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.

ON PRICING CONTINGENT CLAIMS UNDER THE DOUBLE HESTON MODEL

2012 ◽  
Vol 15 (05) ◽  
pp. 1250033 ◽  
Author(s):  
M. COSTABILE ◽  
I. MASSABÒ ◽  
E. RUSSO
Keyword(s):  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Underlying Asset ◽  
State Variable ◽  
Proposed Model ◽  
Volatility Model ◽  
Asset Value

This article presents a lattice based approach for pricing contingent claims when the underlying asset evolves according to the double Heston (dH) stochastic volatility model introduced by Christoffersen et al. (2009). We discretize the continuous evolution of both squared volatilities by a "binomial pyramid", and consider the asset value as an auxiliary state variable for which a subset of possible realizations is attached to each node of the pyramid. The elements of the subset cover the range of asset prices at each time slice, and claim price is computed solving backward through the "binomial pyramid". Numerical experiments confirm the accuracy and efficiency of the proposed model.

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.

APPLICATION OF FLOCKING MECHANISM TO THE MODELING OF STOCHASTIC VOLATILITY

2013 ◽  
Vol 23 (09) ◽  
pp. 1603-1628 ◽  
Author(s):  
SHINMI AHN ◽  
HYEONG-OHK BAE ◽  
SEUNG-YEAL HA ◽  
YONGSIK KIM ◽  
HYUNCHEUL LIM
Keyword(s):  
Stochastic Volatility ◽  
A Priori ◽  
Weighted Average ◽  
Mean Value ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Market Crashes ◽  
Proposed Model ◽  
Volatility Model ◽  
Local Mean

In this study, we present a new stochastic volatility model incorporating a flocking mechanism between individual volatilities of assets. Collective phenomena of asset pricing and volatilities in financial markets are often observed; these phenomena are more apparent when the market is in critical situations (market crashes). In the classical Heston model, the constant theoretical mean of the square of the volatility was employed, which can be assumed a priori. Our proposed model does not assume this mean value a priori, we instead use the flocking effect to continuously update the theoretical mean value using the local weighted average of individual volatility values. To perform this function, we use the Cucker–Smale flocking mechanism to calculate the local mean. For some classes of interaction weights such as all-to-all and symmetric coupling with a positive lower bound, we show that the fluctuations of the square process of volatility are uniformly bounded, such that the overall dynamics are mainly dictated by the averaged process. We also provide several numerical examples showing the dynamics of volatility.

PRICING JOINT CLAIMS ON AN ASSET AND ITS REALIZED VARIANCE IN STOCHASTIC VOLATILITY MODELS

2013 ◽  
Vol 16 (01) ◽  
pp. 1350005 ◽  
Author(s):  
LORENZO TORRICELLI
Keyword(s):  
Stochastic Volatility ◽  
Realized Volatility ◽  
Numerical Results ◽  
Quadratic Variation ◽  
Stochastic Volatility Model ◽  
Realized Variance ◽  
Joint Function ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model

In the setting of a stochastic volatility model, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This provides a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realized volatility or variance. We study the solution under various specific stochastic volatility models, give a formula for the computation of the delta and gamma of these claims, and introduce some new interesting payoffs that can be valued by means of the general pricing equation. Numerical results are given and compared to those from plain vanilla derivatives.

scholarly journals Forecasting Return Volatility of the CSI 300 Index Using the Stochastic Volatility Model with Continuous Volatility and Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xu Gong ◽  
Zhifang He ◽  
Pu Li ◽  
Ning Zhu
Keyword(s):  
Stochastic Volatility ◽  
Prediction Accuracy ◽  
Financial Risk ◽  
Sample Path ◽  
Realized Volatility ◽  
Stochastic Volatility Model ◽  
Stock Index ◽  
Return Volatility ◽  
Volatility Model ◽  
Continuous Volatility

The logarithmic realized volatility is divided into the logarithmic continuous sample path variation and the logarithmic discontinuous jump variation on the basis of the SV-RV model in this paper, which constructs the stochastic volatility model with continuous volatility (SV-CJ model). Then, we use high-frequency transaction data for five minutes of the CSI 300 stock index as the study sample, which, respectively, make parameter estimation on the SV, SV-RV, and SV-CJ model. We also comparatively analyze these three models' prediction accuracy by using the loss functions and SPA test. The results indicate that the prior logarithmic realized volatility and the logarithmic continuous sample path variation can be used to predict the future return volatility in China's stock market, while the logarithmic discontinuous jump variation is poor at its prediction accuracy. Besides, the SV-CJ model has an obvious advantage over the SV and SV-RV model as to the prediction accuracy of the return volatility, and it is more suitable for the research concerning the problems of financial practice such as the financial risk management.

Fat-tailed stochastic volatility model and the stock market returns in China

2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Donglian Ma ◽  
Hisashi Tanizaki
Keyword(s):  
Stock Market ◽  
Stochastic Volatility ◽  
Realized Volatility ◽  
Stochastic Volatility Model ◽  
Stock Market Returns ◽  
Content Type ◽  
Volatility Model ◽  
Out Of Sample ◽  
Day Of The Week ◽  
Daily Returns

Purpose The purpose of this paper is to investigate how the selection of return distribution impacts estimated volatility in China’s stock market. Design/methodology/approach The authors use a Bayesian analysis of fat-tailed stochastic volatility (SV) model with Student’s t-distribution, and conduct an out-of-sample test with realized volatility. Findings Empirical analysis results indicate that fat-tailed SV model performs better in capturing the dynamics of daily returns. The authors find that asymmetry, holiday and day of the week effects are detected in estimated volatility. However, the out-of-sample comparison shows that fat-tailed SV models fail to outperform SV models with normal distribution in fitting and predicting realized volatility. Originality/value The contribution of this paper to existing literature is twofold. First, it proves that fat-tailed SV models with Student’s t-distribution perform better than normally distributed SV models in fitting daily returns of China’s stock market. Second, this paper takes asymmetry, holiday and day of the week effects into consideration at the same time in the fat-tailed SV model.

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