Research On The Theoretical Pricing Model And Numerical Simulation Of Compound Option And Path-dependent Option And Their Applications

The valuation of multi-stage compound option and path-dependent option is the important problem in current financial engineering research. Only in some simple situations the closed-form solution for multi-stage compound option can be derived. Furthermore, there often exists high-dimension nested integral in the closed-form solution, which always costs huge computing resource and limits the development in the theoretical model and application of multi-stage compound option. Compared with the option without path-dependent feature, the multiple state variables in the pricing model of path-dependent option bring the soluting difficulty and make it hard to reflect the impact of complex path-dependent features on option value. This paper extends the theoretical model and application scope of multi-stage compound option and path-dependent option using Finite Difference Method and Finite Element Method. This paper proposes the variable volatilities multi-stage compound real option model and gives its application on venture capital investment valuation; proposes compound option pricing model of convertiable bond; discusses the properties and pricing methods of Parisian option, one kind of path-dependent option, and proposes the half-implicit Finite Difference Method to improve the bad accuracy of the explicit Finite Difference Method, and proves that this method is consistent; presents a pricing model of convertible bond with the soft constraint and notice period constraint call provision, which can reflect the the American and Parisian feature of convertible bond; performs an empirical analysis on convertible bonds of listed companies in China under different scenarios. The result shows that the Finite Difference Method and Finite Element Method have significant advantage on the accuracy, effiency and stability when applied in option valuation; that the variable volatilities multi-stage compound real option model can give more reasonable valuation of venture capital investment and the optimal exercise strategy; that the compound option model can provide a good estimation for the value of convertiable bond; that the call notice period constraint has large impact on the value of convertible bond and the call behavior of issuer; that the game between issuer and investor brings a fixed barrier into the pricing model of convertible bond, which makes the convertible bond's Delta appears non-smooth; that the introduction of soft restraint in the provisions of convertible bond can bring local smoothness to convertible bond's Delta; that there is less relationship between the types of call notice period restraint and the issuer's asset-liability ratio, but there is some relationship between the types and long-term debt/asset ratio.