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...

Business cycles are oscillations in the economy because of recessions and expansions. In this paper we investigate the oscillation of the gross domestic product as a result of its relations with the other main macroeconomic variables such as capital, consumption, and investment.There is a...

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...

Business cycles are oscillations in economy because of recessions and expansions. In this paper we investigate the oscillation of the Gross Domestic Product (GDP) as a result of its relations with the other main macroeconomic variables such as capital, consumption and investment. There is a...

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...

In this paper, we consider the Heston-CIR model with Levy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and uniqueness of the solution to this model. Second, we examine the...