 Finite Difference Method
3.4.1 Structure
3.4.2 The Boundary Condition
4. Numerical Result
4.1 The First Model
4.2 The Second Model
5. Conclusion

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