CAJ | 학술논문

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。
표적자산적국부파동솔문제，무론재이론상환시실제응용중도유착중요적의의。대우구식기권，본문채용대정계수법분석료기권정개적모형，증명료간창기권화간질기권적개격함수적유계성조건，추도출료국부파동솔함수적반현식적해석해적표체식，유효지해결료재기권시장개격이지전제하적국부파동솔교준반문제。수치실례선용료삼수위상수적정형여파동솔수착시간화집행개격적변화정황，수치결과설명료방법적유효성。
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.