Stationary Increment Tempered Fractional Lévy Processes (TFLP) introduced by Boniece, Didier and Sabzikar (2020) are applied to financial data. They are used to model the stochastic drift rate of a mean reverting equation. The new processes are called OU processes with a TFLP drift rate....

We provide explicit, simple price formulas for the Europeanoptions under stochastic volatility and stochastic interest rate. The formulasare as simple as the classical Black-Scholes formula. Moreover, the formulasdo not require the normality of the returns. We do not need to know thedistribution...

This paper explores the capacity of Geometric Brownian Motion (GBM) and Prophet model to predict stock market returns during coronavirus outbreak. To the best of our knowledge this is the first research that compares GBM and prophet model in order to forcast stock market volatility especially...

Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively...

We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time, small-noise. Specialising the results to the Heston model,...

Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with...

An improved efficiency version of the LOESS algorithm is proposed that is applicable to the Monte Carlo pricing tasks common in financial engineering. A self-contained overview of the LOESS algorithm is presented followed by the suggested efficiency modifications and a discussion of strategies...

The Fourier inversion method solves the Heston option pricing formula. However, this method does experience the noteworthy disadvantage of a computationally sedate solution process. As a result, the literature introduces faster approximations with accuracies later improved by the joint...

Simulation studies prove that the asymmetry stochastic volatility (ASV) models infer erroneous return-volatility correlation, due to the unobservability of the true volatility. We propose to incorporate the ex-post volatility in the ASV framework for the identification of the correlation...

We study the problem of dynamically trading futures in continuous time under a multifactor Gaussian framework. We present a utility maximization approach to determine the optimal futures trading strategy. This leads to the explicit solution to the Hamilton-Jacobi-Bellman (HJB) equations. We...