Mathematical Analysis of Financial Model on Market Price with Stochastic Volatility

Abstract

The Heston model is one of the most popular stochastic volatility models for option pricing to measure the volatility of different parameters in the financial market. In this work, we study the statistical analysis of Heston Model by partial differential equations. The model proposed by Heston takes into account non-lognormal distribution of the assets returns, leverage effect and the important mean reverting property of volatility. We have assayed on the return distribution on the basis of different values of correlation parameter and volatility, then we measure the effects of parameters ρ (correlation coefficient) and σ (standard deviation) for different situation such as ρ > 0, σ > 0, ρ = 0, σ = 0, ρ < 0, σ < 0 etc. On return distribution of Heston Model which indicates market condition for buyers and sellers to buy and sell options. All solvers used in this analysis are implemented using MATLAB codes and the simulation results are presented graphically.

Instrumento de cobertura: Heston en MexDer

“…Empleando la metodología descrita, se obtiene el resumen de estadísticos descriptivos (cuadro 1) para establecer el vector inicial, alimento del algoritmo que dará los parámetros estimados. Además, se llevaron a cabo las pruebas de heteroscedasticidad para comprobar que los rendimientos presentan volatilidad estocástica (Lin et al, 2001;Azencott et al, 2015;Mondal et al, 2017) y es estacionaria para obtener precios más justos.…”

Stability and controllability analysis of stochastic model for stock market prices

“…Stock price fluctuations in the stock market are known to be a reflection of the random movements of their values overtime; these movements and other market anomalies has attracted lots of independent researchers in the industries as well as academia (see for example) [9,10] which helped in the development of Black Scholes equation [11] in the early nineteen-seventies. The development of the Black-Scholes equation by Fischer Black and Myron Scholes in their publication of option pricing model in the early 1970s which later became the foundation of financial market analysis and corner stone of all pricing models whose derivatives can be determined with stocks as an underlying asset [12][13][14][15] is one of the major innovation in stock market history which later became the Black-Scholes model. Several other models including the jump diffusion, Markov switching, Heston processes etc., have been developed because of the short coming in the Black Scholes model (see) [3] to capture volatility as a stochastic process with other special features of stock market data especially the financial market.…”

Optimal Control Strategy Applied to Dynamic Model of Drug Abuse Incident for Reducing Its Adverse Effects

“…Several models have been published in recent years considering various problems regarding practical life. The literature and development of mathematical epidemiology are well documented and can be found in [3, 5, 6, 14, 28, 42, 44, 51]. Mathematical modeling has also launched its steps to explain different social problems and find out the alternative ways for reducing those problems.…”