Research On Implicit Volatility Curve Of European Stock Option Based On Local Volatility Variability Hypothesis

AFluctuation rates are often studied extensively as an anomaly in the price of options in financial markets.The so-called volatility smile,describes the implied volatility and the relationship between the implementation price.The B-S model is widely used in option pricing,and the implied volatility is the volatility of the actual option price and other variables into the B-S model.It reflects the investor's expectation of future price volatility of the underlying asset,so the implied volatility of the same underlying asset should be the same.But in fact,the same target residual period of the same but the implementation of different prices of options,through the B-S model reverse the implied volatility is different,the formation of the so-called"volatility smile."Early scholars tried to explain the phenomenon of volatility smile from the volatility itself.The idea is that under the premise that the price of the underlying asset of the option obeys the lognormal distribution,the volatility in the motion path(geometric Brownian motion)is not fixed.However,it is a function of time and asset price.However,the academic community has not explored the relationship between the local fluctuation variability and the implied volatility curve of options.The article will explore the impact of two different local volatility fluctuations on the shape of the implied volatility curve of European stock options by assuming that the local volatility changes only with time and the asset price changes with the target only.The conclusion shows that the implied volatility of the European option is a straight line when the local volatility changes only with time,and the implied volatility curve has the same shape as the volatility function when the local volatility changes only with the underlying asset price.feature.