Numerical Solution of Pricing of European Put Option with Stochastic Volatility
author
Abstract:
In this paper, European option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stockprice from 3/01/2000 to 30/03/2009 is used and resulting partial differential equation is solved byCrank-Nicolson finite difference method for various interest rates and maturity in time. Thesensitivity measures “Greeks” are also determined to validate the model. It is observed that the valueof European put option increases with maturity time and decreases with interest rate.
similar resources
American option pricing under stochastic volatility: an efficient numerical approach
This paper develops a new numerical technique to price an American option written upon an underlying asset that follows a bivariate diffusion process. The technique presented here exploits the supermartingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte–Carlo ...
full textEfficient Numerical Solution of PIDEs in Option Pricing Efficient Numerical Solution of PIDEs in Option Pricing
The estimation of the price of different kinds of options plays a very important role in the development of strategies on financial and stock markets. There many books and various papers which are devoted to the exist mathematical theory of option pricing. Merton and Scholes became winners of a Nobel Prize in economy who described the basic concepts of the mathematical theory development. In th...
full textOption pricing under the double stochastic volatility with double jump model
In this paper, we deal with the pricing of power options when the dynamics of the risky underling asset follows the double stochastic volatility with double jump model. We prove efficiency of our considered model by fast Fourier transform method, Monte Carlo simulation and numerical results using power call options i.e. Monte Carlo simulation and numerical results show that the fast Fourier tra...
full textLong memory stochastic volatility in option pricing
The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes price and random deviation describing the risk from the random volatility. By using the ...
full textOption Pricing under Ornstein-uhlenbeck Stochastic Volatility
We consider the problem of option pricing under stochastic volatility models, focusing on the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probabili...
full textRegime Switching Stochastic Volatility with Perturbation Based Option Pricing
Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations. However such models lack the ability to take into account long term and fundamental economic factors e.g. credit crunch. Regime switching models with mean r...
full textMy Resources
Journal title
volume 24 issue 2
pages 189- 202
publication date 2011-06-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023