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 it is proved that the Black-Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black-Scholes implied volatility that improves on the...

In this paper we present an option pricing model based on the assumption that the underlying asset price is an exponential Mixed Tempered Stable Lévy process. We also introduce a new R package called PricingMixedTS that allows the user to calibrate this model using procedures based on loss or...

Visual representation methods are a common problem in econometrics and finance in order to describe system dynamics. In this paper we address this problem by using the bi-harmonic oscillation process and the Brownian motion components, to generate a three-dimensional volatility surface.The...

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 paper studies the behavior of the smile in the Warsaw Stock Exchange (WSE) during the volatile summer of 2011.We investigate the volatility smile derived from liquid call and put options on the Polish WIG20 index which option series expired on September 2011. In this period, the polish...

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 Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to...

The dynamics of hourly electricity prices in day-ahead markets is an important element of competitive power markets that were only established in the last decade. In electricity markets, the market microstructure does not allow for continuous trading, since operators require advance notice in...

We investigate several promising algorithms, proposed in literature, devised to detect sudden changes (structural breaks) in the volatility of financial time series. Comparative study of three techniques: ICSS, NPCPM and Cheng's algorithm is carried out via numerical simulation in the case of...

The period May 1 to the turn of the month of November (last five trading days October) has historically produced negligible returns. The rest of the year (late October to the end of April) has essentially all the year's gains. In this paper we show that there is a statistically significant...