scholarly journals The Euler–Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model

2012 ◽  
Vol 64 (7) ◽  
pp. 2209-2223 ◽  
Author(s):  
Chaminda H. Baduraliya ◽  
Xuerong Mao
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
The Mean

scholarly journals A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL

2012 ◽  
Vol 15 (02) ◽  
pp. 1250016 ◽  
Author(s):  
BIN CHEN ◽  
CORNELIS W. OOSTERLEE ◽  
HANS VAN DER WEIDE
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Realistic Model ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Fixed Income ◽  
Financial Industry ◽  
Volatility Model ◽  
Discretization Schemes ◽  
Simulation Scheme

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

scholarly journals Approximating Explicitly the Mean-Reverting CEV Process

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
N. Halidias ◽  
I. S. Stamatiou
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Coefficients ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Financial Mathematics ◽  
Two Dimensional ◽  
Nonnegative Solutions ◽  
Volatility Model ◽  
Cev Process ◽  
The Mean

We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form(xt)q,where1/2<q<1. Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameterq. Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the two-dimensional stochastic volatility model with instantaneous variance process given by the above mean-reverting CEV process.

scholarly journals Apreçamento de Ativos Referenciados em Volatilidade

2006 ◽  
Vol 4 (2) ◽  
pp. 203
Author(s):  
Alan De Genaro Dario
Keyword(s):  
Stochastic Volatility ◽  
Foreign Currency ◽  
Asset Price ◽  
Realized Volatility ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Currency Options ◽  
Variance Swaps ◽  
Volatility Model ◽  
Future Realized Volatility

Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993) stochastic volatility model. Additionally, the Heston (1993) model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.

scholarly journals Pricing Various Types of Power Options under Stochastic Volatility

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1911
Author(s):  
Youngrok Lee ◽  
Yehun Kim ◽  
Jaesung Lee
Keyword(s):  
Financial Markets ◽  
Stochastic Volatility ◽  
Asset Price ◽  
Stochastic Volatility Model ◽  
Exotic Options ◽  
Option Prices ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Pricing Power

The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in markets in order to provide high leverage strategy. In pricing power options, the classical Black–Scholes model which assumes a constant volatility is simple and easy to handle, but it has a limit in reflecting movements of real financial markets. As the alternatives of constant volatility, we focus on the stochastic volatility, finding more exact prices for power options. In this paper, we use the stochastic volatility model introduced by Schöbel and Zhu to drive the closed-form expressions for the prices of various power options including soft strike options. We also show the sensitivity of power option prices under changes in the values of each parameter by calculating the resulting values obtained from the formulas.

scholarly journals PERHITUNGAN VALUE AT RISK DENGAN PENDUGA VOLATILITAS STOKASTIK HESTON

2018 ◽  
Vol 7 (4) ◽  
pp. 317
Author(s):  
DESAK PUTU DEVI DAMIYANTI ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
At Risk ◽  
Stochastic Process ◽  
Stochastic Volatility ◽  
Value At Risk ◽  
Financial Risk ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
The Mean ◽  
Simulation Results

Value at risk is a method that measures financial risk of an security or portfolio. The aims of the research is to find out the value at risk of an exchange rate using the Heston stochastic volatility model. Heston model is a strochastic volatility model that assumes that volatility of the security follow stochastic process and consider the mean reversion. Based on simulation results, the value of volatility using Heston volatility estimastor is 0.2887, and the value of Heston VaR with 95 percent confident level is 0.0297. Based on result of backtesting,  there are 48 violations obtained VaR using Heston model, while historical VaR there are 2 violations. Thus, VaR using Heston model is more strict in estimating risk.

scholarly journals A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Elisa Alòs ◽  
Jorge A. León ◽  
Monique Pontier ◽  
Josep Vives
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Asset Price ◽  
Jump Diffusion ◽  
Stochastic Volatility Model ◽  
Time Behavior ◽  
Volatility Model ◽  
Jump Diffusion Model ◽  
White Type ◽  
Short Time

We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.

Research of the Heston Stochastic Volatility Model Within the Framework of the Options Pricing

2016 ◽  
Vol 4 (4) ◽  
pp. 33-36
Author(s):  
Насонов ◽  
A. Nasonov ◽  
Баранов ◽  
V. Baranov
Keyword(s):  
Stochastic Volatility ◽  
Stock Exchange ◽  
Asset Price ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Options Pricing ◽  
Put Options ◽  
Volatility Model ◽  
Anglo American

In this study the issues of the Heston Stochastic Volatility Model application to options pricing were researched. The Heston Model calibration problem in a particular market and time was considered. The comparison of two methods to solve it was carried out. As a result of the calibration the calculation of the price function for put options with different strikes, contract terms and interest rate was made. European options quotes to purchase Anglo American shares, traded on the London Stock Exchange, were used as initial data. The comparison of the Heston Model with the Black–Scholes Model was carried out. The dependencies of the option price on the underlying asset price were built, the estimates of discrepancy between model prices and market prices were found within the framework of these models. The results were analyzed.

scholarly journals Pricing Collar Options with Stochastic Volatility

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Pengshi Li ◽  
Jianhui Yang
Keyword(s):  
Brownian Motion ◽  
Numerical Experiment ◽  
Stochastic Volatility ◽  
Asset Price ◽  
Analytical Approximation ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Underlying Asset ◽  
Volatility Model ◽  
Mean Reverting Process

This paper studies collar options in a stochastic volatility economy. The underlying asset price is assumed to follow a continuous geometric Brownian motion with stochastic volatility driven by a mean-reverting process. The method of asymptotic analysis is employed to solve the PDE in the stochastic volatility model. An analytical approximation formula for the price of the collar option is derived. A numerical experiment is presented to demonstrate the results.

THE EFFECT OF JUMPS AND DISCRETE SAMPLING ON VOLATILITY AND VARIANCE SWAPS

2008 ◽  
Vol 11 (08) ◽  
pp. 761-797 ◽  
Author(s):  
MARK BROADIE ◽  
ASHISH JAIN
Keyword(s):  
Stochastic Volatility ◽  
Variance Reduction ◽  
Asset Price ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Discrete Sampling ◽  
Reduction Techniques ◽  
Volatility Model ◽  
Integration Techniques ◽  
Jump Diffusion Model

We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the Heston stochastic volatility model, the Merton jump-diffusion model and the Bates and Scott stochastic volatility and jump model. We determine fair discrete and continuous variance strikes analytically and fair discrete and continuous volatility strikes using simulation and variance reduction techniques and numerical integration techniques in all models. Numerical results show that the well-known convexity correction formula may not provide a good approximation of fair volatility strikes in models with jumps in the underlying asset. For realistic contract specifications and model parameters, we find that the effect of discrete sampling is typically small while the effect of jumps can be significant.

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