对期权评估模型中隐含波动率的计算分析

Calculation and Analysis of Implied Volatility in Option Valuation Models

以上证50ETF合约为例,通过布莱克-舒尔斯模型和牛顿法计算出该合约对应期权的隐含波动率,在此基础上,通过最小二乘法拟合无风险利率,进一步提高了计算精度。由于隐含波动率提供了市场交易者对未来市场风险的预期和估计,是市场参与者用于判断风险和定价期权的重要指标,然而上证50ETF波动率指数由于种种原因在2018年停止发布,故本方法在达到实践可用水平的前提下,为其他同类期权隐含波动率的计算提供了可供参考的建议,使期权交易者可以通过隐含波动率来估计市场对价格波动的未来预期,可以根据预期来判断期权价格是否高估或低估,并以此作为交易策略的重要依据。

Taking the Shanghai 50 ETF contract as an example,we calculate the implied volatility of the corresponding option using the Black-Scholes model and Newton's method.Based on this,we use the least squares method to fit the risk-free interest rate and further improve the calculation accuracy.Implied volatility provides an important indicator for market participants to judge risk and price options,as it reflects the market traders' expectations and estimates of future market risk.However,the Shanghai 50 ETF volatility index stopped being published in 2018for various reasons.Therefore,this method,while reaching practical usability,provides a reference for calculating the implied volatility of other similar options,allowing option traders to estimate the market's future expectations of price fluctuations through implied volatility.This,in turn,helps them to determine whether option prices are overvalued or undervalued,and use this as an important basis for trading strategies.