变波动率多期复合实物期权定价模型及应用

当前复合期权理论与方法的研究主要集中于两个方面;其一是将简单两期复合期权理论推广至多期情形,其二是建立标的资产具有一般形式随机运动过程的复合期权定价模型及求解方法.本文提出了变波动率多期复合实物期权定价控制方程及相应的边界条件和终端条件,采用隐式差分格式获得了问题的数值解,并结合风险投资的实例展开了讨论.结果表明,与传统复合期权期权定价方法1]相比较,本文给出的方法计算精度高,收敛速度快;常波动率多期复合期权定价模型明显高估了风险投资期初的执行阚值而低估了后期的执行阚值,且低估了风险投资的内在价值.

Time-Dependent Volatilities Multi-Stage Compound Real Option Model and Application

The simple compound option model has many limitations when applied in practice.The research on compound option theory mainly focus on two dimensions.One is the extension from two-stage to multi-stage,and the other is the modification of the stochastic difference equations which describe the movement of underlying asset.This paper extends the simple compound option model in both two dimensions and proposes the Time-dependent Volatilities Multi-stage Compound Real Option Model(TVMCOM).Due to the introduction of time-dependent volatilities,it is difficult to derive the closed-form solution by the traditional analytical approach.This paper presents the pricing governing partial differential equation,proposes the boundary conditions and termial conditions,and gets the numerical solution by Finite Differential Methods.Finally this paper applies TVMCOM to price venture capital investment.The numerical results show that the Fixed Volatilities Multi-stage Compound Real Option Model(FVMCOM)underestimates the intrinsic value of venture capital investment significantly as well as exercise threshold of late stages,but overestimates the exercise threshold of early stages.