Research On Option Pricing Under Incomplete Information

As one of the focuses of academic research, Real Option Theory plays an important partin the field of venture investment. However, the information that investors can obtain is oftenincomplete for the following reasons, such as the deviation, missing and fluctuation of thedata, people’s limited cognitive ability and the information publisher’s deliberate concealing.It poses a serious challenge for the evaluation method of the traditional risks projects basedon the completely supposed information. Therefore, it is of great importance and value toresearch the real option pricing under incomplete information.This thesis studies the real option pricing under incomplete information. The researchwork mainly concentrates on the following two aspects.Based on the condition of cash flow generated in investment progress, this thesis studiesthe pricing theory, in which the research of asset value is in accordance with the stochasticvolatility model. The incomplete information is measured by the observable cash flow duringthe investment process, and then is described as a mean reverting stochastic process. Theconditional expectation and variance are obtained by adding the information model to theunobservable asset value model through filtering theory. In this way, the constantly-updatedinformation is reflected in the risk evaluation process, which makes the evaluation resultsmore reliable. The partial diferential equation that the option price satisfies is obtainedby using Bellman equation and Ito’s formula. Analyze the initial and boundary condition(usually based on the practical background) and then solve the PDE by using numericalmethod. Scientific and rational investment decisions are proposed according to the numericalresults.Based on the condition without cash flow arising in the comparatively longer investmentprocess, the thesis studies the pricing theory and the approach to real option with theJump-Cox-Ingersoll-Ross model. Due to the fact that the normal information and abnormalinformation co-exist simultaneously in the actual investment process, this thesis describesthe stochastic variations of asset value with the addition of discrete Poisson jump processbased on the CIR model. Then the option pricing equation is obtained by using Bellmanequation and Ito’s formula. To solve the equation, we discretize the continuous state space ofthe mixed model. The Markov-chain obtained by the discretization of the continuous state space of the mixed model can be used to analyze the state transition of the asset value.Incomparison to the Jump CIR model, we can expound the potential advantages of the CIRmodel by analyzing the optimal investment threshold and option price.Finally, we convincingly demonstrate the validity and superiority of the model by ana-lyzing the investment case of one real estate company.