Analyzing cryptocurrency risk with a stochastic volatility normal tempered stable process via hybrid optimization

Option pricing and hedging for optimized Lévy driven stochastic volatility models

Option pricing and hedging in incomplete market driven by Normal Tempered Stable process with stochastic volatility

American option valuation under time changed tempered stable Lévy processes

PID controllers play an important function in determining tuning parameters in any process sector to deliver optimal and resilient performance for nonlinear, stable and unstable processes. The effectiveness of the presented hybrid metaheuristic algorithms for a class of time-delayed unstable systems is described in this study when applicable to the problems of PID controller and Smith PID controller. The Direct Multi Search (DMS) algorithm is utilised in this research to combine the local search ability of global heuristic algorithms to tune a PID controller for a time-delayed unstable process model. A Metaheuristics Algorithm such as, SA (Simulated Annealing), MBBO (Modified Biogeography Based Optimization), BBO (Biogeography Based Optimization), PBIL (Population Based Incremental Learning), ES (Evolution Strategy), StudGA (Stud Genetic Algorithms), PSO (Particle Swarm Optimization), StudGA (Stud Genetic Algorithms), ES (Evolution Strategy), PSO (Particle Swarm Optimization) and ACO (Ant Colony Optimization) are used to tune the PID controller and Smith predictor design. The effectiveness of the suggested algorithms DMS-SA, DMS-BBO, DMS-MBBO, DMS-PBIL, DMS-StudGA, DMS-ES, DMS-ACO, and DMS-PSO for a class of dead-time structures employing PID controller and Smith predictor design controllers is illustrated using unit step set point response. When compared to other optimizations, the suggested hybrid metaheuristics approach improves the time response analysis when extended to the problem of smith predictor and PID controller designed tuning.

Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

In this paper, we introduce 4/2 stochastic volatility into the Normal Tempered Stable process (NTS-4/2SV). Furthermore, a L$\acute{\text{e}}$vy-based 4/2 stochastic volatility model considering the leverage effect (NTS-4/2SVR) is also proposed. We prove that explicit formulas for option pricing and variance-optimal hedging strategy still work. As an application, we price VIX derivatives with quasi-closed form solutions under both models.

Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes

We introduce an affine extension of the Heston model, called the ‐Heston model, where the instantaneous variance process contains a jump part driven by ‐stable processes with . In this framework, we examine the implied volatility and its asymptotic behavior for both asset and VIX options. Furthermore, we study the jump clustering phenomenon observed on the market. We provide a jump cluster decomposition for the variance process where each cluster is induced by a “mother jump” representing a triggering shock followed by “secondary jumps” characterizing the contagion impact.

An accurate European option pricing model under Fractional Stable Process based on Feynman Path Integral

Option pricing under stochastic volatility and tempered stable Lévy jumps

To effectively fit the dynamics and structure of frequent small jumps and sparse large jumps in the VIX time series, we introduce the tempered stable process (the CTS process and CGMY process) into the Ornstein–Uhlenbeck (OU) stochastic volatility model to build an OU model with the stochastic volatility process and tempered stable process. Based on two different assumptions for the underlying assets, we derive the formula of pricing models via two methods. Empirical studies are conducted to prove that our pricing models have a better performance in matching the VIX options. Furthermore, we find that the pricing model via the infinitesimal value method yields better results than pricing models with a measure of change. Overall, our proposed models enrich the derivative pricing theory and help investors understand and hedge risks.

This paper provides limit distribution results for power variation, that is, sums of powers of absolute increments under nonequidistant subdivisions of time and for certain types of time-changed Brownian motion and $\alpha$-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial econometrics.

This paper derives the analytic solutions of the pure discount bond price under the various types of -stable Levy process. It is well-known that only a few cases in-stable Levy process have the moment generating function. This paper extends the model to damped-stable Levy processes, which have artificial stable process with the moment generating function. This paper also extends models to stochastic volatility by time change method of Levy process.

Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results

We consider the problem of simulating X conditional on the value of X +Y, when X and Y are independent positive random variables. We propose approximate methods for sampling (X|X +Y) by approximating the fraction (X/z|X + Y = z) with a beta random variable. We discuss applications to Lévy processes and infinitely divisible distributions, and we report numerical tests for Poisson processes, tempered stable processes, and the Heston stochastic volatility model. 1