摘要
在无套利假设下,自由边界的Black-Scholes方程可以等价地转化为一个含有微分算子的互补问题,利用传统差分方法离散微分算子并且将波动率视为变量,原问题变为非线性互补问题;进而转化为优化问题,并且加入新的历史价格约束,给出可求解美式期权价格并可计算隐含波动率的优化模型。数值实验表明其有效性。
Under the assumption of arbitrage possibilities, Black-Scholes model is revised as a partial differential complementarity problem; then we derive the nonlinear complementarity model by using the finite difference approximation with uncertain volatility. Furthermore, it can be transformed as an optimization model. In consideration of the influence of historical data, we add a new constraint according to historical option prices to improve the optimization model. Numerical results show the usefulness and rationality of the proposed model.
出处
《长治学院学报》
2016年第2期56-60,共5页
Journal of Changzhi University
