This paper aims to summarizing the different approaches in determining the implied volatility for the options. This value is of particular importance since it is the main component of the option's price and because, among traders, options are quoted in terms of volatility rather than price....

In this paper, we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. Differently from other solutions proposed in the literature, this formula is invertible; hence, it is useful for...

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from...

This paper has the task of identifying an alternative approach (in terms of a mathematical algorithm) which can determine with speed (i.e. to converge within a few iterations) the value of the implied volatility for the options. This value is of particular importance since it is the main...

This article extends the previous research on the notion of a standardized call function and how to obtain an approximate model of the Black-Scholes formula via the hyperbolic tangent. Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to...

In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional...