In this paper we implement the method of Feynman path integral for the analysis of option pricing for certain L'evy process driven financial markets. For such markets, we find closed form solutions of transition probability density functions of option pricing in terms of various special...

I present a complete numerical study of the implicit-explicit finite difference method used to solve partial integro-differential equations (PIDEs) arising in mathematical finance. The study considers the specific case of the Merton jump-diffusion model, which is used to compute prices of...

Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial...

In this paper a couple of variance dependent instruments in the financial market are studied. Firstly, a number of aspects of the variance swap in connection to the Barndorff-Nielsen and Shephard model are studied. A partial integro-differential equation that describes the dynamics of the...

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...

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper...

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 presents a tractable model of non-linear dynamics of market returns using a Langevin approach.Due to non-linearity of an interaction potential, the model admits regimes of both small and large return fluctuations. Langevin dynamics are mapped onto an equivalent quantum mechanical (QM)...

Bilateral Gamma processes generalize the Variance Gamma process and allow to capture more precisely the differences between upward and downward moves of financial returns, notably in terms of jump speed, frequency, and size. Like in most other pure jump models, option pricing under Bilateral...