The development of a risk-neutral density estimation method

The risk-neutral density (RND) function is the distribution implied by option prices. Broadly, the approaches to extract RND can be classified into four categories; an underlying asset is assumed to follow a stochastic distribution, parametric techniques, semi- parametric techniques and smoothing a volatility function. Smoothing volatility function is a common practice in extracting the RND function. Theoretically, it can be estimated by differentiating the call prices twice with respect to the strike price if the continuous strike prices are available. This paper focuses on the development of the risk-neutral density estimation by using the smoothing implied volatility smile method