scholarly journals The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Raphael Naryongo ◽  
Philip Ngare ◽  
Anthony Waititu
Keyword(s):  
Diffusion Processes ◽  
Asset Returns ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Market Prices ◽  
Asset Return ◽  
Volatility Model ◽  
Squared Bessel Process ◽  
Wishart Processes ◽  
Discretization Technique

This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.

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 INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

2017 ◽  
Vol 20 (08) ◽  
pp. 1750055 ◽  
Author(s):  
ZHENYU CUI ◽  
J. LARS KIRKBY ◽  
GUANGHUA LIAN ◽  
DUY NGUYEN
Keyword(s):  
Stochastic Volatility ◽  
Probabilistic Method ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Probability Densities ◽  
Special Case

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, [Formula: see text], and a special case of the [Formula: see text]-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The [Formula: see text]-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the [Formula: see text] model and a special case of the [Formula: see text]-Hypergeometric model.

A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion

2019 ◽  
Vol 25 (3) ◽  
pp. 239-252
Author(s):  
Yusuke Okano ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Diffusion Processes ◽  
Stochastic Volatility Model ◽  
Weak Approximation ◽  
Numerical Examples ◽  
Control Variate ◽  
Volatility Model ◽  
Multidimensional Diffusion

Abstract The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath–Platen’s scheme for multidimensional diffusion processes. We reformulate the Heath–Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method.

scholarly journals European Option Pricing under Wishart Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Raphael Naryongo ◽  
Philip Ngare ◽  
Anthony Waititu
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Stochastic Volatility Model ◽  
European Option ◽  
Multifactor Model ◽  
Asset Pricing Model ◽  
European Option Pricing ◽  
Volatility Model ◽  
Wishart Processes ◽  
The Fourier Transform

This study deals with a single risky asset pricing model whose volatility is described by Wishart affine processes. This multifactor model with two dependency matrices describing the correlation between the asset dynamic and Wishart processes makes it more flexible enough to fit the market data for short or long maturities. The aim of the study is to derive and solve the call option pricing problem under the double Wishart stochastic volatility model. The Fourier transform techniques combined with perturbation methods are employed in order to price the European call options. The numerical illustrations on pricing predictions show similar behavior of price movements under the double Wishart model with respect to the market price.

Estimation of SV Model with Leverage Effect Based on MCMC Technique

2014 ◽  
Vol 530-531 ◽  
pp. 605-608
Author(s):  
Xiao Cui Yin
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stock Index ◽  
Leverage Effect ◽  
Model Parameters ◽  
Convergence Diagnostics ◽  
Volatility Model ◽  
Mcmc Simulation ◽  
Series Convergence

This paper is to study the estimation of stochastic volatility model with leverage effect using Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation technique. The data used is China's Shenzheng stock index. Estimations of model parameters are achieved by using MCMC technique in Openbugs Software, results show that there is leverage effect in Shenzheng stock series, convergence diagnostics suggest that parameters of the model are convergent.

scholarly journals A Bayesian Semiparametric Realized Stochastic Volatility Model

2021 ◽  
Vol 14 (12) ◽  
pp. 617
Author(s):  
Jia Liu
Keyword(s):  
Stochastic Volatility ◽  
Asset Returns ◽  
Realized Volatility ◽  
Stochastic Volatility Model ◽  
Estimation Bias ◽  
Bayesian Nonparametric ◽  
Proposed Model ◽  
Volatility Model ◽  
Flexible Framework ◽  
Density Forecasts

This paper proposes a semiparametric realized stochastic volatility model by integrating the parametric stochastic volatility model utilizing realized volatility information and the Bayesian nonparametric framework. The flexible framework offered by Bayesian nonparametric mixtures not only improves the fitting of asymmetric and leptokurtic densities of asset returns and logarithmic realized volatility but also enables flexible adjustments for estimation bias in realized volatility. Applications to equity data show that the proposed model offers superior density forecasts for returns and improved estimates of parameters and latent volatility compared with existing alternatives.

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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