重构局部波动率曲面

Calibration of the Local Volatility Surface

标的资产的局部波动率问题,无论在理论上还是实际应用中都有着重要的意义.对于欧式期权,本文采用待定系数法分析了期权定价的模型,证明了看涨期权和看跌期权的价格函数的有界性条件,推导出了局部波动率函数的半显式的解析解的表达式,有效地解决了在期权市场价格已知前提下的局部波动率校准反问题.数值实例选用了参数为常数的情形与波动率随着时间和执行价格的变化情况,数值结果说明了方法的有效性.

It is of great importance to calibrate the local volatility of underlying asserts for both theoretical and practical applications. For European options, we discuss the option price modeling by the method of undetermined coefficients in this paper. A boundary condition is proved for pricing functions of call options and put options, and the semi-analytic solution of the local volatility function is presented, which effectively solves the inverse problem of calibrating the implied volatility on the premise of the market prices. Numerical results verify the effectiveness of the proposed method.