复合期权与路径相关期权定价理论模型、数值模拟及应用研究.pdf

ABSTRACT
The valuation of multi-pound 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-pound option can be derived.
Furthermore, there often exists high-dimension nested integral in the closed-form solution,
which always costs puting resource and limits the development in the theoretical
model and application of multi-pound 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 plex
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-pound real option model
and gives its application on venture capital investment valuation; pound
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 panies 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-pound real option model can give
more reasonable valuation of venture capital investment and the optima