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 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.

scholarly journals A note on stochastic volatility model estimation

2019 ◽  
Vol 17 (4) ◽  
pp. 22
Author(s):  
Omar Abbara ◽  
Mauricio Zevallos
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Parameter Estimates ◽  
Model Estimation ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Monte Carlo Evaluation

<p>The paper assesses the method proposed by Shumway and Stoffer (2006, Chapter 6, Section 10) to estimate the parameters and volatility of stochastic volatility models. First, the paper presents a Monte Carlo evaluation of the parameter estimates considering several distributions for the perturbations in the observation equation. Second, the method is assessed empirically, through backtesting evaluation of VaR forecasts of the S&amp;P 500 time series returns. In both analyses, the paper also evaluates the convenience of using the Fuller transformation.</p>

scholarly journals CAM Stochastic Volatility Model for Option Pricing

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Wanwan Huang ◽  
Brian Ewald ◽  
Giray Ökten
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
The Other ◽  
Stochastic Volatility Models ◽  
Control Variate ◽  
Volatility Models ◽  
Volatility Model ◽  
Cam Model

The coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks) of the model. We also derive an approximation for the characteristic function of the model.

Particle Gibbs with ancestor sampling for stochastic volatility models with: heavy tails, in mean effects, leverage, serial dependence and structural breaks

2015 ◽  
Vol 19 (5) ◽  
Author(s):  
Nima Nonejad
Keyword(s):  
Stochastic Volatility ◽  
Structural Breaks ◽  
Sequential Monte Carlo ◽  
Heavy Tails ◽  
Moving Average ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Model Framework ◽  
Volatility Models ◽  
Volatility Model

AbstractParticle Gibbs with ancestor sampling (PG-AS) is a new tool in the family of sequential Monte Carlo methods. We apply PG-AS to the challenging class of stochastic volatility models with increasing complexity, including leverage and in mean effects. We provide applications that demonstrate the flexibility of PG-AS under these different circumstances and justify applying it in practice. We also combine discrete structural breaks within the stochastic volatility model framework. For instance, we model changing time series characteristics of monthly postwar US core inflation rate using a structural break autoregressive fractionally integrated moving average (ARFIMA) model with stochastic volatility. We allow for structural breaks in the level, long and short-memory parameters with simultaneous breaks in the level, persistence and the conditional volatility of the volatility of inflation.

scholarly journals FAST HILBERT TRANSFORM ALGORITHMS FOR PRICING DISCRETE TIMER OPTIONS UNDER STOCHASTIC VOLATILITY MODELS

2015 ◽  
Vol 18 (07) ◽  
pp. 1550046 ◽  
Author(s):  
PINGPING ZENG ◽  
YUE KUEN KWOK ◽  
WENDONG ZHENG
Keyword(s):  
Stochastic Volatility ◽  
Hilbert Transform ◽  
Asset Price ◽  
Heston Model ◽  
Expiration Date ◽  
Realized Variance ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Volatility Model

Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in the pricing procedure is the incorporation of the barrier feature in terms of the accumulated realized variance instead of the usual knock-out feature of hitting a barrier by the underlying asset price. We construct the fast Hilbert transform algorithms for pricing finite-maturity discrete timer options under different types of stochastic volatility processes. The stochastic volatility processes nest some popular stochastic volatility models, like the Heston model and 3/2 stochastic volatility model. The barrier feature associated with the accumulated realized variance can be incorporated effectively into the fast Hilbert transform procedure with the computational convenience of avoiding the nuisance of recovering the option values in the real domain at each monitoring time instant in order to check for the expiry condition. Our numerical tests demonstrate high level of accuracy of the fast Hilbert transform algorithms. We also explore the pricing properties of the timer options with respect to various parameters, like the volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.

scholarly journals ON THE LOG PERIODOGRAM REGRESSION ESTIMATOR OF THE MEMORY PARAMETER IN LONG MEMORY STOCHASTIC VOLATILITY MODELS

2001 ◽  
Vol 17 (4) ◽  
pp. 686-710 ◽  
Author(s):  
Rohit S. Deo ◽  
Clifford M. Hurvich
Keyword(s):  
Stochastic Volatility ◽  
Long Memory ◽  
Recent Literature ◽  
Stochastic Volatility Model ◽  
Asymptotic Bias ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Memory Parameter ◽  
Memory Series

We consider semiparametric estimation of the memory parameter in a long memory stochastic volatility model. We study the estimator based on a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 221–238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omission of a block of frequencies near the origin. We show that this ability to use the lowest frequencies is particularly desirable in the context of the long memory stochastic volatility model.

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

2020 ◽  
pp. 1-19
Author(s):  
Pengzhan Chen ◽  
Wuyi Ye
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Period Analysis ◽  
New Class ◽  
Volatility Models ◽  
Volatility Model ◽  
Article Study ◽  
Jump Sizes

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

Implied Stochastic Volatility Models

2020 ◽  
Vol 34 (1) ◽  
pp. 394-450 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Chenxu Li ◽  
Chen Xu Li
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Generalized Method Of Moments ◽  
Estimation Method ◽  
Stochastic Volatility Model ◽  
Nonparametric Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Out Of Sample

Abstract This paper proposes “implied stochastic volatility models” designed to fit option-implied volatility data and implements a new estimation method for such models. The method is based on explicitly linking observed shape characteristics of the implied volatility surface to the coefficient functions that define the stochastic volatility model. The method can be applied to estimate a fully flexible nonparametric model, or to estimate by the generalized method of moments any arbitrary parametric stochastic volatility model, affine or not. Empirical evidence based on S&P 500 index options data show that the method is stable and performs well out of sample.

MODELING THE DYNAMICS OF INTERNATIONAL AGRICULTURAL COMMODITY PRICES: A COMPARISON OF GARCH AND STOCHASTIC VOLATILITY MODELS

2018 ◽  
Vol 13 (03) ◽  
pp. 1850010 ◽  
Author(s):  
LU YANG ◽  
SHIGEYUKI HAMORI
Keyword(s):  
Stochastic Volatility ◽  
Value At Risk ◽  
Commodity Prices ◽  
Jump Process ◽  
Stochastic Volatility Model ◽  
Asymmetric Effect ◽  
Agricultural Commodity ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model

In this study, we employ generalized autoregressive conditional heteroscedastic (GARCH) and stochastic volatility models to investigate the dynamics of wheat, corn, and soybean prices. We find that the stochastic volatility model provides the highest persistence of the volatility estimation in all cases. In addition, based on the monthly data, we find that the jump process and asymmetric effect do not exist in agricultural commodity prices. Finally, by estimating Value at risk (VaR) for these agricultural commodities, we find that the upsurge in agricultural prices in 2008 may have been caused by financialization.

scholarly journals Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects

2021 ◽  
Vol 14 (5) ◽  
pp. 225
Author(s):  
Zhongxian Men ◽  
Tony S. Wirjanto ◽  
Adam W. Kolkiewicz
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Foreign Currency ◽  
Asset Returns ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Asymmetric Effects ◽  
Volatility Models ◽  
Volatility Model ◽  
T Distribution

This paper studies multiscale stochastic volatility models of financial asset returns. It specifies two components in the log-volatility process and allows for leverage/asymmetric effects from both components while return innovation terms follow a heavy/fat tailed Student t distribution. The two components are shown to be important in capturing persistent dependence in return volatility, which is often absent in applications of stochastic volatility models which incorporate leverage/asymmetric effects. The models are applied to asset returns from a foreign currency market and an equity market. The model fits are assessed, and the proposed models are shown to compare favorably to the one-component asymmetric stochastic volatility models with Gaussian and Student t distributed innovation terms.

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